Solutions to Exercises and Problems
Solutions to Exercises and Problems
Microeconomics for Business Decisions
Chapter 1 Solutions
1.1 Statements a, c, e, g, and h deal with what are generally considered to macroeconomic issues — inflation, fiscal and monetary policy, government spending, and unemployment. Statements a, a, d, f, and j deal with what are typically regarded as microeconomic issues — the impact of unions and minimum wages on labor markets, antitrust laws, rent controls, import tariffs and quotas, pollution control, and income distribution.
Statements b, c, f, g, and j are positive statements, describing what is or what can be done. Statements a, d, e, h, and i are normative statements, describing what ought to be done. There is much more disagreement among economists where normative issues are concerned.
1.2 By law, nonprofit firms are not allowed to keep the profits that they generate. Profit can be used to provide additional goods or services, or to enhance the quality of service in future periods, however, thus giving the firms an incentive for profit maximization and efficient operation. There are additional benefits to performing efficiently; for example, charities that lower their operating expenses may attract more donors, and universities that lower tuition (while maintaining the quality of education) can attract better students.
1.3 Only a hypothesis that accurately predicts under conditions for which the prediction was made can be considered valid. The farmer’s hypothesis was easy to test. For three straight mornings the farmer gagged his rooster, thereby preventing the bird from crowing. Needless to say, the sun rose each of those three mornings, forcing the farmer to admit that his hypothesis was invalid.
1.4 This was not a good model to use. In the early 1980s, stock prices rose tremendously, but hemlines did not. While the pre-1980s data failed to refute a theory, they did not prove a theory. This example illustrates what is referred to as the false-cause fallacy: assuming cause-and-effect from two correlated, yet unrelated, occurrences. Even though stock prices and hemlines may have been highly correlated for fifty years, it does not follow that one event caused, or is caused by, the other.
1.5 You should agree — if not now, at least by the time you finish reading this textbook. As one example, consider the effect of inclement weather on agricultural markets. By causing a reduction in supply, higher equilibrium prices and lower equilibrium quantities are expected. This model can explain the jump in coffee prices between 1974 and 1975, when a frost damaged a large portion of Brazil’s coffee crop in 1974. In addition, the same model allows one to predict what will happen, for example, to U.S. orange prices in 1993 if both the Florida and California orange groves are damaged by frost in the winter of 1992, or to wheat prices in 1994 if U.S. wheat farms suffer from a long-lasting drought in the summer of 1993. Clearly, this model has both explanatory power and predictive ability.
1.6 Pure competition describes a market situation in which a homogeneous product is traded by many small buyers and sellers. Under perfect competition, two additional characteristics are present: easy entry and exit, and perfect knowledge.
Effective competition describes a market structure in which buyers and sellers act independently, even though the market is not pure or perfect. To be effective, the competitors must be comparable and the competitive process open and free. In a 1982 article entitled, “Cause of Increased Competition in the U.S. Economy, 1939-1980,” economist William G. Shepherd shows that between 1958 and 1980, the share of U.S. economic activity occurring in effectively competitive industries increased from 56.4 percent to 76.7 percent. Shepherd defines effective competition as a situation in which the four largest firms have less than forty percent of the market, market shares are unstable, pricing is flexible, there is little collusion, and profit rates and entry barriers are low.
1.7 A perfectly competitive market is characterized by many buyers and sellers, a homogeneous product, easy entry and exit, and readily available market information. The baseball card market meets all of these requirements. It is characterized by a large number of buyers and sellers — millions of baseball fans and serious collectors buy, sell, and trade baseball cards each year. The cards, which are certainly homogeneous, can be easily bought and sold through mail order advertisers and hobby publications, or by attending sport collectibles shows or conventions. Finally, numerous hobby publications release detailed, up-to-date card price information, and detailed player performance information is available from the sports sections of most major newspapers.
1.8 If barriers to entry were removed, the number of taxis in New York City would undoubtedly increase. Over time, the number of cabs would probably fluctuate, with more cabs on the streets during economic recessions, and fewer taxis around during economic booms. (Can you think of why this pattern would emerge?) The price of a medallion would obviously fall, perhaps to near zero.
1.9 Disputes over Indian water rights currently affect the availability of water for urban use in many western U.S. cities, including Tucson, Phoenix, Albuquerque, and Salt Lake City; for the expansion of hydro-power sources for Seattle and Tucson; and for the maintenance of non-Indian agricultural development in Arizona, Nevada, and Washington. Until these water rights are determined, the sale and transfer of existing rights will be severely impeded, since the prospective buyers cannot be certain they are receiving secure property rights.
1.10 Property rights play a key role in this transformation. For several generations, much of these nations’ productive assets have been owned by the state. If free markets and private enterprise are to replace the old command system, unambiguous and enforceable property rights must be assigned to a wide variety of economic factors of production and to existing economic and business organizations.
1.11 Probably not all the way to zero. Pollution levels could be reduced to zero, but only at a prohibitive cost. The Los Angeles basin of Southern California, for example, could probably rid itself of most pollution simply by banning all automobiles, buses, and trucks, and by closing down all private and public industry. Clearly, the price for zero pollution is unacceptable to most people. More likely, each society will find some level of pollution that is acceptable, given the opportunity cost involved.
1.12 If property rights to air are assigned to the nonsmokers, smokers might try to pay the nonsmokers to let them smoke. If smokers held the rights, however, nonsmokers would have to pay smokers to not smoke. Transactions costs would probably prohibit any effective bargaining, however. By the time the passengers separated into groups (smokers and nonsmokers), elected spokespersons, and carried out negotiations, the plane would be ready to land!
Chapter 2 Solutions
2.1 When Robinson Crusoe is alone on the island, he must certainly face the first two fundamental questions: What to produce (fish and/or coconuts); How to produce (catch fish with a spear, with a net, with his hands). Since he is the only member of the economy, however, he doesn’t have to worry about the third question — For whom to produce? Anything he produces will be for his own consumption. Once Friday arrives on the island, all three economic questions are relevant.
2.2 Since efficiency involves using resources without waste, the situation in Spain cannot be considered as one of efficient production. With 20 percent of the labor force unemployed, the nation is certainly not getting the most output possible from its available labor resources. At 4 percent, however, this economy may be operating efficiently since a certain amount of “frictional” unemployment is required as resources are reallocated to alternative uses.
2.3 The distribution in an ideal communist state would be much more equal than the type of distribution generated in a capitalist society. For a strictly capitalist society, a more appropriate rule might be “to each according to ability — from each according to need.”
2.4
(a)
[pic]
(b) If 800 turtles are being caught, 29 tons of fish can be caught, assuming efficient production (the island is operating on its PPC). If 84 tons of fish are being caught, the maximum number of turtles that can be caught is 300.
(c) With 300 turtles, you can catch 84 fish. If you get 100 more turtles, you can only catch 75 fish. You give up 84 – 75 = 9 fish.
(d) You must give up 100 turtles to get 6 fish. Therefore, to get 1 fish, you give up about 100/6, or 16 2/3, turtles.
(e) Consider the opportunity cost of catching turtles, starting at the point where the nation is catching 105 tons of fish and no turtles: to gain the 1st 100 turtles, you must give up 6 fish; to gain the 2nd 100 turtles, you must give up 7 fish; to gain the 3rd 100 turtles, you must give up 8 fish. Turtles are getting more expensive — the law of increasing opportunity cost does hold.
(f) At point E, inside the PPC, unemployment, under utilization, or inefficient use of their resources is taking place.
(g) Since this combination is outside the PPC, it is currently unattainable. The island would need more workers, more boats, a new technology, or perhaps specialization and trade with another island to reach point F.
2.5
(a) The first 1,000 Sno-Cones cost 15,000 – 10,000 = 5,000 sweaters.
(b) The third 1,000 Sno-Cones cost 6,000 – 3,000 = 3,000 sweaters.
(c) No. It seems to obey a law of decreasing cost. The more Sno-Cones they produce, the fewer sweaters it costs them.
(d) This does not seem realistic. It implies that, starting at point A, Freon would first divert those resources least suited to sweater production.
2.6 (a)
X: 0 1 2 3 4 5 6 7 8 9 10
Y: 100 99 96 91 84 75 64 51 36 19 0
[pic]
(b) When X = 1, MRT = 2; when X = 4, MRT = 8; and when X = 8, MRT = 16.
(c) As you move down the PPC, the opportunity cost of producing more X increases. Note: The first unit of X costs 1 unit of Y; the last unit of X costs 19 units of Y.
(d) MRT = –(slope of PPC) = –∂Y/∂X = 2X.
2.7
(a, b) The opportunity costs (trade-offs) are constant: 1 fish for 3 coconuts for Robinson Crusoe, and 1 fish for 5 coconuts for Friday. See the graphs below.
(c) Robinson Crusoe has the absolute advantage in both activities.
(d) Robinson Crusoe: 1 more fish costs 3 coconuts; Friday: 1 more fish costs 5 coconuts. Robinson Crusoe has the comparative advantage in fishing; Friday has the comparative advantage in collecting coconuts (for Friday, 1 coconut costs 1/5 of a fish; for Robinson Crusoe, 1 coconut costs 1/3 of a fish).
(e) Robinson Crusoe should produce fish.
(f) 1 F for 1 C wouldn’t be acceptable to Crusoe. 1 F for 8 C wouldn’t be acceptable to Friday. In each case, they could each do better without trading. An acceptable exchange rate would be 1 fish for 4 coconuts (anything between 1 F for 3 C and 1 F for 5 C would be acceptable.)
(g) Crusoe can produce 16 F, trade 4 to Friday for 16 C, and Friday winds up with 4 F and 24 C.
[pic]
2.8
(a) U.S.: 1 more unit of wheat costs 1 unit of oil; Saudi Arabia: 1 more unit of wheat costs 3 units of oil. The U.S. has a comparative advantage in wheat production; the Saudis have a comparative advantage in oil production.
(b) Acceptable terms of trade: 1 wheat for 2 oil. The U.S. can get 8 units of oil for their 4 units of wheat, giving them 96 wheat and 58 oil. Saudi Arabia ends up with 92 oil and 54 wheat.
(c) Both countries benefit from the trade, moving outside their PPCs.
2.9
(a) Point A represents unemployment, under utilization, or inefficient use of some resources.
(b) Point B represents a currently unattainable point.
(c) More natural gas can be produced with the existing level of resources. Since this increase in natural gas production does not influence fish production, the PPC will rotate as shown:
[pic]
2.10 In 20 years, Thriftland’s economy will probably have enjoyed a higher rate of growth due to their larger investment in capital goods. This will enable them to produce more of both types of goods. See the following figure.
[pic]
2.11
(a) Yes, for instance, Japan has high saving and investment rates while the U.S. does not.
(b) The scatter plot does show a strong positive correlation between investment rates and growth rates.
(c) This might imply that other factors (in addition to the investment rate) influence the rate of economic growth.
2.12 In the Soviet Union, the State Committee for Economic Planning (GOSPLAN) was responsible for drawing up and implementing the state’s economic plans. A key component of these plans was the materials balance — achieving a balance between Qd and Qs for all raw materials and intermediate goods used in the production of final consumer and capital goods. With literally billions of raw materials and intermediate goods to consider, the plans for materials balances alone filled 70 volumes, or 12,000 pages, each year.
2.13
(a) Sales = (125 x $1.00) + (75 x $0.60) + (20 x $0.75) + (10 x $1.00) = $195.00.
(b) TC = $40 + $3 + $13 + $2 + $4.50 [$4,500/1,000] + (125 x $0.36) + (75 x $0.33) + (20 x $0.33) + (10 x $0.40) = $142.85.
(c) Accounting profit = $195 – $142.85 = $52.15.
(d) Include forgone earnings = $60 ( = 8 hours x $7.50/hr). He is not earning an economic profit. TR – TC = $195 – $202.85 = $ –7.85.
(e) A typical implicit cost, forgone interest on money used to start the business, does not apply to Louie’s situation. His money would earn no interest in its next best alternative use — sitting under his mattress!
2.14 Some alternatives include: sales maximization, management utility maximization, and satisficing.
2.15
[pic]
Chapter 3 Solutions
3.1
(a) Slope = –1/2. For every dollar increase in price, Qd falls by 500,000 bushels.
(b) Qd. = 25 million; Qd. = 20 million; Qd. = 17.5 million.
(c) 30 million.
(d) $60.
(e) Inverse demand: p = 60 – 2Qd..
[pic]
(f) Qd = 55 million; Qd = 50 million; Qd = 47.5 million.
(g) a normal good; an increase in demand.
3.2
Huey’s Dewey’s Louie’s Market
Price Demand Demand Demand Demand
$2.00 10 0 0 10
1.50 12 8 0 20
1.00 14 12 8 34
0.50 16 16 10 42
0.00 18 20 12 50
[pic]
3.3 The article confuses a change in demand with a change in quantity demanded. Lower prices do not cause an increase (shift) in demand, but merely a movement along a demand curve.
3.4 Some typical examples are macaroni & cheese, hamburgers, potatoes, and generic brand goods. Of course, just because you behave as if some good were inferior (your demand decreases when your income increases) doesn’t mean that the whole market will react the same way.
3.5
(a) QC = 24 – 25(2) + 8(2) + 10(4) = 30 pounds. (b) QC = 24 – 25pC + 16 + 40 = 80 – 25pC. (c) QC = 24 – 50 + 8M + 40 = 14 + 8M. See the figure. (d) ordinary demand curve; Engel curve. (e) QC = 24 – 50 + 16 + 10pB = –10 + 10pB. See the figure.
[pic] [pic]
(f) ordinary demand; cross-price demand.
3.6 The demand for solar power and hydroelectric power — substitute goods — will probably increase. The demand for large cars — complementary goods — will probably decrease.
3.7
(a) Slope = 3. For every dollar increase in price, Qs rises by 3 million bushels. (b) Qs = 4.5 million bushels; Qs = 6 million bushels; Qs = 9 million bushels. (c) p = $2. (d) See graph.
[pic]
(e) Qs = 7.5 million bushels; Qs = 9 million bushels; Qs = 12 million bushels.
(f) an increase in supply.
3.8 (a) pe = $2.00; Qe = 4 million. (b) Qd = 4.5 million; Qs = 2.5 million; shortage of 2 million. (c) Qd = 3 million; Qs = 7 million; surplus of 4 million. (d) See table. (e) higher pe; higher Qe.
Price Qd (after ads)
$1.00 7.0
1.50 6.5
2.00 6.0
2.50 5.5 1; when vertical intercept is positive, ηs < 1; when supply comes from the origin, ηs = 1.
Chapter 5 Solutions
5.1 (a) M = (40)($3) = $120. (b) Budget line equation: 3S + 2E = 120, or E = 60 – (3/2)S. (c) slope = –3/2, or –1.5; for every extra sundae bought, 1.5 bottles of Evian must be given up. (d) See graph. A on budget line. B in attainable set (inside budget line). C outside attainable set.
[pic]
5.2 (a) pC = $120/10 = $12; pN = $120/4 = $30. (b) No — outside her attainable set: 3($30) + 5($12) = $150. (c) Now she can afford 3 Nitwitto games and 5 CDs:
[pic]
(d)
[pic]
5.3
(a) M = pXXa + pYYa = 2 x 40 + 4 x 20 = 160.
(b) The maximum level of X that can be consumed is M/pX = 160/2 = 80, and the maximum level of Y that can be consumed is M/pY = 160/4 = 40.
(c) The consumer’s original budget line is shown on the following graph:
[pic]
(d) After changes ΔpX = 2 and ΔM = 80, the maximum level of X that can be consumed is (ΔM + M)/(ΔpX + pX) = 240/4 = 60, and the maximum level of Y that can be consumed is (ΔM + M)/pY = 240/4 = 60. This new budget line is shown on the previous diagram.
(e) This new bundle C must be to the left of A because otherwise the weak axiom would be violated. The new bundle being chosen must not be on or below the old budget line.
5.4
(a) Yes, A revealed preferred to B is consistent with the revealed preference approach to consumer choice because B is affordable when A is chosen. To see this, just compute the level of income required to purchase each when prices are pX = $3, pY = $3.
(b) No, B revealed preferred to A is not consistent with the revealed preference approach to consumer choice because A is not affordable when B is chosen. To see this, just compute the level of income required to purchase each when prices are pX = $3, pY = $6.
5.5 (a) pA = $20,000/10 = $2,000. (b) rising (c) elastic (d) falling (e) inelastic (f) Yes. At higher prices, demand is relatively more elastic (and vice versa).
5.6 Yes. The extra money compensates Jack for the price-induced income effect. There will still be a substitution effect, since egg rolls are now relatively more expensive. Jack will buy fewer egg rolls and more hamburgers.
5.7 (a) pr,H = $2.00; pr,D = $1.50; pr,L = $1.00. (b) intensive; extensive.
5.8 (a)
[pic]
(b) When income is between $1,000 and $2,000, normal. When income is between $2,000 and $2,500, inferior.
5.9 (a) UA = UB = UC = 100.
(b)
[pic]
(c) X = Y = (1/2)(20 + 5) = 12.5; U = 156.25. (d) See graph. (e) Yes. With convex indifference curves, a weighted combination of two bundles will always yield a higher level of utility than either bundle consumed separately.
5.10 (a) Left and right shoes are perfect complements. (b) Salt from either store is a perfect substitute. (c) Superman’s preference is to stay away from Kryptonite. (d) Bugs wants more carrots but is indifferent to the number of peas he has. (e) When the other person has more income than Phil, he won’t give easily, but he will give up some income if the other person has less than Phil.
[pic]
5.11 (a) UA = 121, UB = 100, and UC = 144. UC is highest, then UA, then UB. (b) VA = 11, VB = 10, and VC = 12. VC is highest, then VA, then VB. (c) WA = 71, WB = 50, and WC = 94. WC is highest, then WA, then WB. (d) No, the rankings are the same. The utility functions in (b) and (c) are monotonic transformations of the function in (a).
5.12
[pic]
(a) F = $1,000/$4 = 250. (b) F = $400/$4 = 100. (c) F = $800/$4 = 200. (d) F = $800/$4 + $600/$4 = 350. (e) See graph. (f) It would extend all the way to the vertical axis, since she could trade food stamps for other goods in the market. (g) With a low preference for food, Cindy could reach a higher level of utility by selling some of her food stamps.
5.13 (a) For (i), yes, because MRS = Y/X, which falls as consumption of X increases. For (ii), no, because MRS = 8/4 = 2, which is constant. (b) See graph. For straight-line indifference curves, the MRS is constant. For convex indifference curves, the MRS diminishes as the individual consumes more X.
[pic]
5.14 (a)
[pic]
(b) MRS = MUH/MUS = 1/3; pH/pS = 1/2. (c) No, because the MRS is not equal to the price ratio. (d) 1 more lb. of steak; MU gained = 3. 2 lbs. of hamburger; MU lost = 2. (e) More. (f) See graph where utility is maximized at B.
5.15
(a) Sam’s marginal rate of substitution is MRSXY = MUX/MUY = 2X + 2Y/2X + 2Y = 1.
(b) Lynn’s marginal rate of substitution is MRSXY = MUX/MUY = 1/1 = 1
(c) Yes, they have identical preferences because they have the same MRS for every X and Y.
(d) W2 = (X + Y)(X + Y) = X2 + 2XY + Y2 = U.
5.16 (a)
X Y U(X, Y) X Y U(X, Y)
2 0 4 1 2 7
2 4 4 2 3 7
0 2 4 2 1 7
4 2 4 3 2 7
(b) The indifference curves are a set of concentric circles.
(c) The critical values = 2 and Y* = 2. At this point utility is U* = 8.
(d) The economic region is the area of a square defined by X from zero to X* and Y from zero to Y*.
(e) The critical point (X*, Y*) is called a bliss point. At this point, Wally is said to be satiated with respect to both X and Y simultaneously.
(f) If Wally has $4 to spend, he will consume 1 hamburger and 2 ounces of water.
(g) If the price of hamburgers falls to pX = $2, Wally will consume 2 hamburgers and 2 ounces of water.
(h) If the price of hamburgers falls to pX = 50¢, Wally will consume 2 hamburgers and 2 ounces of water.
(i) If both X and Y are free, Wally will consume 2 hamburgers and 2 ounces of water.
(j) According to economic theory, there must be at least one other good for Wally to consume because total satiation consumption with respect to all goods simultaneously is ruled out as implausible for rational economic decision makers.
5.17 Since B and C lie on the same indifference curve, neither is preferred over the other and they both generate the same level of utility.
5.18
(a) MRSXY = MUX/MUY = 2XY/X2 = 2Y/X .
(b) 2X + 4Y = 180.
(c) After substitution, the two equations are: (i) 2Y/X = 2/4 or 4Y = X; (ii) 2X + 4Y = 180. Simultaneous solution yields A = {Xa = 60, Ya = 15}. The budget line and current choice A are shown on the diagram below.
(d) The tangency equations become: (i) 2Y/X = 4/4 or 2Y = X; (ii) 4X + 4Y = 180. Simultaneous solution yields B = {Xb = 30, Yb = 15}.
(e) ΔM = XaΔpX = 60(2) = 120.
(f) After compensating for the price change, the tangency equations become: (i) 2Y/X = 4/4 or 2Y = X; (ii) 4X + 4Y = 300. Simultaneous solution yields C = {Xc = 50, Yc = 25}.
(g) The total effect of the price change is Xb – Xa = 30 – 60 = –30. The substitution effect is Xc – Xa = 50 – 60 = –10. The price-induced income effect is Xb – Xc = 30 – 50 = –20. The sum of the substitution and income effects of the price change is (–10) + (–20) = –30.
[pic]
(h) The total effect corresponds to the change in X between A and B, the substitution effect corresponds to the change in X between A and C, and the price-induced income effect corresponds to the change in X between C and B.
5.19 (a) Cookie Monster maximizes utility at point A. (b) No, the MRS increases as more cookies are consumed. (c) He might consume only other goods and no cookies, such as at B. For example,
[pic]
(d) Such all or nothing behavior is not consistent with the type of behavior generally seen in the real world. While people choose to consume zero units of many goods, an increasing MRS would be strange indeed.
5.20
[pic]
5.21 (a, b)
[pic]
(c) See graphs. The budget line still passes through the original endowment point because the existence of a black market doesn’t change the fact that the consumer can still buy that bundle. (d) selling. See graph. (e) buying. See graph. (f) increase.
5.22 (a) pgas = $15,000/15,000 = $1/gallon. (b, c, d) See graph. (e) income; substitution. (f) Critics were wrong. Even after compensation, the relatively higher price of gas leads people to consume less (the substitution effect). However, to determine the compensating change in income required to keep utility constant, you would have to know this consumer’s utility function.
[pic]
5.23
(a) See the following figure.
[pic]
(b) At the price pL = $5, his consumption expenditure on other goods is $400.
(c) At the price pL = $10, his consumption expenditure on other goods is $800.
(d) On the graph, the substitution effect occurs between A and C and the income effect occurs between C and B.
(e) The fisherman views lobster as a normal good because the income effect of the price change for this endowment good is direct — more lobster is demanded when its price goes up.
(f) No, he still consumes 20 lobsters.
(g) Yes, if his income effect of the price change were a little stronger, he easily could wind up at a point to the right of B, meaning that at higher prices he consumed more lobster.
5.24
(a) The budget line is horizontal between A and G, but it coincides with the budget line without the NIT to the left of A as can be seen on the next figure.
(b) When t =1, bundle G will be chosen. Why work if you can have more leisure without reducing consumption?
(c) The total effect of implementation occurs between A and C. To isolate the substitution effect of the change in the tax rate (real wage rate), shift the segment BG back parallel to itself until A is just affordable once more. D must be to the right of A according to the weak axiom, and C must be to the right of D if leisure is a normal good.
(d) Yes, because the reduction in the tax rate causes real income to increase thereby causing the quantity of leisure demanded to increase. This reinforces the substitution effect.
(e) Work effort L must decrease because the demand for leisure l must increase.
(f) If there is any impact of the NIT for a person already at G, they will move to a choice like C and work effort will increase.
[pic]
5.25
(a) There are 25 units of each good. (b) Alan’s utility is UA = 10 and Betty’s utility is UB = 10.
[pic]
(c) At C, Alan will have X = 20 and Y = 5, and Betty will have X = 5 and Y = 20. Alan’s utility is UA = 10 and Betty’s utility is UB = 10. Neither of them is better off with this trade.
(d) At B, Alan will have X = 10 and Y = 10, and Betty will have X = 15 and Y = 15. Alan’s utility is UA = 10 and Betty’s utility is UB = 15. Alan is no worse off but Betty is better off. This is called a Pareto efficient trade because at least one person is better off and no one is worse off.
(e) At A, Alan will have X = 15 and Y = 15, and Betty will have X = 10 and Y = 10. Alan’s utility is UA = 15 and Betty’s utility is UB = 10. Betty is no worse off but Alan is better off. This is also a Pareto efficient trade.
(f) At D, Alan will have X = 12.5 and Y = 12.5, and Betty will have X = 12.5 and Y = 12.5. Alan’s utility is UA = 12.5 and Betty’s utility is UB = 12.5. Both are better off. This is called a Pareto superior trade because both were made better off.
(g) The contract curve is the straight line segment between A and B — all Pareto efficient exchanges.
(h) The equilibrium trading bundle must lie at the intersection of the contact curve and some budget line, and also MRSA = MRSB is required for equilibrium, and so D qualifies. You can verify this by noticing that MRSA = 1, MRSB = 1, and pX/pY = 1 simultaneously at D, and D is on the budget line so expenditure equals income for both traders.
5.26
(a) L = [$2.25(200) + $4.75(180) + $1.60(300)]/[$2(200) + $4(180) + $1.50(300)] = 1.137, or 13.7% inflation. (b) P = [$2.25(220) + $4.75(150) + $1.60(350)]/[$2(220) + $4(150) + $1.50(350)] = 1.129, or 12.9% inflation. (c) The Laspeyres index.
5.27 Don’t hire him. The Paasche price index can’t even be calculated until after the economist has revealed his consumption pattern for the next year.
Chapter 6 Solutions
6.1 Use the future value formula, FVt = (1+i)tM At 6 percent: after 1 year, FV = $106; after 2 years, $112.36; after 10 years, $179.08. At 9 percent: after 1 year, FV = $109; after 2 years, $118.81; after 10 years, $236.74. The higher the rate of interest, the faster your money will grow; that is, the higher is its future value.
6.2 $1,150.25 = (1 + i)2 $1,000; i = .0725 or 7.25%.
6.3 Use the present value formula: PV = Mt/(1+i)t. (a) PV = $627,412.37. (b) PV = $496,969.34 (c) PV = $540,268.88 (d) higher; farther.
6.4 Amazingly, it’s only about 97 cents! (PV = $1,000/(4.00)5.)
6.5
(a) $200 + $250/(1.08) = $431.48. She can’t borrow $250 because next period she must pay back the amount borrowed plus interest.
(b) $250 + $200(1.08) = $466.
(c) See the figure. Note: slope = – $466/$431.48 = –1.08.
[pic]
(d) See graph above.
(e) She could have $250 + $200 (1.06) = $462 in t2; in t1, Ima could have $200 + $250/(1.06) = $435.85.
(f) lower; Less.
(g) Ima Borrower.
6.6
(a) The interest rate i must satisfy the equation for the maximum level of future consumption, thus M1(1 + i) + M2 = 30(1 + i) + 40 = 80 and i = 1/3.
(b) C2a = [M1(1 + i) + M2] – [C1a(1 + i)] = 30(4/3) + 40 – 35(4/3) = 33 1/3.
(c) At A, the level of borrowing is Sa = M1 – C1a = –5.
(d) At A, the amount that must be paid out of future income is 40 – 33 1/3 = 6 2/3.
(e) The interest rate now is determined by M1(1 + i) + M2 = 30(1 + i) + 40 = 100, and so i = 1. (f) C2b = [M1(1 + i) + M2] – [C1b(1 + i)] = 30(2) + 40 – 25(2) = 50.
(g) At B, saving is Sb = M1 – C1b = 5.
(h) See the next figure.
(i) This person has switched from being a borrower to being a lender (and a saver) as the interest rate rose.
[pic]
6.7 (a) This person is worse off at B than at A because B was attainable when A was chosen, and so A was revealed preferred to B. (b) No, you cannot tell whether this person is better off or worse off at C than at A because neither was attainable when the other was chosen.
6.8 (a)
Net Present Values
i = 6% i = 9% i = 12%
Investment A $130.51 $126.23 $122.23
Investment B 135.88 125.70 116.55
Investment C 133.65 126.56 120.09
(b) When i = 6%, Investment B. (c) When i = 9%, Investment C. (d) When i = 9%, Investment C. (d) When i = 12%, Investment A. (e) sensitive.
6.9 There is no most appropriate interest rate. Since the interest rate measures the opportunity cost of funds, the rate of return on the next best alternative of similar risk and uncertainty should be used. Generally, economists prefer real (as opposed to nominal) rates.
6.10 (a) ρ = (0.07 – 0.03)/1.03 = 0.0388 or 3.88%; approximate ρ = 7 – 3 = 4%. The approximation overstates ρ by 0.12%. (b) ρ = (0.80 – 0.60)/1.60 = 0.125, or 12.5%; approximate ρ = 80 – 60 = 20%. The approximation overstates ρ by 7.5%. (c) small.
6.11 Use formula on page 209 of textbook: If i = 5%, PV = $623,110.52; if i = 10%, PV = $425,678.19; and if i = 15%, PV = $312,966.57. As the interest rate rises, the present value of an annuity falls.
6.12 At i = 8%, value of annuity = ($1,000/0.08)[1 – 1/(1.08)20] = $9,818.15. Value of perpetuity = $800/0.08 = $10,000, choose the perpetuity. At i = 10%, value of annuity = ($1,000/0.10)[1 – 1/(1.10)20] = $8,513.56. Value of perpetuity = $800/0.10 = $8,000, choose the annuity.
6.13 PV = ($2,000/.05)[1 – 1/(1.05)50] = $36,511.85.
6.14 Use formula on page 210 of textbook: (a) If i = 6%, PV of the bond = $926.39. (b) if i = 8%; PV = $798.69; if i = 10%, PV = $692.77; PV varies inversely with i.
6.15 (a) $1,000(1.1) = $1,100; buy back A for $1,050; profit = $50. (b) decrease; fall (c) $95.45. Note: $105/$95.45 = 1.10. (d) forgone interest = $90; sell A for $1,050; profit = $150 – 90 = $60. (e) increase; rise; $95.45. (f) $95.45.
6.16 Use formula from page 213 of textbook. (a) At i = 7%, NPVα = $494.53; at i = 9%, NPVα = – $249.64. (b) At i = 7%, NPVβ = $2,447.54; at i = 9%, NPVβ = $1,100.14. (c) less; positive, negative. (d) Solve by trial and error: mα = 8.32% and mβ = 10.743%.
6.17 (a) If i = 4%, NPVX = $127,610 and NPVY = $90,660. (b) mX is about 9%; mY is about 9.4%. (c) Project Y has a higher m, but Project X has a higher NPV when i = 4%. Choose the investment with the higher NPV, Project X.
6.18 Yes. Someone over 40 has fewer years of working life in which to recoup the college expenses and forgone income (which may also be higher than for the 20-year-old).
6.19 Completely specific training has no effect on productivity that is useful to other firms. Thus the wage a worker can get elsewhere is independent of the specific training received, and the firm pays the going market wage. The firm will be willing to pay the cost of specific training only if it can collect a return on the investment in human capital in the form of higher productivity. Thus the willingness of the firm to pay for the specific training depends on the likelihood of labor turnover, and so a firm will be reluctant to hire someone with a high probability of leaving the firm after a short time. Statistically, women have higher turnover rates than men, and so firms will be more reluctant to hire women into jobs that require a considerable amount of specific training unless they are willing to bear the cost of that training by accepting a lower starting wage. Women, therefore, gravitate toward jobs that require general training that can be transferred elsewhere. At the same time, men receiving specific training become more productive and are subsequently paid a higher wage, and so their age/earnings profile is steeper than the females’ on average.
6.20 (a) Project D, by Invisible Inc. Firm will borrow $20,000. (b) Project A, by IOU Corp. Firms will now borrow $30,000. (c) more. The MEI curve represents the demand for loanable funds, as well as the supply of capital value.
[pic]
6.21 Investment demand will increase and that will push interest rates upward:
[pic]
6.22
[pic]
Private good: p = 30 – (1/2)Q, or Q = 60 – 2p. Public good: p = 60 – 2Q, or Q = 30 – (1/2)p.
6.23
(a) p = 1,000 – 10Q. See the following figure.
(b) Set 1,000 – 10Q = 100; Q = 90 units.
(c) TC = $100(90) = $9,000 and is shaded on the diagram. Per-person cost = $9,000/1,000 = $9.
(d) TB is the sum of both shaded areas, TB = $49,500, per-person TB = $49.50.
(e) CS is area of the shaded triangle on graph, CS = $40,500. Per-person CS = $40.50.
(f) New demand: p = 990 – 9.9Q; Q = 89.9 units.
(g) TC = $100(89.9) = $8,990. Per-person cost = $8,990/990 = $9.08.
(h) TB is slightly less, TB = $101(89.9) + 0.5(1,000 – 101)(89.9) = $49,489.95. Per-person TB = $49,489.95/1,000 = $49.49.
(i) CS is slightly less, CS = $40,410.50. Per-person CS = $40.82.
(j) $49.49 – $40.50 = $8.99; $40.50 – $40.82 = –$0.32 or 32¢ loss; strong; weak.
[pic]
Chapter 7 Solutions
7.1 Customers who carry month-to-month balances have the most to gain by the lower (capped) interest rate. We would expect that a disproportionate share of people applying for lower interest rate cards would be these customers. This problem is a variation on the adverse selection (lemons) problem. Banks can check the credit histories of their applicants, however, to gain some information on their credit worthiness.
7.2
(a) pL = (220 – 200)/0.004 = $5,000; pG = (240 – 200)/0.004 = $10,000.
(b) Lemon owners will try to sell at pG = $10,000; price will fall.
(c) At p = $8,000, QL + QG = 220 – 0.004(8,000) + 240 – 0.004(8,000) = 396. Qs = 400. Some sellers, who can’t sell their cars, will be disappointed. Some buyers, who will get stuck with lemons, will be disappointed, also.
(d) None, since they are worth $8,000 to their owners.
(e) This market could end up with only lemons.
7.3 As long as the conditions of the separation theorem hold, the agents don’t have to know anything about the stockholders’ preferences. All they have to do is maximize the present value of what has been entrusted to them; Fisher’s theorem assures us that this will enable the principals to be as well off as possible.
7.4 (a) Risk — subjective risk. (b) Uncertainty — probability of events unknown. (c) Risk — objective risk. (d) Uncertainty — events unknown.
7.5
(a) U(10,000) = 0.5U(25,000) + 0.5U(0) = 0.5(1) + 0.5(0) = 0.5.
(b)
[pic]
(c) EMV = 0.5(25,000) + 0.5(0) = $12,500.
(d) Yes, he is risk-averse. He reaches the same level of U receiving a sure $10,000 (at a) as he does with a gamble whose EMV is higher, at $12,500 (at b). Notice also the concave shape of the utility function.
(e) EMV = 0.33(10,000) + 0.66(25,000) = $20,000.
(f) EU = 0.33U(10,000) + 0.67U(25,000) = 0.33(0.5) + 0.66(1) = 0.83. See point c.
7.6
(a) E[U(gamble)] = 0.5U(900 – 800) + 0.5U(900) = 500.
(b) To find R: U(900 – R) = 500; R = $400.
(c) Expected payoff = 0.5(800) = $400. Insurance company has just enough to compensate Joe Cool for his expected losses; there is nothing left to cover operating (administrative) costs.
(d) E[U(gamble)] = 0.5U(900 – 800) + 0.5U(900) = 410,000.
(e) To find R: U(900 – R) = 410,000; R = $260.
(f) No, their losses are even greater in this case. Most people must be risk averse; otherwise, there’d be no insurance companies left in business.
(g) At e, EU = 410,000; certainty equivalent, at c, is $640. Recall that Eva will only pay $260 to avoid this gamble.
[pic]
7.7
(a) For Bea Careful, EU = 0.5+ 0.5= 1.58, which is less than U(5) = = 2.24. She won’t play.
(b) For I. M. Wilder, EU = 0.5(10)2 + 0.5(0) = 50, which is more than U(5) = (5)2 = 25. He will play.
(c) For Bea Careful, solve EU = P= for P = 0.71. She won’t take the double-or-nothing bet unless P is at least 71%. For I. M. Wilder, solve EU = (10)2P = 52, P = 0.25. He’ll take the bet as long as P is above 25%.
7.8
(a) EMV = 0.8(10) + 0.2(50) = $18,000; EU corresponds to c on line segment ab.
(b) Fair premium = 0.8(40,000) = $32,000. Yes. By paying $32,000, this person could wind up at d, a higher level of U.
(c) EMV = 0.2(10) + 0.8(50) = $42,000; EU corresponds to e on line segment ab.
(d) Fair premium = 0.2(40,000) = $8,000. Yes. By paying $8,000, this person could wind up at f.
(e) EMV = $30,000; point g.
(f) High-risk group moves to d; low-risk group moves to h.
(g) High-risk people — the lemons. The insurance company can’t make money unless is raises premiums drastically.
(h) Low-risk people could identify themselves to the insurance company by accepting higher deductibles than would a high-risk person.
7.9 Less likely. The insurance company can reduce the extent of moral hazard by requiring certain types of behavior as a condition of being insured. For example, they could offer homeowner’s policies only to people with burglar alarm systems, or at least offer lower premiums to those who have installed such systems.
7.10
(a) μeggs = (1/2)12 + (1/2)0 = 6.
(b) μeggs = (1/4)12 + (1/2)6 + (1/4)0 = 6.
(c) With 1 trip, P = 1/2; with 2 trips, P = 1/4.
(d) With 1 trip, σ2 = (1/2)(12 – 6)2 + (1/2)(0 – 6)2 = 36. With 2 trips, σ2 = (1/4)(12 – 6)2 + (1/2)(6 – 6)2 + (1/4)(0 – 6)2 = 18. For 1 trip, σ = 6; for 2 trips, σ = 4.24.
(e) For 1 trip, v = 6/6 = 1; for 2 trips, v = 4.24/6 = 0.71.
(f) The mean-variance rule says that if two alternatives have equal means, choose the one having the smaller variance. If trips are costless, take the eggs home in two trips.
(g) In real life, examples of diversification abound. Individuals seldom holding all of their wealth in a single asset, and banks limiting how much they’ll lend to any one borrower, are two examples.
7.11
(a) μC = 6; σC = 0. μR = 30; σR = 2. See the figure for C and R.
[pic]
(b) See the graph. The slope of this line is (μR – μC)/σR = 12. This slope measures the price of risk — the increase in the expected return for every one unit increase in σ.
(c) μ/σ = (μR – μC)/σR = 12.
(d) μ = μC + [(μR – μC)/σR]σ = 6 + 12σ.
(e) Set the slope of the budget line equal to –MRS to get σP = 0.5.
(f) μP = 12%. P* is indicated on the graph.
(g) Substitute μP and σP into the equation for the portfolio to find k = 1/4.
(h) $7,500 in T-bills. $2,500 in the risky asset.
7.12
Percent gain
A B f(A, B) (A – μA) (A – μA)2 (B – μB) (B – μB)2 (A – μA)(B – μB)
10 1 0.2 2.8 7.84 –2.9 8.41 –8.12
8 2 0.3 0.8 0.64 –1.9 3.61 –1.52
6 6 0.4 –1.2 1.44 2.1 4.41 –2.52
4 7 0.1 –3.2 10.24 3.1 9.61 –9.92
Percent gain
C D f(C, D) (C – μC) (C – μC)2 (D – μD) (D – μD)2 (C – μC)(D – μD)
20 3 0.2 5.6 31.36 –2.6 6.76 –14.56
16 4 0.3 1.6 2.56 –1.6 2.56 –2.56
12 7 0.4 –2.4 5.76 1.4 196 –3.36
8 10 0.1 –6.4 40.96 4.4 19.36 –28.16
(a) µA = 7.2; µB = 3.9. (b) σA2 = 3.36; σB2 = 5.49. (c) σAB = –4.08.
(d) µC = 14.4; µD = 5.6. (e) σC2 = 13.44; σD2 = 4.84
(f) σCD = –7.84; (g) ρAB = –0.95.; ρCD = –0.972.
(h) A and B are less strongly correlated and their covariance is smaller. Correlation is better.
7.13
(a) Yes, the beta can be negative. This means that when the return to the market as a whole goes up, the return paid to the asset tends to go down — they have negative covariance.
(b) Yes, the beta of an asset can be zero. No, this does not mean that the asset has no risk. Rather, it means that market return and the return to the asset are not correlated.
(c) Yes, the beta of an asset can be positive. This means that when market risk tends to increase, so does the riskiness of the asset.
7.14
(a) If the stock market and gambling on NFL games seem worlds apart, the difference is more illusory than real, and can probably be explained by the social stigma attached to gambling. Both markets have in common the characteristics which are ascribed to perfectly competitive markets: large numbers of participants, easy entry, and extensive, and easily attainable, market knowledge.
(b) Research has shown that it is virtually impossible to make above-average profits in either market by playing a system; in other words, both markets are efficient.
7.15
(a) Adjusted rates are 9%, 11%, and 13% for periods 1, 2, and 3.
(b) NPVβ = –27,000 + 5000/(1.09) + 5000/(1.11)2 + 5000/(1.13)3 + 20,000/(1.07)3 = $1,436.48, which is still greater than NPVα.
(c) NPVβ = –27,000 + 5000/(1.09) + 5000/(1.11)2 + 5000/(1.13)3 + 20,000/(1.13)3 = –$1,028.48. Not only does Project α have a higher NPV, but Project β would not even be recommended.
7.16
(a) His potential revenue will fall by 25¢ per bushel.
(b) His potential revenue will increase by 25¢ per bushel.
(c) He loses 25¢ for each bushel grown and sold, but he gains 20¢ for each bushel bought and sold. The net decrease is 5¢ per bushel.
(d) He gains 25¢ for each bushel grown and sold, but he loses 30¢ for each bushel bought and sold. The net decrease is 5¢ per bushel.
(e) There will be a net decrease in potential revenue. Ole will undertake such a hedge only if the 5¢ per bushel cost is worth the avoidance of an even greater potential loss, and so it depends on how risk-averse Ole is.
7.17 By buying when a product is relatively plentiful (and its price is low), speculators raise its price; by selling when the product is relatively scarce (and its price is high), they help lower its price. Their activity smooths out some of the price fluctuations that normally would occur in markets.
7.18
(a) If I1 is chosen, worst is 0% (S1 or S4); if I2 is chosen, worst is 0% (S4). Choose I3, best of the worst = 5%.
(b) If I1 is chosen, best is 15% (S3); if I2 is chosen, best is 10% (S2 or S3). Choose I4, best of the best = 20%.
(c) Choose I1, which has the lowest maximum regret.
[pic]
(d) EV(I1) = (1/4)0 + (1/4)5 + (1/4)15 + (1/4)0 = 5%; choose I2, since EV(I1) = 6.25% and for all other I’s, EV = 5%.
(e) Choose I2, since its EV is the highest of the four (and equal to the following): EV(I2) = (1/8)5 + (1/2)10 + (1/4)10 = 8.125.
7.19 (a) Payoff table of utilities:
[pic]
(b) EUA = (5/8)6 + (3/8)5 = 5.625; EUB = (5/8)4 + (3/8)7 = 5.125. Platform A gives the maximum EU.
(c) EU of a perfect prediction = (5/8)6 + (3/8)7 = 6.375.
(d) EU of perfect information = 6.375 – 5.625 = 0.75.
(e) Since U = , M = U2 = (0.75)2 = 0.5625; he is willing to pay up to $562,500 for the perfect information.
Chapter 8 Solutions
8.1 (a) The scatter plot and plot of the estimated equation are
[pic]
(b) [pic] = 70; [pic] = 100.
(c) Cov(X, Y) = –3,550/12 = –295.8333.
(d) The negative sign indicates that when one is low the other tends to be high. When X tends to be above its mean, Y tends to be below its mean, and when X tends to be below its mean, Y tends to be above its mean . The variables are inversely related.
(e) Var(X) = 2,250/12 = 187.50, and Var(Y) = 6,300/12 = 525.00.
(f) [pic]
(g) [pic]
(h) [pic]
(i) [pic]210.446 – 1.5778(70) = 100.
(j) See the figure. The coefficient [pic] is the estimated slope, Y decreases 1.5778 units when X increases by one unit. The coefficient [pic] is the estimated intercept, but caution should be exercised here because it is dangerous to conclude that Y will be equal to [pic] when X = 0.
(k), (l) Table 8.1 (continued)
Day(i) Quantity (Yi) Cents (Xi) [pic] (Yi – [pic]) (Yi – [pic])2 ([pic] – [pic]) ([pic] – [pic])2
1 55 100 52.666 2.334 5.4476 –47.334 2,240.5076
2 70 90 68.444 1.556 2.4211 –31.556 995.7811
3 90 80 84.222 5.778 33.3853 –15.778 249.9453
4 100 70 100.000 0 0 0 0
5 90 70 100.000 –10.000 100.0000 0 0
6 105 70 100.000 5.000 25.0000 0 0
7 80 70 100.000 –20.000 400.0000 0 0
8 110 65 107.889 2.111 4.4563 7.889 62.2363
9 125 60 115.778 9.222 85.0453 15.778 248.9453
10 115 60 115.778 –0.778 0.6053 15.778 248.9453
11 130 55 123.667 6.330 40.1069 23.667 560.1269
12 130 50 131.556 –1.556 2.4211 31.556 995.7811
Sums: 1,200 840 1,200.0 0.0 698.8889 0.0 5,602.2689
(m) The standard error of regression is a measure of the spread of the conditional distribution of Y given X,
[pic]
(n) The standard error of [pic] is a measure of the spread of the distribution of [pic] about its mean:
[pic]
(o) R2 measures the proportion of the total variation in the dependent variable explained by the regression equation, R2 = 5,602.2689/6,300 = 0.8892.
(p) The adjusted R2 is always lower than R2:
[pic]
8.2
(a) The estimated beta of the asset for Mobil is 0.7815. The estimated beta of the asset for Motorola is 1.3381.
(b) Both have t-ratios that are greater than two in absolute value, and so both are fairly precise. This should be expected if the CAPM works in the real world.
(c) Neither of the estimated intercept terms are significantly different from zero. This is to be expected since an intercept is included only so that the estimated beta, and the R2, for each equation are not biased.
(d) The standard error of the estimate for β1 is 0.7815/5.974 = 0.1308. The standard error of the estimate for β2 is 1.3381/8.482 = 0.1578.
(e) To test a null hypothesis that β = 1 against the alternative that β ≠ 1, the rule of thumb suggests that the appropriate t-ratio should be
[pic]
For Mobil, this t-ratio is –0.2185/0.1308 = –1.6705, and so Mobil’s beta is not significantly different from 1 according to the rule of thumb. For Motorola, this t-ratio is –0.3381/0.1578 = 2.1426, and so Motorola’s beta is significantly different from 1 according to the rule of thumb.
(f) For Mobil, the proportion of the total variation attributed to market risk is 0.3810 or about 38 percent, and the proportion of the total variation attributed to asset-specific risk is 0.6190 or about 62 percent. For Motorola, the proportion of the total variation attributed to market risk is 0.5536 or about 55 percent, and the proportion of the total variation attributed to asset-specific risk is 0.4464 or about 45 percent.
(g) The Mobil asset is less risky than the market as a whole because its beta is less than 1. The Motorola asset is more risky than the market as a whole because its beta is greater than 1.
8.3
(a) The proportion of the variation in the dependent variable explained is greater than 0.82 or 82 percent, a pretty good overall fit. The adjusted R2 has the advantage of adjusting R2 downward to compensate for the fact that R2 always increases whenever an explanatory variable is added to the regression. In contrast, the adjusted R2 may fall if a statistically insignificant explanatory variable is added to the regression.
(b) Yes, the signs of the estimated coefficients are consistent with expectations. Miles per gallon falls with increased weight, falls for a car with an automatic transmission, and increases for a car with a diesel engine. The sign of the coefficient on the Ei should be positive if you think that actual mileage is directly related to the published estimates.
(c) The predicted miles per gallon falls by 2.76 when the car has an automatic transmission, and the predicted miles per gallon increases by 3.28 when the car has a diesel engine.
(d) All of the estimated coefficients have t-ratios that are greater than or equal to 2 in absolute value, so each coefficient can be considered to be fairly precise.
(e) Lowell must have included Ei as an explanatory variable in order to see if the estimates published by the EPA, estimates that are provided to prospective consumers at the time of sale, are accurate. If the EPA estimates are accurate, then the coefficient of the Ei variable should be equal to 1.
8.4
(a) The estimate of 0.70 or 7 percent is very reliable according to the rule of thumb. However, there are many relevant but excluded variables, and so the estimate is likely to be biased because of specification error. Notice the very small R2.
(b) A constant rate of return is plausible, but then so is a diminishing rate of return. Perhaps the specification should be modified to capture that possibility.
(c) The new estimate of the rate of return to schooling is 0.107 or slightly more than 10 percent. Yes, the signs of the coefficients attached to X and X2 are plausible because they imply that the return to experience increases at a decreasing rate. An examination of age-earnings profiles confirms this shape. These coefficients are very precise because each standard error is quite small compared to the estimated coefficient. The proportion of the variance in the dependent variable explained increased by 0.218 — almost 22 percent more of the variation in ln E has been explained by adding X and X2 to the regression.
(d) When X = 8, we have 17.4% at S = 8; 15.1% at S = 12; and 12.8% at S = 16.
(e) X* = 31.6 at S = 8; X* = 26.8 at S = 12; X* = 22.0 at S = 16. Thus, ln E is maximized at age 45.6 for elementary school graduates, 44.8 for high school graduates, and 44.0 for college graduates. At different levels of schooling, there is no big difference in the ages at which earnings is maximized.
(f) It follows that the age-earnings profile is steeper for the more highly educated men.
8.5
(a) R2 = 0.908 or about 91 percent.
(b) Multicollinearity.
(c) They are all fairly precise because the absolute values of the coefficients are all twice the size of their standard errors.
(d) The coefficient for D61 is not statistically different from zero, but the others are statistically significant.
(e) The signs are all negative and they increase in magnitude indicating that price has fallen over this period.
(f) Examples might include: reliability; ease of use; speed of retrieval from media storage; compatibility with other devices.
8.6
Estimated Price
Year Coefficient Antilog Index
1960 –0.1045 0.9008 1.0000
1961 –0.1398 0.8695 0.9653
1962 –0.4891 0.6132 0.6807
1963 –0.5938 0.5522 0.6130
1964 –0.9248 0.3966 0.4403
1965 –1.1630 0.3125 0.3469
The average annual growth rate in the quality-adjusted price of computers from 1960 to 1965 is about 18.5 percent. To calculate this, you must calculate the percent changes in the index from one period to the next, add them, and then average.
8.7 Perfect multicollinearity will be encountered. The usual solution is to drop one of the three variables from the regression.
8.8 (a) The explanatory variable is said to be stochastic. (b) The ordinary least-squares estimate of β will be biased. (c) The technique is to use an instrumental variable for X.
8.9 (a)
[pic]
(b) Cov(p, Q) = 0, and so [pic] = 0; [pic] = [pic]. The problem is identification.
(c) These look like demand curves.
(d) These look like supply curves.
(e) Each is identified because there is an excluded exogenous variable for each that is included in the other equation.
(f) Qs = (50/3)p, because [pic] = is 50/3, [pic] = 50, and the intercept is –200.
(g) Qd = 250 – (50/3)p + 5M, because [pic] –50/3, [pic] = 5, and the intercept is 250.
8.10 Stage one: estimate the reduced form equation for every endogenous variable for which you need an instrumental variable. Stage two: estimate any identified structural equation for each endogenous variable using predicted values from stage one in place of any endogenous variables being used as explanatory variables.
8.11
(a) The price of beer is endogenous because it is determined simultaneously by demand and supply.
(b) α1 < 0, β1 > 0.
(c) The demand equation is exactly identified. The supply equation is over identified.
(d) The reduced form equation is [pic].
(e) The demand and supply equations to be estimated using the instrument are:
Qd = α0 + α1 [pic] + α2 pW + α3 A + εd
Qs = β0 + β1 [pic] + β2 Z + εs
(f) The 2SLS coefficient estimates are still biased but they are consistent.
8.12
(a) No, heteroscedasticity does not cause bias in estimating regression coefficients because positive errors and negative errors of similar magnitude are equally probable.
(b) Yes, heteroscedasticity does compromise the use of the rule of thumb because the standard errors are biased.
8.13
(a) Your graph should look something like this,
[pic]
(b) Heteroscedaticity is evident by looking at this scatter plot.
(c)
i Y X [pic] Y – [pic]
1 50 2 46.86322 3.13678
2 40 4 48.53799 –8.53799
3 50 8 51.88754 –1.88754
4 50 10 53.56231 –3.56231
5 60 12 55.23708 4.76292
6 40 14 56.91185 –16.91185
7 90 18 60.26140 29.73860
8 80 20 61.93617 18.06383
9 40 22 63.61094 –23.61094
10 80 24 65.28571 14.71429
11 40 26 66.96049 –26.96049
12 120 28 68.63526 51.36474
13 30 30 70.31003 –40.31003
(d) Your graph should look something like this:
[pic]
(e) If the estimated error is spreading (or shrinking) as X increases, that is probably due to heteroscedasticity. Moreover, that explanatory variable can probably be used to create a weight 1/X to perform weighted least squares.
8.14
(a) The WLS equation for the model is
[pic]
(b) The other characteristic different from the usual ordinary least-squares model is that the WLS model has no intercept term, and so you must estimate without a constant.
8.15 (a)
|Xt |Yt |[pic] |[pic] |[pic] |
| 1 | 2 | 5.014286 |–3.014286 |— |
| 2 | 4 | 5.491729 |–1.491729 |–3.014286 |
| 3 | 7 | 5.969173 | 1.030827 |–1.491729 |
| 4 | 5 | 6.446617 |–1.446617 | 1.030827 |
| 5 | 9 | 6.924060 | 2.075940 |–1.446617 |
| 6 | 12 | 7.401504 | 4.598496 | 2.075940 |
| 7 | 9 | 7.878947 | 1.121053 | 4.598496 |
| 8 | 9 | 8.356391 | 0.643609 | 1.121053 |
| 9 | 11 | 8.833835 | 2.166165 | 0.643609 |
| 10 | 12 | 9.311278 | 2.688722 | 2.166165 |
| 11 | 8 | 9.788722 |–1.788722 | 2.688722 |
| 12 | 9 | 10.26617 |–1.266166 |–1.788722 |
| 13 | 8 | 10.74361 |–2.743608 |–1.266166 |
| 14 | 9 | 11.22105 |–2.221052 |–2.743608 |
| 15 | 8 | 11.69850 |–3.698496 |–2.221052 |
| 16 | 11 | 12.17594 |–1.175940 |–3.698496 |
| 17 | 14 | 12.65338 | 1.346617 |–1.175940 |
| 18 | 12 | 13.13083 |–1.130827 | 1.346617 |
| 19 | 15 | 13.60827 | 1.391729 |–1.130827 |
| 20 | 17 | 14.08571 | 2.914286 | 1.391729 |
(b)
[pic]
(c) The points tend to be in the lower-left and upper-right quadrants, and so ρ is probably positive.
[pic]
8.16 The Durbin-Watson d-statistic will be close to zero when [pic] is approximately 1 because the difference between [pic] and [pic] will be small.
8.17 d ≈ 0 when there is nearly perfect positive first-order serial correlation. d ≈ 4 when there is nearly perfect negative first-order serial correlation.
Chapter 9 Solutions
9.1
(a) For the first quarter of 1988, t = 21, and so the forecast is 28.8004. For t = 22, the forecast is 29.2034. For t = 23, the forecast is 29.6064. For t = 24, the forecast is 31.0094.
(b) If a dummy variable were used also for the first quarter there would have been perfect multi-collinearity — the dummy variable trap.
(c) Since none of the standard errors of the dummy variables are statistically significant, there is no need for seasonal adjustment.
9.2
(a) No trend is apparent. Yes, this series may have cyclical movement — it swings from high to low and back again.
(b) For the first quarter of 1988, t = 21, and so the forecast is 29.3119. For t = 22, the forecast is 29.8656. For t = 23, the forecast is 30.4331. For t = 24, the forecast is 31.0144.
(c) This forecast is increasing at an increasing rate. This is not reasonable if there is a cycle because the series will never turn downward.
(d) Yes, this is a reasonable forecasting model — more so than the quadratic at least. For forecasting, the overall goodness of fit is more important than the statistical significance of individual coefficients. Moreover, the cubic is better than the quadratic because it will not continue to increase forever.
9.3
(a) Not unless you know what Xt will be in the future, and that is not very likely.
(b) The forecast X88:1 = 171.6035. Yes, Y88:1 = 28.7522. This model will work well only if the forecast of Xt is good.
(c) For the model with quarterly dummys:
[pic] [pic]
1988:1 171.9095 28.80607
1988:2 173.7295 29.12639
1988:3 176.0720 29.53867
1988:4 178.7870 30.01651
The model does a fair job within the sample, but it doesn’t follow all the dips and blips. There is some tracking in the residual. It will only do a fair job forecasting beyond the sample for the same reason. In addition, there seems to be some error autocorrelation present, which is why the researcher cited in the textbook application attempted to correct for that.
9.4 (a)
period Yt Xt Yt–1 Xt–1
87:1 27.52 164.2 26.98 160.7
87:2 27.78 165.6 27.52 164.2
87:3 28.24 164.7 27.78 165.6
87:4 28.78 171.7 28.24 164.7
(b) Both Yt–1 and Xt–1 added to the predictive power of the model as is evident by looking at their small standard errors. In time series, lagged values of the dependent variable are almost always highly correlated with the current value — especially if the periods are short. Likewise, if Xt is highly correlated with Yt, then Xt–1 is almost surely highly correlated with Yt. Multicollinearity may become a problem, but that is not evident here.
(c) Y88:1 = 29.8994.
(d) This forecasting model does perform better than the model of problem 9.3 because it tracks the dips and blips more closely. This is due to the autocorrelation which is controlled better by having Yt–1 on the right-hand side.
9.5
(a) The Super Bowl indicator is a leading indicator.
(b) The hemline indicator is called a coincident indicator.
(c) We would not have been willing to put all our investments in stocks because the relationships are probably spurious. And there is no reason we can think of to believe that there is some other outside force that is causing these things to occur together. Besides, it’s always a bad idea to put all your eggs in one basket — the golden rule for investing is to diversify.
9.6 Important economic variables include the good’s price, prices of substitutes and complements, and consumer income. These are virtually required in any demand study. In addition, you might try to capture the effects of changing tastes, product innovation, and expectations. The ability of consumers to finance the good may be relevant as well as the appropriate interest rate.
9.7
(a) When a series has trend, the sample ACF values are likely to be large and positive for short lags, decreasing slowly as the lag length increases. Clearly the series Yt has trend.
(b) Clearly these estimates are not statistically significant, and so the series ΔYt has no trend.
(c) Based on the above analysis, d = 1.
(d) No, neither of these patterns is evident.
(e) No, this series is not a good candidate for ARIMA estimation because none of the ACF or PACF coefficients are statistically significant.
9.8
(a) Yes, at least there is no evident trend.
(b) A pure AR(1) process is evident.
(c) Yt = β0 + β1Yt–1 + εt where β1 < 0. (If β1 > 0, the PACF coefficients would not be switching signs.)
9.9
(a) Yes, at least there is no evident trend.
(b) A pure MA(1) process is evident.
(c) Yt = θ0 + εt + θ1εt–1 where θ1 > 0. (If θ1 < 0, the PACF coefficients would be switching signs.)
9.10
(a) These patterns are typical of a pure MA(1) process.
(b) Yt – Yt–1 = θ0 + εt – θ1εt–1; θ1 < 0.
(c) Yt = Yt–1 + εt + [pic]0 + [pic]1εt–1 where E(εt) = 0.
9.11
(a) The first autocorrelation coefficient is not very big, and so there is no trend evident.
(b) No, a mixed model is indicated since the ACF does not die out or decay.
(c) The number of AR terms should be less than the number of MA terms because the AFC drops off at its beginning, and so p should be less than q in this case.
(d) The PACF cuts off after lag 3, and so there should be no more than 3 MA terms in the model.
(e) We want to keep the specification as parsimonious as possible. Because we found that p < q ≤ 3, let’s try p = 1 and q = 2. If this doesn’t work well, then try p = 1, q = 3; then p = 2, q = 3. Initially, the first model to try is ARIMA(1, 0, 2):
Yt = β1Yt–1 + θ0 + εt – θ1εt–1 – θ2εt–2.
(f) Yt = [pic]1Yt–1 + [pic]0 + εt – [pic]1εt–1 – [pic]2εt–2 where E(εt) = 0.
Chapter 10 Solutions
10.1 (a), (b)
[pic]
(c) When L = 2 and K = 4, a small increase in L yields MPL = 1, and it remains constant. For small increases in K, MPK = 0, and it remains constant.
(d) When L = 4 and K = 4: MPL = 0, MPK = 0.
(e) At L = 4 and K = 4, when they change to L = 5 and K = 5, output changes from Q = 4 to Q = 5. The 25 percent increase in both inputs caused the same percent increase in output. The technology exhibits constant returns to scale.
(f) MRTS = 0. This means that L and K are perfect complements.
10.2 (a)
[pic]
(b) L1 = 16; L2 = 4. When output was quadrupled, all inputs had to be increased by the same proportion. This production function exhibits constant returns to scale.
(c) With 8 pounds of lemons and one hour squeezing lemons, Q = 2. One more hour squeezing yields ΔQ = 1, and so MPL = 1.
(d) With 8 pounds of lemons and 2 hours of squeezing, Q = 1. She has no more lemons , and so the marginal product of labor is MPL = 0.
10.3 (a), (b):
[pic]
(c):
[pic]
(d) Process A is now technologically dominated by Process B. If labor were free, then it would not cost more in money terms to use A, but that certainly is technologically inefficient because you use labor that could be used elsewhere. Even if both inputs were free, you would still want to use B or C because they are more efficient than A under this third state of technology.
10.4 (a)
[pic]
(b) Law of diminishing returns does hold. As more HP is used, its MP falls:
18-inch pipeline
HP Output MP AP
20 115 — 5.75
30 130 1.50 4.33
40 140 1.00 3.50
50 148 0.80 2.96
60 154 0.60 2.57
(c) Both AP and MP rise when the fixed input increases:
22-inch pipeline
HP Output MP AP
20 148 — 7.40
30 170 2.20 5.67
40 185 1.50 4.625
50 195 1.00 3.90
60 204 0.90 3.40
(d) MP is below AP, and AP is falling.
(e) 60,000 barrels/day; 185,000 barrels/day. Since Q more than doubles, increasing returns to scale are implied.
(f) ηE = 1/3.5 = 0.28; (0.28)(5) = 1.4% increase in oil pumped.
10.5 Fixed inputs are those which do not change as short-run production levels change, such as large capital equipment items — buildings and machines. Variable inputs typically include those which can be easily varied in response to changing production activity — labor, raw materials, and electric power.
10.6
(a) At point A: as L increases, Q decreases from Q2 to Q1 to Q0. MPL = 0 at A; stage III in production.
(b) At point B: as K increases, Q decreases from Q2 to Q1 to Q0. MPK = 0 at B; stage III in production.
(c) At point C: both MPs are negative. Increasing either input results in less Q.
(d) The economic region is shaded on the graph.
[pic]
10.7
(a) K = 10: 100 = 40 + 2L, L = 30; L = 25: 100 = 4K + 50, K = 12.5.
(b) MRTS = 1/2 and is constant; you can always trade 2L for 1K; L and K are perfect substitutes.
[pic]
(c) Q = 40 + 2(31) = 102; MPL = 2 and doesn’t change as more L is used.
(d) Q = 4(13) + 50 = 102; MPK = 2/0.5 = 4 and it doesn’t change.
(e) Q = 4(20) + 2(20) = 120; Q = 4(40) + 2(40) = 240; constant returns to scale, because Q doubled when both inputs were doubled.
(f) Q = 2(28) + 4(11) = 100; 2(–2) + 4(1) = 0.
10.8
[pic]
10.9 ηL = 10/16 = 0.625; Stage II; MPL = ηL APL = (0.625)(24) = 15 units of output/hour.
10.10 %∆Q = (0.4)(5) = 2%; %∆K = %∆Q/ηK = 10/0.4 = 25%.
10.11
Amount of food (lbs.) Amount of fish (lbs.) AP MP
400 200 0.50 —
600 400 0.67 1.0
800 700 0.88 1.5
1,000 940 0.94 1.2
1,200 1,140 0.95 1.0
1,400 1,280 0.91 0.7
1,600 1,340 0.84 0.3
1,800 1,240 0.69 –0.5
2,000 1,040 0.52 –1.0
(a) MP is above AP up to Q = 1140, and AP is rising. Stage I.
(b) MP is below AP for Q = 1280 and beyond, and AP is falling. Stage II.
(c) When MP > 0, TP is rising; when MP < 0, TP is falling.
(d) Yes. Even though MP rises initially, the law of diminishing returns merely states that eventually the MP will fall.
10.12
Plant 1 Plant 2
Labor MP TP Labor MP TP
0 — 0 0 — 0
1 10 10 1 14 14
2 8 18 2 12 26
3 6 24 3 10 36
4 4 28 4 8 44
5 2 30 5 6 50
6 0 30 6 4 54
(a) With more modern capital equipment, the MP in Plant 2 is higher at every level of output.
(b) Q = 54 (54,000 lbs. of grain).
(c) Loss = 4,000; gain = 10,000; net increase of 6,000 lbs.
(d) 24,000 lbs. in Plant 1 + 36,000 lbs. in Plant 2 = 60,000 lbs.
(e) Loss = 6,000; gain = 8,000; net increase of 2,000 lbs.
(f) To maximize Q: send 2 workers to Plant 1, and 4 workers to Plant 2. Q = 18,000 + 44,000 = 62,000 lbs. of grain. MPL1 = MPL2 = 8.
10.13
(a) The points are plotted on this graph.
[pic]
(b) MRTS = [0.5(K/L)0.5]/[0.5(L/K)0.5] = K/L.
(c) At L = 10, MRTS = 40/10 = 4; at L = 20, MRTS = 1; at L = 40, MRTS = 0.25. Yes, MRTS diminishes as more L is used.
(d) At A, ∆K/∆L = –4; at B, ∆K/∆L = –1; at C, ∆K/∆L = –1/4.
(e) APL = Q/L = (K/L)0.5. Since APL = 2MPL, APL > MPL. With MPL > 0, this function is in stage II of production everywhere.
10.14
(a) %∆Q = 0.88%∆L + 0.12%∆K.
(b) ηL = 0.88; Q will increase by (0.88)(5) = 4.4%; Q will fall 8.8%.
(c) ηK = 0.12; Q will increase by (0.12)(25) = 3%; Q will fall 1.2%.
(d) Q will increase (0.88)(14) + (0.12)(14) = 14%.
(e) constant returns to scale; one.
(f) L = 100: MPL = 0.88(1) = 0.88; L = 200: MPL = 0.88(0.5)0.12 = 0.81; L = 300: MPL = 0.88(0.33)0.12 = 0.77. K = 50: MPK = 0.12(4)0.88 = 0.41; K = 100: MPK = 0.12(2)0.88 = 0.22; K = 200: MPK = 0.12(1) = 0.12.
(g) Both MPs decrease; diminishing returns is short-run; returns to scale is long-run.
10.15
(a) The marginal product of L decreases for small increases in L holding K constant.
(b) The marginal product of K increases for small increases in K holding L constant.
(c) MRTSLK = MPL/MPK = (3L–1/2K3/2)/9L1/2K1/2 = (1/3)(K3/2K–1/2)/(L1/2L1/2) = K/3L.
(d) Yes.
(e) This technology exhibits increasing returns to scale. You can tell because the sum of the exponents in this Cobb-Douglas type production function is greater than unity.
(f) The law of diminishing marginal productivity.
10.16
(a) V = LWH = (200)(100)(50) = 1 million cubic feet. S = 2LW + 2WH + 2LH = 2(200)(100) + 2(100)(50) + 2(200)(50) = 70,000 square feet of material.
(b) S = 2(400)(200) + 2(200)(100) + 2(400)(100) = 280,000 sq. ft.; increase by a factor of 4.
(c) V = (400)(200)(100) = 8 million cu. ft.; increase by a factor of 8.
(d) They should not necessarily be made as large as possible. As ships get larger, loading and unloading cargo becomes an increasingly difficult and costly process. The geometric advantage of increasing returns to scale must be weighed against these logistical cargo handling problems.
10.17
(a) Q = [0.5(729)1/6 + 0.5(64)1/6]6 = 244.14.
(b) MPL = 0.5(244.14/729)5/6 = 0.201; MPK = 0.5(244.14/64)5/6 = 1.526.
(c) Q = [0.5(800)1/6 + 0.5(64)1/6]6 = 258.18; MPL = 0.5(258.18/729)5/6 = 0.195.
(d) ρ = –1/6, and so σ = 1/(1 – 0.833) = 1.2.
(e) less.
(f) Since K and L are closer substitutes in agriculture, its isoquant is straighter:
[pic]
10.18 In a constant returns to scale industry, there is no optimum plant size. All firms would be able to survive. With increasing returns to scale, large firms would be more likely to survive; with decreasing returns to scale, small firms would have the advantage.
10.19 GA = GX – ηL1GL1 – ηL2GL2 – ηKGK = 4.1 – (0.43)(1.8) – (0.23)(1.5) – (0.37)(1.2) = 1.537%. Possibly yes. Since this input was excluded, the estimate of technical change is probably overstated; part of what is being attributed to technical growth might be an increased use of the energy input.
10.20 The Japanese application of robotics in production is a case of process innovation. The development of robots in the U.S. is a case of product innovation.
10.21 (a) At E, QA = 10 and QB = 10. See graph for the current isoquants.
[pic]
(b) At C, QA = 10 and QB = 10.
(c) At A, QA = 15 and QB = 10.
(d) At B, QA = 10 and QB = 15.
(e) At D, QA = 12.5 and QB = 12.5.
(f) If all inputs are used in the production of A, QA = 25 and QB = 0. If all inputs are used in the production of B, QA = 0 and QB = 25.
(g) See the preceding graph for the efficiency curve.
(h) See the following graph for the PPC.
(i) This PPC is linear. There are two reasons, and both must be present. First, both production functions have constant returns to scale. Second, the input proportions are constant along the efficiency curve.
[pic]
Chapter 11 Solutions
11.1 The economic cost of the chips is $23. If Apple does not use the chips, the price at which they could be sold to other computer companies (the next best alternative use) would be the current market price. Nevertheless, the Apple executive instead based his pricing decision on the original purchase price of $38 per chip. As a result, Apple memory was very expensive. Consumers responded by buying stripped-down models of the Mac with little memory, and adding on memory cards from other companies (who were using the correct, lower cost to determine their prices). As a result of its failure to use economic cost, Apple’s profits fell and they were stuck with millions of unsold chips. Ultimately, the person responsible for this pricing decision was reassigned to a job with less responsibility, though the company denied that this mistake was the reason.
11.2 His analysis is not sound. It ignores the opportunity cost of his family's time — they could be out working and earning wages in other forms of employment.
11.3
(a) Q = 180; Q= 300; Q = 400. (b) No. Any worker after the 7th has zero marginal product; stage III. (c) stage I; stage II. (d) 3 workers/day; 4 workers/day; 5 workers/day. (e) Up through Q = 400, stage I; after Q = 400, stage II.
[pic]
(f) Yes, exactly the same shape. The vertical axis will represent $ and will be scaled-up by a factor of 40.
11.4
Food (lbs.) Fish (lbs.) AP MP TVC AVC MC
400 200 0.50 — $2,400 $12.00 —
600 400 0.67 1.0 3,600 9.00 $6.00
800 700 0.88 1.5 4,800 6.86 4.00
1,000 940 0.94 1.2 6,000 6.38 5.00
1,200 1,140 0.95 1.0 7,200 6.32 6.00
1,400 1,280 0.91 0.7 8,400 6.56 8.57
1,600 1,340 0.84 0.3 9,600 7.16 20.00
(a) Up to Q = 1,140, MC < AVC; AVC is falling; stage I.
(b) After Q = 1,140, MC > AVC; AVC is rising; stage II.
(c) At Q = 400, AVC = 9 = 6/0.67, MC = 6 = 6/1.0. At Q = 700, AVC = 6.86 = 6/0.875; MC = 4 = 6/1.5, etc.
(d)
Fish (lbs.) AVC MC
200 $16.00 —
400 11.94 $8.00
700 9.09 5.33
940 8.51 6.67
1,140 8.42 8.00
1,280 8.79 11.43
1,340 9.52 26.67
(e) At the point where diminishing returns set in, MC begins to rise.
11.5
(a) MC = $9; ATC = $7; AVC = $4; AFC = ATC – AVC = $3.
(b) TC = ATC x Q = $7(9) = $63; VC = AVC x Q = $4(9) = $36; FC = AFC x Q = $3(9) = $27. TC is area ofgh, VC is area oijh, FC is area ifgj.
(c) TC = $7(5) = $35; VC = TC – FC = $35 – 27 = $8; ATC = $7. TC is area ofln; VC is area okmn; FC is area kflm.
(d) At point b.
11.6
(a) 1 quart: TC = (4)($2) + (1)($5) = $13; 2 quarts: TC = (8)($2) + (2)($5) = $26; 3 quarts: TC = (12)($2) + (3)($5) = $39; TC = 13Q.
[pic]
(b) MC is always equal to (4)($2) + (1)($5) = $13/quart. Note: MC = ∆TC/∆Q = $13/1 = $13 using information from part (a).
(c) AC = TC/Q = 13Q/Q = $13; AC coincides with MC.
(d) MC shifts upward; now, MC = (4)($2.50) + (1)($5) = $15/quart.
11.7 Average cost is $10.32. Average cost will fall if total factor productivity increases because there is an inverse relationship between cost and productivity.
11.8
(a) See the following graph; fixed cost = $20.
(b) Up to Q = 200, MC = 180/200 = 0.9; after Q = 200, MC = 100/400 = 0.25.
(c) Up to Q = 200, AVC = 0.9; after Q = 200, AVC gradually declines; for ATC: at Q = 200, ATC = 200/200 = 1.0; at Q = 600, ATC = 300/600 = 0.5.
(d) ATC > MC for all levels of output.
[pic]
11.9
(a) A change in the variable input price would affect all of the cost curves except FC and AFC.
(b) A change in the fixed input price would affect FC, TC, AFC, and ATC.
(c) A unit tax: same effect as part (a).
(d) A fixed tax: same effect as part (b).
(e) A profits tax would not affect any of the cost curves.
11.10
(a) $24/12 = $2; $30/18 = $1.67.
(b) $24(1.1) = $26.40; $26.40/12 = $2.20; increase of $0.20.
(c) $30(1.1) = $33; $33/18 = $1.83; increase of $0.16.
(d) U.S. dollar productivity would have to increase to $1.87, which means that one hour of American labor would have to generate ($1.87)(18) = $33.66 in revenue, an increase of 12.2% in physical productivity.
11.11
(a) w = 5,000/400 = $12.50/hour; pC = 5,000/200 = $25/ton.
(b) 25C + 12.5L = 5,000, or C = 200 – 0.5L.
(c) No, this would cost (100)($25) + (280)($12.50) = $6,000.
(d) See the figure. C = 240 – 0.5L; now they can afford 100 tons of cement and 280 person-hours of labor.
(e) See the figure. If pC = $20/ton, C = 250 – 0.625L; if w = $16, C = 200 – 0.64L.
[pic]
11.12 (a)
[pic]
(b) MRTS = MPP/MPN = 3/4; pP/pN = 24/36 = 2/3.
(c) No. MRTS is not equal to the input price ratio.
(d) Buy 15 more lbs. of phosphate; extra product gained = (15)3 = 45 bushels. Give up 10 lbs. of nitrate; extra product lost = (10)4 = 40 bushels.
(e) More phosphate; less nitrate.
(f) See graph where B is the optimum point.
11.13
(a) MRTSSU = MPS/MPU = U/S.
(b) Returns to scale are constant.
(c) Set R = 200: 20; and set MRS = price ratio: U/S = $250/$10 = 25. S* = 2; U* = 50.
(d) The long-run average cost curve is constant because there are constant returns to scale.
(e) At R = 200, C = $250x2 + $10x50 = $1,000.
11.14
(a) At w = $4 and r = $10, set K/L = 4/10 and set 20LK = 200. Simultaneous solution is L = 5, K = 2.
(b) At w = $2 and r = $10, set K/L = 2/10 and set 20LK = 200. Solution is L = 5, K = .
(c) The quantity of labor demanded increased, and the quantity of capital demanded decreased.
11.15
(a) No effect. He minimizes costs at A, which he can still reach.
(b) Yes, it will have an impact. To minimize the cost of producing 20,000, he should use B. He is forced to use D, which is associated with a higher isocost line.
(c) Bundle B, Cost = 200($5,000) = $1,000,000; bundle D, Cost = 250($5,000) = $1,250,000.
(d) Higher by $250,000.
(e) For Q = 8,000, TC = 199($5,000) = $500,000. For Q = 24,000, TC = 250($5,000) = $1,250,000.
[pic]
(f) Between A and B, economies of scale; between B and C, diseconomies of scale.
11.16 In the long run, a firm can follow its expansion path, on which it minimizes costs. In the short run, the firm is often off its expansion path, where costs are higher.
11.17
(a) Increasing returns to scale. The exponents sum to more than one.
(b)
[pic]
(c) Few firms, since LAC continually declines.
11.18 (a) SAC = SMC at point a. (b) SMC = LMC at point b. (c) SAC = LAC at point b. (d) LMC is always above LAC; therefore, LAC is always rising.
[pic]
11.19
(a) LMC = LAC/DSE = $25/1.67 = $15; increasing scale economies.
(b) DSE = LAC/LMC = $30/36 = $0.83; decreasing scale economies.
(c)
[pic]
(d) At p = $20, Q = 480 – 4(20) = 400. The MES is q = 100; four identical-sized firms can satisfy the market demand.
(e) fall, to $7.50; all 4 firms cannot survive, since p < LAC.
(f) At p = $25, Q = 370 – 4(25) = 270. The MES is q = 90; three identical-sized firms can satisfy the market demand.
11.20
(a) Cα = $66. (b) Cβ = $38. (c) Cα + Cβ = $104. (d) Cα+β = $62.
(e) S = 0.677 or 67.7%.
(f) S measures the percentage reduction in cost as a result of jointly producing the goods at their current levels rather than producing them separately.
11.21 Scale effects describe how cost changes as the firm moves along its expansion path, minimizing long-run cost. Economies of scale occur when AC falls as the scale of plant increases. In a decreasing cost industry, each firm's cost curves fall as industry production expands.
11.22
(a) More labor; less capital. In agriculture, K/L will rise by σ times %∆(w/r) = (1.2)(10) = 12%. In apparel, K/L will fall by (0.42)(10) = 4.2%.
(b) Less labor; more capital. In agriculture, K/L will fall by (1.2)(5) = 6%. In apparel, K/L will rise by (0.42)(5) = 2.1%.
11.23 (a) AC = 3 – 2Q + 3Q2. (b) Set AC = MC yielding Q = 1/3. (c) FC = 0. (d) No, because there is no fixed cost. (e) AC = 3 – 2(1/4) + 3(1/4)2 = 2.6875; MC = 3 – 4(1/4) + 9(1/4)2 = 2.5625. Since AC > MC, this corresponds to stage I of production.
11.24 (a) The estimated returns to scale parameter is [pic] = 1/[pic]q = 1/0.8214 = 1.2174 > 1, and so the estimated returns to scale is increasing.
(b) The returns to scale parameter is significantly different from 1 because [pic]q is significantly different from 1. That can be seen by calculating its standard error as 0.8214/61.003 = 0.013, and so (0.8214 – 1)/0.013 = –13.7.34, which is much greater than 2 in absolute value.
11.25 (a)
[pic]
(b) See previous figure. Process B will be chosen, resulting in a total cost of C = $10,000.
(c) See the following figure. When the price of machine units increases to $40 per hour, Process A will be chosen, resulting in a total cost of C = $18,000.
[pic]
(d) See the following figure. Under the new production technology and the new prices, Process B will be chosen, resulting in a total cost of C = $10,000.
[pic]
Chapter 12 Solutions
12.1
(a) TR = $200; TR = $400; TR = $600.
(b) MR = $20.
(c) p = TR/q = $200/10 = $20; for a competitive firm, MR and price are the same.
(d) π = 0 where TR = TC; at q = 20 and q = 40.
(e) At q = 30, MR = MC and π hits its maximum level of $600 – 500 = $100.
(f) At q = 10, MR = MC and π hits its lowest level of $200 – 300 = –$100.
(g)
[pic]
12.2
[pic]
(a) q* = 9; TR = $9(9) = $81; TC = $7(9) = $63; π = TR – TC = $18; profit is shaded area on graph.
(b) q* = 8; TR = $6(8) = $48; TC = $6(8) = $48; π = TR – TC = $0.
(c) q* = 7; TR = $3(7) = $21; TC = $6.4(7) = $44.8; π = TR – TC = –$23.80. Yes. p > AVC (or TR > TVC). If firm shuts down, they will lose fixed costs of $27.
(d) Below minimum of AVC, which is about $1.50.
(e) Supply curve coincides with dark part of the MC curve.
12.3
(a) Qs = 1,000qs = –100,000 + 50,000p.
(b) Set Qd = Qs: 140,000 – 10,000p = –100,000 + 50,000p. p* = $4; Q* = 140,000 – 10,000(4) = 100,000 plants. q* = 100,000/1,000 = 100 plants.
(c) η = 10,000 (4/100,000) = 0.4; inelastic.
(d) 200 = 40,100 – 10,000P, p* = $3.99; little impact.
(e) η = 10,000(4/100) = 400; almost perfectly elastic.
12.4 You should not agree. Their TR of $110,000 is insufficient to cover their variable costs, which is the correct way to analyze the situation. If the firm shuts down in the short-run, they’ll lose only the fixed cost of $80,000.
12.5
(a) Set p = MC: q2 – 12q + 32 = 12, q* = 10. π = pq – TC = ($12)(10) – [(1/3)(1,000) – 6(100) + 32(10) + 45] = $21.67.
(b) FC = $45, so TVC = TC – 45 = (1/3)q3 – 6q2 + 32q; AVC = TC/q = (1/3)q2 – 6q + 32.
(c) AVC = MC; q2 – 12q + 32 = (1/3)q2 – 6q + 32, q* = 9.
(d) Shut down price = min. AVC = (1/3)(81) – 6(9) + 32 = $5.
12.6
(a) Set p = MC to get q(p) = 0.5p .
(b) Q = Q(p) = Σq(p) over the 800 firms, and so Q(p) = 400p.
(c) At $8 a ton, Q* = 3,200 tons. Miller produces q* = Q*/800 = 4 tons.
12.7 For a competitive firm, short-run profits are maximized where p = MC. Actually, we’re using the following type of marginal reasoning: “produce more so long as MR (price) > MC, and p > AVC.” For kisses: q = 300 and p = MC (both are $4.50), but as you produce more, p > MC. It pays to keep producing, all the way out to Q = 600. There, losses are minimized at $50. (Note: Shutting down, you’d lose FC of $150. Also, when q = 600, p > AVC [AVC = $2600/600, or $4.33].) For jellybeans: p = MC (both are $7.50) at two places, q = 20 and q= 50. When this happens, the higher output, where MC is rising, is always the better of the two. Here, however, at q = 50, p < AVC (AVC = $410/50 = $8.2). By producing 50, the firm loses $135. By shutting down, they lose only FC, which are $100.
12.8
(a) Since $1 worth of wax is used for each candle (1/2 lb. x $2/lb), MCT = 0.02q + 1.
(b) Set p = $6 = MC: 6 = 0.02q + 1, q* = 250 candles/day. TR = $6(250) = $1500.
(c) TVCL = 0.01q2, and wax costs (125)($2) = $250, thus TC = 0.01q2 + 600. At q = 250, TC = $1225, and π = $1500 – 1225 = $275.
(d) Each candle now requires (1/2 lb. x $3/lb) = $1.50 worth of wax, so MCT = 0.02q + 1.5; set p = MC: 6 = 0.02q + 1.5, q* = 225 candles/day.
(e) MC rises; q falls.
12.9
(a) VMP = (10/)10 = 100/.
(b) 100/= 4, = 25, so L* = 625 workers/hour. They produce q = 500 bushels/hour.
(c) 10 = q/50, q* = 500 bushels/hour.
(d) L = q2/400 = (500)2/400, L* = 625 workers/hour.
(e) Yes, the answers match. By using either the output market or the input market, it is possible to determine how much output should be produced and how much labor should be used. This symmetry applies to the use of any input.
12.10 (a)
Amount of Amount of
Food (lbs.) Fish (lbs.) MP VMP TVC MC
400 200 — — $2,400 —
600 400 1.0 20 3,600 $6.00
800 700 1.5 30 4,800 4.00
1,000 940 1.2 24 6,000 5.00
1,200 1,140 1.0 20 7,200 6.00
1,400 1,280 0.7 14 8,400 8.57
1,600 1,340 0.3 6 9,600 20.00
(b) Set VMP = w: produce 1,340 fish, using 1,600 lbs. of food.
(c) π = TR – TC = ($20)(1340) – ($9,600 + 10,000) = $7,200.
(d) p and MC are both equal to $20 at Q = 1,340.
12.11
(a) p = min. LAC = $4/bushel. Qd = 2,800,000 – 100,000(4) = 2,400,000 bushels.
(b) Number of farms = 2,400,000/1,000 = 2,400.
(c) Set Qd = Qs: Qs = 2,400,000 = 3,000,000 – 100,000p, p* = $6/bushel. π = (p – AC)Q = ($6 – 4)(1,000) = $2,000.
(d) Again p = min. LAC = $4; Qd = 3,000,000 – 100,000(4) = 2,600,000 bushels. Now there are 2,600 farms.
(e) enter; equal to.
(f) LRS is a horizontal line at p = $4; constant cost industry.
12.12 (a)
T-shirts Total Cost MC
0 $90 —
10 120 3.0
20 135 1.5
30 153 1.8
40 177 2.4
50 210 3.3
60 252 4.2
70 306 5.4
80 375 6.9
90 462 8.7
100 570 10.8
(b) qs* = 90, where p = MC; Qs* = 100(90) = 9,000.
(c) No. At p = $8.70, total demand = 5,000. There is an excess supply of 4,000.
(d) At p = $5.40, Qd = Qs = 7,000.
(e) Yes; π = ($5.40)(70) – $306 = $72.
12.13
(a) He won’t respond. A fixed fee doesn’t change his profit-maximizing output level, and with the fee set at $200/day, he still makes an economic π of $75/day, so he won’t exit the industry.
(b) Yes, he will modify his level of production. Now, MCT = (0.02q + 1) + tax, so MCT = 0.02q + 2. Set p = MCT: 6 = 0.02q + 2, q* = 200 candles/day.
12.14
(a) q = 400. The firm is making a profit of $2,000.
(b) q = 800.
(c) The long-run equilibrium price will be p = $8. At this price, the profit maximizing level of output for HBG is q = 500, the optimal scale is AC2, and profit is $0.
(d) Its profits would become negative.
(e) HBG should choose AC2 because if it doesn’t it will suffer a loss. Market price will eventually fall below HBG’s average costs at any other scale as competitors expand and as entry takes place.
(f) Long-run equilibrium price will increase. Entry and exit and long-run changes in scale will force economic profits to zero.
12.15
(a) For this Cobb-Douglas function, MRTS = K/L. Since w/r = 2/2 = 1, firms will use the same amounts of K and L, a one-to-one ratio.
(b) TC = 2L + 2K = 4L; AC = 4L/Q = 4L/= 4L/= $4; MC = $4.
(c) MC = p = $4, so Q* = 600,000 – 50,000(4) = 400,000 bricks; q* = 400,000/1,000 = 400 bricks/firm.
(d) q = 400 = = L, so 400 workers are hired per firm, and 400,000 by the industry.
(e) K/L = w/r = 3/2, so K = 1.5L; TC = 3L + 2K = 3L + 3L = 6L; AC = 6L/Q = 6L/= 6/= $4.90; MC = $4.90.
(f) p = AC = $4.90; Q* = 600,000 – 50,000(4.9) = 355,000 bricks; each firm produces 355 bricks; q = L, so L* = 355/(1.5)1/2 = 290 workers, or about 290,000 workers for the whole industry.
(g) L* = 400,000/= 327,000 workers; 400,000 – 327,000 = 73,000; substitution; 37,000; expenditure.
12.16 Since this is a decreasing cost industry, LRS would have a negative slope.
12.17
(a) Equilibrium p and Q rise in both industries; see p2 and Q2 on the following figures.
[pic]
(b) profits; entry.
(c) Industry A: up, above. Industry B: down, below.
(d) See preceding figures.
(e) upward-sloping; downward-sloping.
12.18
(a) MRS = C/l. (b) MPL = 4/. (c) Set C = 8= C = 8. That and C/l= 4/= 4/yields l* = 16. (d) L* = 24 – l* = 8. (e) C* = 8= 22.6274. (f) See graph.
[pic]
12.19 The result is remarkable and, yes, profound because it says that a market economy can achieve any desired position along its production possibilities curve by redistributing income and wealth. Thus, economic efficiency need not be sacrificed by transferring income and wealth from rich people to poor people. Market efficiency is not incompatible with welfare programs.
12.20 (a) π = $50L + $30S.
(b) The resource constraints are: 20L + 10S ≤ 1,000; 4L + 7S ≤ 400.
(c)
[pic]
(d) See graph. L* = 30, S* = 40, and π* = $2,700.
Chapter 13 Solutions
13.1
(a) The profit maximizing level of output is Q* = 20.
(b) The profit maximizing price is p* = $6.
(c) The unit cost when this firm is maximizing profit is AC* = $4.
(d) The maximum level of profit is π* = (p* – AC*)Q* = $40.
13.2
[pic]
(a) Set MR = MC. 100 – Q = 20; Q* = 80,000 flags.
(b) p* = $100 – 0.5(80) = $60.
(c) π is area abde on graph, which = ($60 – $20)(80,000) = $3.2 million.
(d) η = 2(60/80) = 1.5
(e) $60 = $20/(1 – 1/1.5).
(f) If demand is inelastic, marginal revenue is negative.
(g) CS is area bcd on graph, CS = 0.5($100 – 60)(80,000) = $1.6 million.
13.3
(a) Set p = MC: 100 – 0.5Q = 20; Q* = 160,000 flags.
(b) higher; lower.
(c) CS is area acf, which is 0.5($100 – 20)(160,000) = $6.4 million.
(d) 80,001st: MB = 100 – 0.5(80.001) = $59.99; MC = $20. Yes, MB > MC. For 100,000th, MB = $50 > $20.
(e) Welfare loss is area def, which = 0.5($60 – 20)(80,000) = $1.6 million. ∆CS = $6.4 – 1.6 = $4.8 million, which = $3.2 million + $1.6 million.
(f) TR = $60(80,000) = $4.8 million; 33% of sales; 3.3% (this number is actually well within the range estimated by empirical studies for the U.S. economy).
(g) Yes. They should be willing to pay up to the level of their economic profits, $3.2 million (unless the company can earn above-normal profits in some other enterprise).
13.4
(a) Set MC = MR = (1 – 1/η): For vacationers, 30 = p(1 – 1/2); p* = $60. For business travelers, 30 = p(1 – 1/1.2); p* = $180.
(b) inelastic — higher price; elastic — lower price.
13.5 A supply curve is a function matching various market prices and the corresponding quantities a producer will bring to the market. For the monopolist, there is no one curve that does this. Optimal Q is determined by a comparison of MR and MC; once Q* is found, the monopolist charges the highest price at which that Q can be sold, which is determined by the demand curve.
13.6 (a)
p ($/bottle) Q (bottles) TR MR
$55 750 $41,250 —
50 1,000 50,000 $35
45 1,250 56,250 25
40 1,500 60,000 15
35 1,750 61,250 5
30 2,000 60,000 –5
25 2,250 56,250 –15
(b) p* = $40, where MR = MC; Q* = 1,500 bottles.
(c) TVC = $15(1,500) = $22,500; TC = $22,500 + 20,000 = $42,500. π = $60,000 – 42,500 = $17,500.
(d) If fee = $10,000, no. They still maximize π at same p, Q point, but now π is down to $7,500. If fee = $20,000, they will go out of business in the long run, since no profits can be earned.
(e) Yes. Now, MC = $25. To maximize π, charge p* = $45, sell 1,250 bottles.
(f) lump-sum fee; excise tax.
13.7
[pic]
13.8 Research has shown, for example, that the average price of eyeglasses in states that barred advertising was more than double the average price in states where advertising was allowed (Lee Benham, “The Effect of Advertising on the Price of Eyeglasses,” The Journal of Law and Economics 15, October, 1972). Advertising, by providing information on prices and quality, makes the demands for the products of the separate suppliers more elastic and, thus, lowers price. This type of advertising fosters price and quality competition. Similar results have occurred for generic drugs. You can probably think of many other examples.
Advertising can also lead to reductions in production costs due to economies of scale made possible by increased demand. This seems to have been the result in the beer industry and the cigarette industry. Reduced costs can be passed along to the consumers in the form of lower prices.
13.9
[pic]
(a) Pharaoh’s demand: QL = QT – QF = (100 – p) – (2/3)p = 100 – (5/3)p.
(b) p = 60 – 0.6QL; MR = 60 – 1.2QL.
(c) Set MRL = MCL: 60 – 1.2QL = 1.2QL; QL = 25 million; p* = $45.
(d) QT = 100 – 45 = 55 million; QF = 45/1.5 = 30 million.
(e) If the competitive fringe firms are earning economic profits, new firms will enter the plumbing market. Unless this entry is limited, the dominant firm’s share of the market and its profits will decline.
(f) The deadweight loss in the competitive fringe is (70 – 45)(40 – 30)/2 = 125. The deadweight loss in the dominant firm sector is (45 – 30)(33.33 – 25)/2 = 62.5. Thus the total deadweight loss is $187.5. The reason that there are deadweight losses from each sector is that if the dominant firm were to behave competitively, its “supply curve” (MCL–1) would be added to SF to get a total market supply curve.
13.10
(a) Furniture, LI = 1/1.26 = 0.794, or 79.4%; coal, LI = 3.125, or 312.5%; movies, LI = 0.27, or 27%; metals, LI = 0.658, or 65.8%; transportation, LI = 1.0, or 100%.
(b) LI = 0.0001, or 0.01%. Yes; wheat farmer is a price taker with no power to raise price. In such a market, p = MC so that there is virtually no markup.
13.11
(a) Tobacco, η = 1/2 = 0.5; jewelry, η = 1/2.5 = 0.4; new cars, η = 1/0.833 = 1.2.
(b) Yes. If a market is contestable, firms will not establish a short-run profit-maximizing price. Instead, price will be somewhat lower. The implication, given these markups, would be that demand is less elastic than calculated.
13.12
(a) Aluminum foil does not seem to be a substitute; wax paper and (especially) polyethylene do appear to be substitutes.
(b) In the second case, all three cross-price elasticities are very close to zero, indicating that these products are probably not substitutes for DuPont’s cellophane. (Note: In 1953, the Supreme Court actually did accept DuPont’s argument that cellophane had many substitutes.)
13.13 (a) 4-firm ratio = 0.67, or 67%. (b) Herfindahl index = 0.143. (c) ∆(4-firm ratio) = 0.06; ∆H = 0.018. (d) ∆(4-firm ratio) = 0.10; ∆H = 0.072. (e) Herfindahl index is more sensitive.
13.14 Yes, there are characteristics of a contestable market in this case. Hit-and-run entry is entirely feasible because other air carriers can switch service into Redding overnight if it were profitable to do so. The start-up costs are minuscule because they use the city airport, and so few added facilities would be required. Thus, American Eagle is forced to keep its price low enough to discourage such entry. Their fares are probably not much greater than that sufficient to cover their opportunity costs. As an illustration of how expensive it can be to service such a town, the last time one of the authors of this study guide flew into Redding from San Francisco, he was the only passenger on the turbo-prop.
13.15
(a) 100 – Q = 4Q; Q* = 20, or 20,000 clams; p* = $90.
(b) Since 20 = , L* = 80 workers.
(c) MR = 100 – .
(d) MRP = [100 – ][5/2] = (250/) – 2.5
(e) L* = 80 workers; Q* = = 20, or 20,000 clams.
(f) Yes, the answers match. By using either the product market or the labor market, it is possible to determine how much output should be produced and how much labor should be hired. This symmetry applies to the use of any input.
13.16
(a) The perceived isocost lines are flatter resulting a new expansion path:
[pic]
(b) Actual prices, however, have not changed, and so the real slope of the isocost lines is the same as before. Therefore, the firm’s input mix is biased toward using too much labor and too little capital. Q1 now costs C1*, more than C1; similarly for Q2 and Q3.
(c) The AJ effect has firms using more K when K is “subsidized.” Here, firms will use more L when L is “subsidized.” In both cases the cost of producing any given level of output is higher than before thereby shifting average and marginal costs upward. Employment effects are unclear. At any product price, output will be lower, and the higher costs will put pressure on product prices to rise, pushing output levels even lower. It is possible for this economy to have even lower levels of employment than before as it moves to an even less efficient position within its production possibilities set.
13.17
(a) w = $10; wage bill = $5000.
(b) w = $12; wage bill = $7200.
(c) MFC = $22; MFC = 11 + 550(2/100) = 22.
(d) Set VMP = MFC: 42 – 0.02L = 0.04L; L* = 700.
(e) VMP = 42 – 0.02(700) = $28. For wage, use supply: w = 700/50 = $14.
(f) ηs = 1. MI = 1 = (28 – 14)/14.
(g) L* = 1000; L* = 850; L* = 600.
(h) In the case of monopsony, minimum wage can increase or decrease the amount of unemployment.
13.18
(a) Firm A has monopoly power, and firm B has monopsony power.
(b) Firm A prefers price p2 and wants to sell Q2 to B.
(c) Firm B prefers to buy at price p1 and A wants to buy Q1 units from A. Firm B prefers to sell at price p2.
(d) If A prevails, A’s profits will be equal to area abcd = $100, and B’s profits are zero
(e) If B prevails, A’s profits will be equal to zero, and B’s will be equal to area abfe = $200.
(f) The solution is indeterminate because the firms have contrary objectives.
(g) If they merge, total profit will be equal to $200. If A buys B it can double its potential maximum profit to $200. If B buys A it can force A to charge a transfer price that enables B to achieve its maximum profit potential of $200. In either case the profit can then be divided between the wholesale and retail operations. Which firm gains or loses depends on the bargained price, but collectively they must be better off under a merger unless B completely dominated the outcome.
(h) When there are many other competitors in the final market, firms A and B will sell at that competitive price and both earn zero economic profits.
(i) Sears or other big discounting stores are examples.
13.19
(a) Yes, there is vertical integration because TCI not only develops programming but it also owns the local cable networks. Competition is thwarted among firms trying to sell to the cable franchises, and market entry is more difficult at either end of the distribution system.
(b) Yes, there is horizontal integration because TCI owns much of the programming development as well as most of the delivery system at the retail level. Market concentration is increased at both ends, and the firm gains market power at both ends. Fewer substitutes means that its demand curve will be less elastic.
(c) Yes, the fact that TCI affiliates can charge monthly rates for added hook-ups is a departure from marginal cost pricing because the marginal cost after the initial hook-up is virtually zero.
(d) The industry appears to be one of a dominant firm and a competitive fringe rather than an oligopoly.
(e) Lawsuits against governments attempting to start their own cable service do not result in more or better cable service, they merely transfer rents to lawyers and lobbyists.
(f) Yes, the fact that TCI spends considerable money trying to thwart potential entrants, government-owned services, and the development of competition by the phone company is evidence of rent seeking.
(g) Economic theory suggests that a monopolist would be willing to spend all of its revenues in excess of its opportunity cost in rent seeking. After all, economic profits are defined as revenues above opportunity cost, and so the monopolist can’t do any better anywhere else. Thus, TCI may be willing to spend all but the last 1¢ of its profits on rent seeking.
Chapter 14 Solutions
14.1
(a) QC = 50 – 2(30) + 30 = 20; QP = 20. πC = πP = (30 – 10)(20,000) = 400,000 baubles. Industry π = 800,000.
(b) QC = 50 – 2(29) + 30 = 22; πC = (29 – 10)(22,000) = 418,000. QP = 50 + 29 – 2(30) = 19; πP = (30 – 10)(19,000) = 380,000.
(c) QP = 50 + 29 – 2(28) = 23; πP = (28 – 10)(23,000) = 414,000.
(d) p = 10; QC = QP = 50 – 2(10 + 10 = 40; π = zero (p = MC = AC).
(e) QP = 50 – 2(12) + 10 = 36; πP = (12 – 10)(36,000) = 72,000.
(f) QC = 50 + 12 – 2(14) = 34; πC = (14 – 10)(34,000) = 136,000.
14.2
(a) Its demand curve will be kinked, and so this firm must believe that its demand curve is elastic above the current price (at the kink) and inelastic below that price.
[pic]
(b) Current price must be p = $100, and current output must be q = 100.
(c) MR = 200 – 2q for q ≤ 100; MR = 500 – 8q for q ≥ 100.
(d) Marginal cost is the slope of the TC curve, and so MC = $50.
(e) MC is constant, and so AC = MC. Thus unit profit is p – AC = 100 – 50 = $50, and so total profit is (p – AC)q = $5,000. This firm can do better because MR ≠ MC at the current price and output.
(f) The firm should set price and output so that MR = MC. Thus, p* = $125 and q* = 75 units.
(g) π* = (p* – AC)q* = 75 x 75 = $5,625.
14.3
(a) Pharoah’s share = 25/55 = 45.5%; CS = 0.5(100 – 45)(55) = $1,512.5 mil.
(b) Set new MCL = MRL: 0.8QL = 60 – 1.2QL, QL = 30; p = 60 – 0.6(30) = $42. QF = 28.
[pic]
(c) Leader’s market share increases. Pharoah’s share = 30/58 = 51.7%
(d) CS increases by (3)(55) + 0.5(3)(3) = $169.5 million.
14.4
(a) Check the position of DL relative to DT. At any price, DL is one-half of DT. For example, at p*, QL* = Qd/2.
(b) See graph. Produce up to where MR = MC. Price = p*; Quantity = QL*; Profits = shaded area.
[pic]
(c) Price = p*; Quantity = Qd/2; profits = shaded area.
(d) No. Follower can maximize π by producing Q associated with point where MRF = MCF.
(e) Yes. Leader merely has to set p below the minimum of follower’s AC. Leader may not want to eliminate follower. The presence of a second firm may prevent antitrust action from being taken against the leader.
14.5
(a) RC = 15qC – (1/2)qC2 – (1/2)qCqS; RS = 15qS – (1/2)qS2 – (1/2)qCqS. The marginal revenues are : MRC = 15 – qC – (1/2)qS; MRS = 15 – qS – (1/2)qC.
(b) For Cournot Sanders: qC = 9 – (1/2)qS. For Stackle Burgers: qS = 9 – (1/2)qC.
(c) Q* = 6; p* = $9; πc = πS = (9 – 6)(6) = $18; πT = $36.
(d) If QC = 7, p = 15 – (1/2)(13) = $8.50, πC = (8.50 – 6)(7) = $17.50. If QC = 5, p = 15 – (1/2)(11) = $9.50, πC = (9.50 – 6)(5) = $17.50
(e) lower; does.
(f) Set MR = MC: 15 – Q = 6, Q* = 9. Each firm produces 4.5; p* = 15 – (1/2)(9) = $10.50; πT = (10.50 – 6)(9) = $40.50. Each firm’s profits = $20.25.
(g) p = 15 – (1/2)(10) = $10; π = (10 – 6)(5.5) = $22; does; is not.
14.6
(a) TRC = 50pC – 2pC2 + pCpP; TRP = 50pP – 2pP2 + pCpP.
(b) MRC = 50 – 4pC + pP; MRP = 50 – 4pP + pC.
(c) For Cokesky: pC = 10 + (1/4)pP; for Pepsky: pP = 10 + (1/4)pC
(d) pC = pP = 13.33 baubles; QC = QP = 36.67
(e) For each firm, π = (13.33 – 10)(36.67) = 122.22 thousand baubles. These profits are lower than those earned when the firms act as a monopolist.
(f) QC = 50 – 2(14.67) + 13.33 = 34; π = (14.67 – 10)(34) = 158.78 thousand baubles. The firm can increase its profits by raising price. This is not a Nash equilibrium.
14.7
(a) Since QA = 3MCA and QB = 5MCB, QT = 8MCT, or MCT = (1/8)QT.
[pic]
(b) MR = 30 – (1/4)Q.
(c) Set MR = MC: (1/8)Q = 30 – (1/4)Q; Q* = 80, p* = $20; MR = $10.
(d) QA = 30, QB = 50.
(e) πA = (20 – 6)(30) = $420; πB = (20 – 12)(50) = $400.
(f) Yes. Firm B has the larger market share (62.5% vs. 37.5%) yet earns less π.
14.8
(a) For BAD-TV, S1 is a dominant strategy; for PU-Vision, S3 is dominant.
(b) BAD-TV gains 4 market share points.
(c) Neither would change. This is a Nash equilibrium.
14.9
(a) Neither station has a dominant strategy.
(b) Lose 4; lose 3; gain 1.
(c) Lose 4; lose 1; lose 6.
(d) BAD chooses S3; PU choose S2.
(e) Yes, the game has a saddle point, since maximin = minimax.
(f) Yes. Neither firm can gain by changing its strategy, given its opponent’s choice.
14.10
(a) BAD-TV chooses S3; PU-Vision chooses S1.
(b) No saddle point; the minimax is not equal to the maximin (BAD losing 2 points is not equal to PU losing 2 points).
(c) S2; S1; S1; S3. No saddle point.
(d) Yes. We can eliminate S2 for BAD (dominated by S1) and S3 for PU (dominated by S2).
(e) When PU selects S1, BAD’s EV1 = –3P1 – 2(1 – P1). When PU selects S2, BAD’s EV2 = 4P1 – 2(1 – P1). When BAD selects S1, PU’s EV1 = –3Q1 + 4(1 – Q1). When BAD selects S3, PU’s EV3 = 2Q1 – 2(1 – Q1).
(f) For BAD: –3P1 – 2(1 – P1) = 4P1 – 2(1 – P1). P1 = 4/11. For PU: –3Q1 + 4(1 – Q1) = 2Q1 – 2(1 – Q1). Q1 = 6/11.
(g) BAD will choose S1 4/11 of the time and S3 7/11 of the time. PU will choose S1 6/11 of the time and S2 5/11 of the time. The expected payoffs for each station are: BAD: –3(4/11) + 2(7/11) = 2/11; PU: –3(6/11) + 4(5/11) = 2/11.
14.11 (a)
Iceler
No increase Increase by $50 million
No increase πF = $200 million πF = $110 million
Fjord πI = $200 million πI = $240 million
Motor
Company Increase by πF = $240 million πF = $150 million
$50 million πI = $110 million πI = $150 million
(b) Both firms have a dominant strategy to increase advertising expenditures.
(c) Joint profits = 150 + 150 = $300 million.
(d) If each maintains its current level of advertising, joint π = $400 million.
(e) Each firm is afraid to keep advertising at its current level, since the other firm could then capture $90 million of its market.
(f) They should agree to maintain current levels of advertising. Since each is afraid to do so, they will probably both increase advertising expenditures, lowering their joint profits by $100 million. Over-advertising has taken place in the industry.
14.12
(a) Yes, this scenario is realistic. This is because when both run different lead stories some people will buy both newspapers, but when each runs the same lead story some of those same potential customers buy only one newspaper.
(b) This is not a zero-sum game. This is because the gains to one newspaper do not equal the losses to the other.
(c) Yes, the Star has a dominant strategy — lead the rape story — because the Star has higher sales no matter what the Enquirer does.
(d) No, the Enquirer does not have a dominant strategy because its best choice is not independent of the Star’s strategy. If the Star leads the rape story, the Enquirer will do better by leading the chief-of-staff story, but if the Star leads the chief-of-staff story, the Enquirer will do better by leading the rape story.
(e) If the payoffs to the Star are known by the Enquirer , it can identify the Star’s dominant strategy, and so the Enquirer can figure out what the Star will do. Even though the Enquirer does not have a dominant strategy, the Star can anticipate the Enquirer’s choice because the Star can assume the Enquirer knows the Star’s dominant strategy, and so the Enquirer will choose to lead the chief-of-staff story.
The Enquirer’s choice matters to the Star only because sales will be affected — its choice of strategy will not. The Star will choose the rape story regardless because that is its dominant strategy. Because the Enquirer will anticipate this and lead the chief-of-staff story, the solution to this game is (7.0, 3.0) — the Star sells 7 million copies and the Enquirer sells 3 million.
(f) No, collusion is not likely in this case because combined sales cannot be made larger — this is not a prisoners’ dilemma game. However, if production costs differ between the papers, a different solution might generate greater combined profits. Under such circumstances, collusion and profit sharing might make both papers better off. But that is a different game.
14.13 (a) The sequence is P, P, P, P, P, P, . . . . . There is peace forever.
(b) The sequence would have been war forever.
(c) As soon as a warlike move is made by one family, the other retaliates. There will be war until they call a truce or until a peaceful move is made by one family.
(d) When the truce is called on round 9, there will be peace until a warlike move is perceived.
(e) Any misperception will cause a switch from one state to the other, and there will be periods of peace followed by periods of war.
(f) These families will be at war half of the time. No, it does not matter what the odds are of making a mistake. No matter what the odds, 50 percent of the time there will be war, and 50 percent of the time there will be peace. The length of the sequences between switches will be longer if the odds of making a mistake are small, but that doesn’t change the fact that there will be war 50 percent of the time.
(g) You should always start out with a peaceful move to foster cooperation. You should not rush to judgment if you perceive a warlike move because you might be wrong. If your opponent continues making warlike moves, say, for two or three times out of five, then revert to tit-for-tat. If your opponent makes several warlike moves over any long period, say twenty moves, revert to tit-for-tat. If your opponent reverts to peaceful moves after a long period of war, revert to tit-for-tat but put him on probation — revert to tit-for-tat quickly when your opponent has not earned your trust. Of course, none of this will work if you can kill your opponent on any move because you’ll never get to play tit to your opponent’s tat.
(h) Sequential gaming can yield important insights for the business environment too, especially in this world of international economic and business rivalry. Trade policy has been described as having “strategic” elements. We have learned that trade is mutually beneficial in a competitive environment, but when there are market imperfections it may be stupid for one country to continue to try to foster cooperation when the other does not. You may have to punish your rival to force cooperation. Before doing that, however, you should carefully weigh the long-run costs and benefits.
Chapter 15 Solutions
15.1
(a) p = 5(1 + .25) = $6.25.
(b) m = (19.5 – 15)/15 = 0.3, or 30 percent.
(c) ATC = 23/1.15 = $20.
15.2
(a)
Industry Elasticity Markup
Gasoline η = 1.5 m = 2, or 200%
Tobacco η = 1.9 m = 1.11, or 111%
New cars η = 2.4 m = 0.714, or 71.4%
(b)
Industry Price markup Elasticity
Residential natural gas m = 0.909, or 90.9% η = 2.1
Rail travel m = 0.454, or 45.4% η = 3.2
Shoes m = 5.00, or 500% η = 1.2
15.3 This price changing strategy by retailers seems to be consistent with the idea that price markups are set with profit-maximization goals in mind. Markups are higher on goods that are in demand (which probably have less elastic demands than goods which are not in demand).
15.4
(a) Set MR = 0: 100 – 4Q = 0, Q = 25; p = 100 – 2(25) = 50 francs. Qd = 25. Royalties = 0.25(50)(25,000) = 312,500 francs. Publisher’s π = (50 – 30)(25,000) – 312,500 = 187,500 francs. Royalties + publisher’s π = 500,000 francs.
(b) Regular MR = 100 – 4Q, and so MRn = (1 – 0.25)(100 – 4Q) = 75 – 3Q.
(c) Set MRn = MC: 75 – 3Q = 30, Q* = 15,000. p* = 100 – 2(15) = 70 francs. π = (70 – 30)(15,000) – 0.25(70)(15,000) = 337,500 francs. Royalties = 0.25(70)(15,000) = 262,500 francs. Royalties + publisher’s π = 600,000 francs.
(d) Set MR = MC: 100 – 4Q = 30, Q* = 17,500; p* = 100 – 2(17.5) = 65 francs. TR = (65)(17,500) = 1,137,500 francs. π = TR – (30)(17,500) = 612,500 francs.
(e) As one example, if royalty rate = 23.5%, royalty = 267,312.50 francs and π = 345,187.50 francs. Both benefit if royalty rate is between 23.08% and 24.18%.
15.5
(a) Set MR = 100 – 2Q = 20: Q1 = 40 and p1 = $60. See the following figure: π is area abde, which = $1600. CS is area bcd, which = $800.
(b) At p = $60, Q2 = 0; at p = $40, Q2 = 20; at p = $20, Q2 = 40. See graph.
(c) Set MR = 60 – 2Q = 20: Q2 = 20 and p2 = $40. π is area fgjk, which = $400. CS is area ghj, which = $200.
(d) At p = $40, Q = 60. π = 20(60) = $1200; CS = 0.5(60)2 = $1800.
(e) π has increased by $800. CS decreases by $800.
[pic]
15.6 See the following figure:
[pic]
(a) p = 11 – Q; when p = $4, Qd = 7,000. See graph.
(b) When p = $6, Qd = 6,000. p = 12 – Q. See graph.
(c) Snob demand: p = 18 – 2Q.
(d) steeper; less elastic.
(e) It probably operates only in limited instances. Otherwise, demand would not be downward sloping. All empirical evidence substantiates the downward sloping demand.
(f) Tastes must be changing as price changes, and so price enters into some consumers’ utility functions. This doesn’t seem very “rational” to us.
15.7
(a) If A = 0: Q = 20 – p, or p = 20 – Q and MR = 20 – 2Q. In order to maximize π, set MR = MC: 20 – 2Q = 10, Q* = 5; p* = $15; π = 5(15) – 10(5) + 15 = $10.
(b) Q* = (20 – 15)(1 + 0.3 – 0.09) = 6.05; TR = 15(6.05) = $90.75; TC = 10(6.05) + 15 + 3 = $78.50; π = TR – TC = $12.25
* Optional exercise: Let B = 1 + 0.1A – 0.01A2. Then π = TR – TC = p(20 – p)B – 10Q – 15 – A = (20p – p2)B – (200 – 10p)B – 15 – A. To maximize π: ∂π/∂p = (20 – 2p)B + 10B = 0; p* = $15, no matter what level of B is chosen.
(c) Q* = 5(1 + 0.5 - 0.25) = 6.25; TR = 15(6.25) = $93.75; TC = 10(6.25) + 15 + 5 = $82.50; π = TR – TC = $11.25.
(d) higher demand, but less profit.
15.8
(a) Once level expenditure level A* is reachedat d, any additional advertising leads to a decrease in demand.
(b)
[pic]
(c) Certainly. That’s why companies are so particular concerning who endorses, and who doesn’t endorse, their products.
15.9 Utilities experience periodic surges in demand. For instance, the demand for electricity is lowest around midnight. But this seemingly uniform product is also more costly to produce during peak demand periods because older, less efficient production methods are used to meet the surge. Thus, if such a firm were to engage in marginal cost pricing (which we know to be socially efficient), it will raise price as marginal cost rises as it brings more costly processes on line to meet the upswing in demand.
15.10
(a) $10.50, his entire willingness to pay for the 1st one.
(b) For the 2nd, $7.50; for the 3rd, $4.50; for the 4th, $1.50
(c) No. Carl’s must charge at least $1.50, but Bob isn’t willing to pay $1.50 for the fifth pancake breakfast.
(d) Extra π = $18 (see shaded area on graph).
[pic]
(e) Zero. There is no consumer surplus when the seller can practice perfect, or 1st degree, price discrimination.
15.11
(a) First, construct MR (see graph). p* = 5 cents/kwH. Q* = 1,000 kwH. π is area abce, which equals (0.02)(1,000) = $20. CS is area bdc, which equals (0.5)(0.02)(1,000) = $10.
[pic]
(b) He’ll demand an extra 500 kwH at p = 4 cents/kwH. π now includes area efgh. Total π = $20 + (0.01)(500) = $25. CS now includes area fcg. Total CS = $10 + 0.5(0.01)(500) = $12.50
(c) Q = 1500 kwH. π is area adcfgh, which = $35. CS is area fcg, which = $2.50.
(d) Yes. Entry fee = 0.5(0.01)(500) = $40. Regular p = 3 cents/kwH. π is area adj, which = $40; CS = 0. There is no welfare loss.
15.12
(a) Set MR = MC: 200 – 0.1Q = 0.1Q, Q* = 1,000; p* = 200 – 0.05(1000) = $150; π = (150)(1000) – [0.05(1000)2 + 10,000] = $90,000.
(b) ηR = 10(150/900) = 1.67; ηP = 10(150/100) = 15. Poors’ is more elastic.
(c) pR = 240 – 0.1Q, so MRR = 240 – 0.2Q; pP = 160 – 0.1Q, and so MRP = 160 – 0.2Q.
(d) Set MRR = MC, and MRP = MC. Solve the two equation system: 3QR + QP = 2400, QR + 3QP = 1600. QR = 700, pR = $170; QP = 300, pP = $130. Yes, rich customers, with the less elastic demand, are charged the higher price.
(e) π = (170)(700) + (130)(300) – [0.05(1000)2 + 10,000] = $98,000, which is $8,000 more.
15.13 This is a case of tied sales — the products of Jerrold Electronics could not be purchased separately. The courts ruled that such tie-ins are permitted when a firm is in a formative industry, but tied sales are anticompetitive when practiced by a dominant firm in a mature industry. Tying by a dominant firm reduces competition by foreclosing entry by potential rivals; therefore, the practice can be an attempt to monopolize or an exercise of existing monopoly power. In addition, tie-in pricing always has elements of price discrimination. The supplier is able to extract more consumer surplus by offering a bundle at a package price that is lower than the sum of their prices when sold separately. If such pricing is harmful to competition, then it is illegal.
15.14
(a) MR = 200 – 4Q; MC = pL + MCC = 50 + 2Q.
(b) Set MC = MR: 50 + 2Q = 200 – 4Q; Q* = 25; p* = 200 – 2(25) = $150.
(c) Set MCL = MRL: 2.5Q = 50, QL = 20. The firm will produce QL = 20 no matter what amount of final good they produce. (d) less; buy 5 units.
(e) After 20 units of lumber have been produced, it is cheaper to buy it through the external market (pL < MCL).
(f) MC = MCL + MCC = 4.5Q. Set MC = MR: 4.5Q = 200 – 4Q, Q* = 23.53, p* = 200 – 2(23.53) = $152.94 (g) Set transfer price = MCL: pT = 2.5(23.53) = $58.82.
15.15
(a) MCT = $500; (b) p(Q) = 1,000 – 100Q; (c) pr = $500. Q = 5 thousand.
[pic]
(d) Q = 3 thousand. Is it not reasonable for the exporter to do this when its profit-maximizing price is pw = $400 because quantity falls below the exporter’s desired level.
(e) p = $700, and the quantity will be Q = 5 thousand. See graph.
(f) The increase in marginal cost, given the new demand has caused a decrease in CS of $800 thousand. The increase in demand given the new MC has caused an increase in CS of $800 thousand. Those areas are marked on the graph. The net change in CS is zero. No, this is not advantageous to the exporter because the exporter is neither better off nor worse off.
(g) The extra value required is $300 rather than $200 because the exporter wants to shift the domestic demand out to where it intersects the MCT curve at Q = 6 thousand. That way he can still sell cameras at the export price of $400 and sell Q = 6 thousand units. For him to be successful, however, he must induce the retailers to provide this value without affecting their marginal cost further — otherwise the retailers will adjust price, and then quantity will change.
15.16
(a)
[pic]
(b) QA = 30, pA = $160. (c) QB = 45, pB = $150. (d) QC = 90, pC = $120. (e) Q = 165.
15.17
(a) The joint product demand is kinked: for Q < 5,000, p = 72 – 12Q; for Q > 5,000, p = 42 – 6Q.
[pic]
(b) See curve S on the graph.
(c) 72 – 12Q = 6Q, Q* = 4,000 wells. pO = 30 – 6(4) = $6. pNG = 42 – 6(4) = $18.
(d) Joint product demand: for Q < 4,333, p = 46 – 6Q; for Q > 4,333, same as before. Set quantity demanded equal to quantity supplied: 46 – 6Q = 6Q, and so Q* = 3,833 wells.
(e) pNG = 42 – 6(3.833) = $19; pO = $4 — the price ceiling.
(f) No shortage of natural gas, Qd = 7 – (1/6)19 = 3.833 = Qs. Shortage of oil, at $4/unit buyers want to buy the output from 4,333 wells, but only 3,833 wells are producing.
15.18
(a) MRB = 30 – 0.4QB; MRH = 14 – 0.2QH. See the following figure.
(b) MRT = 44 – 0.6Q for Q < 70; MRT = MRB for Q ≥ 70.
(c) QB = 40, and pB = $22. QH = 40, and pH = $10.
(d) No, is it not possible for the firm to produce more of one good than the other because they must be produced in fixed proportion. Yes, it is possible to sell more of one than the other. That will be the best choice if MC intersects below the kink in the MRT curve, which can be seen on the following figure. Below the kink QH = 70 and QB > 70, hence the firm has to dispose extra beef.
[pic]
Chapter 16 Solutions
16.1 Plumbers’ and electricians’ services are not typically performed on a continuous basis for their customers. Licensing, therefore, provides the buyer with some information (and assurance) about the quality of the service to be rendered. Beauticians and doctors are both allegedly licensed to protect the health (or welfare) of the public. Of course, the consequences of a botched operation are more severe than those of a bad haircut.
16.2 If patents lasted for only seventeen months, it would become much more difficult for a firm inventing a new product or production process to earn substantial profits from their invention. They would quickly (about 1 1/2 years) discover imitators producing their product or using their process. As a result, entrepreneurs would be much less likely to take risks and develop new technologies.
16.3 Throughout the 1980s, the Japanese curtailed their auto exports to the U.S. voluntarily. Economic analyses of this practice have indicated that it resulted in higher prices for both U.S. and Japanese cars, with the total cost of the restriction being about $4.3 billion per year. Since about 26,000 jobs per year were saved, the annual cost per job saved comes to about $165,000.
16.4
(a) New supply: p = 3.25 + 0.125Q.
(b) p* = $5.50/bushel; Q* = 17.5 million bushels.
[pic]
(c) Welfare loss is area abc, which is 0.5(0.75)(2.5) = $ 937,500.
(d) too much output; price is too high.
16.5 (a)
Number of Filters Total Cost Remaining Emissions MCA
0 $0 400.0 —
1 500 200.0 $2.50
2 1,000 100.0 5.00
3 1,500 50.0 10.00
4 2,000 25.0 20.00
5 2,500 12.5 40.00
(b)
[pic]
(c) E* = 50 tons. (d) Fee = $10/ton; firm pays (5)($10) = $500 in taxes; buys 3 filters; TC = $500 + $1500 = $2,000.
16.6 (a) Fee = $1,000/ton. (b) Standard = 120 tons; social loss is area abc. (c) Fee = $800/ton; social loss is area dae. (d) smaller.
[pic]
16.7 (a)
[pic]
(b) TC1 = $2600; TC2 = $1900; together, TC = $4500.
(c) Firm 1, MC20 = $160; Firm 2, MC20 = $115.
(d) Set MC1 = MC2: 100 + 3w1 = 75 + 2w2; also w1 + w2 = 40. Solution: w1 = 11, w2 = 29 as illustrated on the following figure. Optimal emissions tax = $133/ton. Revenue = (20 tons still dumped) x $133/ton = $2660. Note: The emissions tax that the firms must pay are not included as part of social cost, since this money is not lost to Smogville. It can be used to reduce taxes, or to improve other city services.
[pic]
(e) The firms would dump 20 tons (as allowed by the permits) and have to treat 40 tons — meeting the city council’s goal.
(f) $160; $115.
(g) 11 tons; 29 tons. This is the same result as in part (d).
16.8 (a)
[pic]
(b) Yes. AC continually declines as Q increases.
(c) Set MR = MC: 35 – 2Q = 10, Q* = 12,500 households; p* = $22.50 (see point c).
(d) AC = 100 + 100/12.5 = $18; TC = ($18)(12.5) = $225,000; π is area abcd, = $56,250.
(e) Set MR = MC: 35 – 4Q = 10, Q* = 6,250 households for each firm; p* = $22.50.
(f) For each firm: AC = 100 + 100/6.25 = $26; TC = $162,500; π = –$21,875 < 0. Together, TC = $325,000, which is greater than TC for the natural monopolist in part (d).
(g) MC pricing (at point g): Q* = 25,000 households; the firm incurs a loss of ($10 – 14)(25) = –$100,000.
(h) pAC = $15; QAC = 20,000 households; welfare loss is area efg.
16.9
(a) The deadweight loss is area D. D = ΔpΔQ/2 = $40.0575 million.
(b) The surplus lost by consumers is area E. E = Q2Δp = $1,118.808 million (over 1 billion).
(c) The cost savings is area C. C = Q2ΔMC = $912.4 million.
(d) The net efficiency change is area D less area C. The value of this loss is –$206.408 million.
(e) There are equity (fairness) considerations.
(f) It is possible that GM and other domestic manufactures may learn form the Japanese how to make better cars more cheaply. Moreover, improvements in process technology may be passed on to other industries. Thus, there could be long-run gains not evident in the short-run welfare calculations. However, an independent economic consultant recommended against the joint venture, but the FTC approved it anyway.
16.10 (a) vertical (b) vertical, although this case had elements of horizontal integration because Brown also ran some retail outlets (c) horizontal (d) conglomerate.
16.11
(a) Herfindahl-Hirschman index = 1430.
(c) Cosmair-Revlon merger will change HH by 2(18)(13) = 468. Not allowed; Odorbegone-Sam’s merger will be allowed, since it changes HH by only 2(8)(6) = 96. Change in HH if Goodscent & Odorbegone merge is 2(8)(9) = 144. Not allowed.
16.12 These are forms of price discrimination, designed to take advantage of the more elastic demand in these segments of the market. The discrimination causes no significant injury to competition, though, and is permitted to take place.
16.13 The fact that price was set below cost makes this a candidate for predatory pricing. However, Kodak was new to this market and was facing an established virtual monopoly (Polaroid). Therefore, this pricing is more characteristic of penetration pricing which, if successful, would ultimately make the market more competitive.
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- solutions to exercises and problems
- econ 201 exams 3 professor twomey um d
- answers to questions in chapter 1
- chapter eight
- lecture 1 introduction to macroeconomics
- fiscal federalism and macroeconomic performance
- chapter 1 exam the nature of economics
- answers to even numbered questions
- ap macroeconomics 2nd semester final exam project
Related searches
- solutions to biodiversity loss
- solutions to lowering college tuition
- complex solutions to quadratic equations
- solutions to quadratic equations calculator
- solutions to quadratic equations pdf
- solutions to inequalities calculator
- integer solutions to inequalities calculator
- solutions to the inequality calculator
- solutions to water pollution
- solutions to water pollution pdf
- solutions to the education system
- solutions to inequalities