FIRST PRELIM - Cornell University



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PRELIM 1- ECON 4260/Public Finance - Cornell University - J. Wissink – Fall 2019 – Oct 8

Directions: Write legibly, concisely, & coherently. Label all axes, functions, & variables you use. Make your graphs big enough to allow for the best grading possibilities. READ QUESTIONS CAREFULLY. Draw pictures whenever possible. MAKE SURE YOU TRY ALL PARTS OF EACH QUESTION.

Total time for the test is 75 minutes. Total points on exam = 100, each question is worth 20 points.

Good luck and have a great Fall Break. (But there still is class on Thursday before you go!)

One more time, please…

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1. Consider the graph below. The aggregate production point "E" with division of two purely private goods as represented by individual allocation "e" in the graph is not Pareto efficient in an economy with only 2 factors of production (K and L), 2 goods (F and C), and two people (I and J).

a) Identify and explain what conditions that characterize Pareto efficient allocations in a 2x2x2 economy are being met, and which are not being met.

b) Construct a brief argument to demonstrate to me that “E/e” is NOT Pareto efficient. Just saying a condition is not being met is insufficient. Prove to me it is not Pareto efficient using the definition of Pareto efficiency.

c) Draw a very typical nicely behaved “efficient grand” utility possibility frontier (UPF) and indicate loosely where uI and uJ would be when the economy is at the allocation E/e.

Key

PP=Production Possibilities Frontier

OV=total production of food

OT=total production of clothing

UI=I's indifference curve at point e

UJ=J's indifference curve at point e

OU=I's consumption of F at point e

UV=J's consumption of F at point e

OS=I's consumption of C at point e

ST=J's consumption of C at point e

ANSWER SPACE:

2. Consider Felix and Oscar and suppose: uFelix = min{1X, 1Y} and uOscar = 1X + 1Y. Assume there is no production in this economy. Assume the total amount of X is 100 and the total amount of Y is 200. Felix is endowed with all the X. Oscar is endowed with all the Y.

a) Is the endowment point Pareto efficient? Briefly, illustrate why or why not in an Edgeworth-Bowley box.

NOTE: Put X on the horizontal axis and Y on the vertical axis.

Put Felix at the “bottom-left” and Oscar at the “top-right” for your answers.

b) Illustrate the entire set of Pareto efficient allocations in your Edgeworth-Bowley box diagram using these particular preferences.

c) Derive the utility possibilities frontier (UPF) for this economy and make sure to label the utility values at the intersection with both the vertical and horizontal axes.

NOTE: Put Felix’s utility on the horizontal axis and Oscar’s utility on the vertical axis.

d) What is the Rawlsian social optimum? Illustrate in your UPF graph.

e) What is the Benthamite/Utilitarian social optimum? Illustrate in your UPF graph.

ANSWER SPACE

ANSWER SPACE

3. Suppose G is a purely public good. Suppose $MCprivate=$MCsocial = 30 at all values of G.

Suppose there are three people with the following marginal benefit functions.

$MBA=15 - 3G

$MBB=17 - 2G

$MBC=19 - 2G

a) If the collective consumption nature of this good is ignored, and we consider a market-based outcome, how much G would be purchased by each person in a Walrasian/market-based solution?

b) Suppose we recognize the collective consumption nature of this good. What is the Pareto efficient amount of G? Show your work!

c) Suppose the “law of the land” is that the cost of the public good G will be split in the following way: tA=$15 per unit, tB=$10 per unit, tC=$5 per unit. What will be the outcome of using the method of majority voting to determine G? Will this result in the Pareto efficient amount of public good being provided? Briefly defend your answers.

d) How do you predict A, B and C will react to this plan to deal with the collective consumption good? Who is happy and who is not and why?

ANSWER SPACE

ANSWER SPACE

4. Suppose Abe, Betty and Charlie are asked for their personal money-evaluations of a new lighthouse on Cayuga Lake. If the lighthouse is built, their true values are: vAbe = $200, vBetty = $-145, vCharlie = $-70. If the lighthouse is not built, each person has a value of vi=$0. Suppose the lighthouse is being donated by an anonymous goodhearted person who lives in another country but went to Cornell. Assume Abe, Betty and Charlie are the only people who really matter in this story.

a) Should the lighthouse be built? Explain why or why not.

b) Suppose each person’s vi is private information. If these people were simply asked their evaluations, would they tell the truth? Explain why or why not.

c) If the government ran a Clarke/pivotal mechanism (as defined in class) to determine if the lighthouse should be built, what would happen? Would the government collect any tax revenue in the course of running the mechanism? How much, if any, and from whom?

d) What is Abe’s payoff (payoff would be defined as $vAbe-$taxAbe) from playing the mechanism?

e) Assuming that Betty and Charlie tell the truth, demonstrate to me that Abe has no incentive to lie about his true value and announce a value other than vAbe when confronted with the mechanism.

ANSWER SPACE:

ANSWER SPACE:

5. Suppose Abe, Betty, Charlie and Dave have the following preferences (listed from best to worst) over days of the week for office hours: (M=Monday, T=Tuesday, W=Wednesday, F=Friday)

|ABE |BETTY |CHARLIE |DAVE |

|M |T |T |W |

|T |M |W |M |

|W |F |M |F |

|F |W |F |T |

a) What are the axioms that Arrow insisted on regarding finding a rule to determine a social preference ordering from a set of people? (Feel free to use Arrow’s terms OR Blair & Pollak’s terms.)

b) What is the basic Arrow result?

c) What would happen if we used the method of majority voting over each pair of alternatives to determine the social ordering? If there is a tie in the vote, then the days are to be regarded as indifferent to each other in the social ordering.

d) Suppose we decide to weaken Arrow’s notion of collective rationality to only asking for P-transitivity. What method for aggregating preferences can be used to satisfy P-transitivity and all the other original axioms?

e) Apply the social choice rule you have suggested above to this set of people. That is, how will society rank each pair of days now?

ANSWER SPACE

ANSWER SPACE

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Who do you think will win the “Nobel Prize” in Economics this year? You can “guess” up to 3 names.

1. _______________________

2. _______________________

3. _______________________

Did you know…Actually it’s not really a Nobel Prize… it came after they started and it’s officially called the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.

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