NAME:__________



NAME:__________

FINAL EXAM

If there is a question that is unclear to you, simply ask. Show all work for partial credit opportunities. Use the space provided to answer the following questions. There is additional space on the back.

1. Consider the model of a firm that employs inputs (labor at a price w, and capital at a price r) to produce the highest level of output Q, without spending more than a given level of total cost.

a. What is this producer’s constrained optimization problem? Include a mathematical description. (4 points)

b. What is comparative statics analysis? Give an example with this particular model. (6 points)

Information, please read carefully. The following passages are excerpted from “Taking the Energy Out of Retailers”[1]

The nation's retailers are growing increasingly worried that as consumers pour more money into their gas tanks, they will devote less to filling up their shopping carts, with industry bellwether Wal-Mart Stores Inc. yesterday blaming higher prices at the pump for its weakest quarterly performance in four years.”

So far, the relentless climb of oil and gas prices has pinched discount chains and dollar stores, which cater to lower-income shoppers. But if prices continue to rise, the pain could soon spread to chains that have long considered their customers immune to the fluctuating price of fuel, retail analysts said.

With oil and gas prices hovering in record territory, retailers are feeling yet another pressure: Their everyday cost of doing business is surging. A Barbie costs more to make. A diaper costs more to distribute. And a store costs more to cool and heat.

2a. Use supply and demand analysis to describe the impact of rising energy prices on the market for goods like Barbie dolls and diapers. Include a clearly labeled diagram to show changes in this market. Explain your comparative static analysis. (6 points)

Information, please read carefully. The following passages are also excerpted from “Taking the Energy Out of Retailers”

Consumers, stung by escalating gas prices, say they are switching from name brands to generic ones, avoiding pricier chains in favor of cheaper competitors and abstaining from impulse purchases.

The national average for a gallon of regular unleaded gas hit $2.52 yesterday, according to the auto club AAA.

Shopping at Ross Dress for Less in Alexandria yesterday, Shirley Lee, a retiree from Mount Vernon, was tempted to buy a lunchbox and container of gumdrops for her granddaughter.

Then she thought about filling her gas tank -- a $40 task -- and took a pass on the gifts. "I'm trying to cut down," she said.

Or, as Janine Whitfield, a teacher from Tysons Corner, put it, "we are going to have to rethink how we spend money and how we drive."

2b. Use budget constraints, before and after the sudden increase in energy prices, and indifference curves to show how Shirley Lee made the choice described above. Put gasoline on the x-axis and gumdrops on the y-axis. Clearly label your diagram and explain your comparative static analysis. (10 points)

Information, please read carefully. The following passages are also excerpted from “Taking the Energy Out of Retailers”

Most retailers are eating the costs of higher fuel rather than raising prices. "We are investing in our customers to stay competitive," said Greg TenEyck, a spokesman for Safeway Inc., which said its transportation costs have surged.

That is scant relief for shoppers such as Franklin Crawford, who spends $45 gassing up his 2002 Ford Explorer. He saw a $39 mattress cover he liked at Bed, Bath & Beyond but opted instead for a $12 version he found at Wal-Mart.

He walked out of the Wal-Mart in Alexandria yesterday carrying a McDonald's Quarter Pounder and french fries, along with the mattress cover.

Crawford used to pay at least $8 to sit down and eat at his favorite buffets, but with gas prices escalating, he has downsized to McDonald's. "My hamburger is my steak," he said, "my french fries are my caviar."

2c. Use budget constraints, before and after the sudden increase in energy prices, and indifference curves to show how Franklin Crawford made the choice described above. Put meals at McDonald’s on the x-axis and meals at his favorite buffet on the y-axis. Clearly label your diagram and explain your comparative static analysis. (10 points)

3. Scumbag, Inc. is a firm that uses units of labor and capital to produce swimming pool filters.

a. Scumbag hires labor and capital at a weekly total cost of $600,000, paying $1000 per unit of labor and $4000 per unit of capital. What is the specific equation for their weekly isocost function? (4 points)

b. In general, what is the tangency condition that must be satisfied for Scumbag to be hiring the least-cost combination of labor and capital? (3 points)

c. If the production function is given by Q = (1/3)LK, solve for the cost-minimizing combination of labor and capital that will use their entire weekly total cost. How much weekly output will this combination provide? Illustrate the least-cost employment decision in a clearly labeled graph below. (9 points)

d. In the short run capital is fixed. Now the demand for Scumbag’s product, the pool filters, decreases and they have orders for 5000 units. How much labor and capital will be employed in the short run? How much total cost will be incurred in the short run? A diagram is not necessary. (6 points)

e. In the long run, Scumbag can completely adjust to the new demand for pool filters. Find the new least-cost combination of labor and capital and the cost that will be incurred. A diagram is not necessary. (5 points)

4. Why is it impossible for two consumer indifference curves to intersect? Use a diagram to assist your explanation. (6 points)

5. A major city wishes to redevelop an old waterfront area that has fallen into disrepair. Five years ago the city hired a consulting firm to study the feasibility of the redevelopment project. The consultants reported that the project would indeed be profitable and beneficial for the city. The city cleared the land and prepared it for redevelopment. The cost of the consultants and preparing the land was $5 million. Just recently, new and unanticipated problems arose, and the city was forced to revise the economic analysis. Economists determined that the project would require an additional $6 million of cost, but would generate monetary benefits of $8 million. Should the city continue with the project of redeveloping the old waterfront area, or should the city scrap the idea altogether? Explain your response. (6 points)

6. A perfectly competitive firm has a cost function: TC(Q) = 1.5Q3 - 24Q2 + 300Q + 700

a. Derive expressions for ATC, AVC, and MC. (6 points)

b. Explain the shut down decision. If all fixed costs were sunk, at what price would the firm shut down? (5 points)

c. If the market price was $500, what would the profit maximizing quantity be? (3 points)

d. At this profit maximizing quantity, would you expect this industry to expand or contract? Explain, being as specific as possible. (5 points)

e. At what price will firms in the industry have no incentive to exit and there will be no incentive for outside firms to enter this industry? (4 points)

7. Suppose demand for good A is given by QdA = 60 – 2(PA) + 5(PB) + .01(I) where PA is the price of good A, PB is the price of some other good B, and I is income. Assume that PA is currently $15, PB is currently $3, and I is currently $800.

a. What is the price elasticity of demand for good A? Interpret this measure. (6 points)

b. What is the cross-price elasticity of demand for good A with respect to the price of good B? Interpret this measure. (6 points)

c. What is the income elasticity of demand for good A? Interpret this measure. (6 points)

8. Two firms are competing in an oligopolistic industry. Firm 1, the larger of the two firms, is contemplating its capacity strategy, which we might broadly characterize as “aggressive” and “passive”. The aggressive strategy involves a large increase in capacity aimed at increasing the firm’s market share, while the passive strategy involves no change in the firm’s capacity. Firm 2, the smaller competitor, is also pondering its capacity expansion strategy; it will also choose between an “aggressive strategy” or a “passive strategy”. The table below shows the profits associated with each pair of choices made by the two firms:

| | | |

| | |Firm 2 |

| | |Passive |Aggressive |

| |Passive |28,19 |23,25 |

|Firm 1 | | | |

| | |31,13 |24,15 |

| |Aggressive | | |

If both firms decide their strategies simultaneously, what is the Nash equilibrium? Is this an example of a classic “prisoner’s dilemma”? Explain. (6 points)

9. The market for corn is perfectly competitive. The demand curve is: Qd = 20 – P. The supply curve is Qs = P.

a. Illustrate the corn market and solve for the equilibrium price and quantity. (6 points)

b. At the competitive equilibrium, calculate the consumer and producer surplus. (4 points)

c. The government imposes a price control at $14. In a new diagram below, show how this price control will impact the corn market. Recalculate consumer and producer surplus and dead weight loss. (6 points)

d. From society’s perspective, why is dead weight loss worth measuring? (5 points)

10a. Can marginal revenue be negative for a perfectly competitive firm? Explain. (3 points)

b. Why is it possible for a monopolist’s marginal revenue to be negative for some levels of output? Why is marginal revenue negative in the inelastic range of monopoly demand? Feel free to use diagrams and/or equations to help your explanations. (4 points)

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[1] Michael Barbaro and Anjali Athavaley, Washington Post, August 17, 2005.

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