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PRELIM 1- ECON 3350 - Cornell University - J. Wissink – Fall 2012 – Oct 2
Directions: Write legibly, concisely, & coherently. Label all axes, functions, & variables you use. 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.
P.S.: WHO DO YOU THINK WILL WIN THE NOBEL PRIZE FOR ECONOMICS THIS YEAR?
(It will be announced very soon, probably sometime over Fall Break.)
And the 2012 Nobel in Economics goes to:……………………………………………….…………………..
Document1
1. Consider Abe and Betty and suppose: uA = 1F + 3C and uB = 3F + 1C where u=utility,
F = food and C = clothing. Assume there is no production in this "economy" and that Abe is
endowed with only 90 units of food while Betty is endowed with only 90 units of clothing.
a. Putting food on the horizontal and clothing on the vertical, and Abe at the “bottom-left” and
Betty at the “top-right” use an Edgeworth-Bowley box to illustrate the endowment point.
b. Illustrate the contract curve on your carefully labeled Edgeworth-Bowley box diagram using
these particular preferences.
c. Identify the core allocations of this particular 2 person pure exchange economy.
d. Putting Abe’s utility on the horizontal and Betty’s utility on the vertical derive the utility
possibilities frontier (u.p.f) for this economy. For full credit, make sure you label endpoints with
numerical values, and also indicate numerical values at any other critical points.
e. What is the functional form for a Bergson-Samuelson Social Welfare Function that is described
as a Benthamite-Utilitarian one?
f. What point/s on the u.p.f. for this situation is/are optimal if we use a Benthamite-utilitarian social
welfare function?
ANSWER SPACE:
2
ANSWER SPACE:
3
2. Suppose that the small town of Spectacular is planning for its Octoberfest. People seem to think
fireworks would be a good idea for this event. Assume there are 50 residents in Spectacular.
Assume that the social, as well as private, marginal cost of each minute of fireworks is $100 per
minute no matter how many minutes are planned. For each resident the marginal benefit function
for minutes of fireworks is given by: $mbi = 10 – (1/10)Q, for i = 1, ..., 50 where "Q" is the number
of minutes.
a. If residents had to privately buy minutes of fireworks in a market at market marginal cost, how
many minutes would each individual resident buy for himself/herself?
b. The mayor realizes that fireworks are a pure public good and he decides the town will put on a
show. The display will be free to residents. An anonymous former resident has generously
agreed to finance the cost of the event. The mayor needs to determine the optimal number of
minutes of fireworks they should have but he does not know the marginal benefit functions of his
residents. So he sends a questionnaire to each resident to obtain this information. If each
resident reports his/her true marginal benefit function, how many minutes of fireworks should be
provided in order to be Pareto efficient?
c. If one savvy resident believes that all the others will report their marginal benefit functions
truthfully, does that particular savvy resident have an incentive to also behave truthfully? If not,
what do you predict this person will do? Briefly explain/defend your assertion.
d. Suppose everyone does report the truth. Now suppose that it becomes common knowledge that
the anonymous donor has fallen on hard times and consequently the town decides to pay for the
fireworks display by taxing the residents. The mayor is “The Decider” and must form a tax
policy quickly. If you were the mayor, how would you tax the residents to pay for the fireworks
and how would you defend your decision?
ANSWER SPACE:
4
ANSWER SPACE:
5
3. Consider the graph below of a two-by-two-by-two production economy with only 2 factors of
production (K and L), 2 goods (F and C), and two people (I and J). PPF=Production Possibilities
Frontier. The curve from OI to OJ is a set of points where I’s and J’s indifference curves are tangent
when the economy produces aggregate point “E”. The curve from OI to OJ-hat is a set of points
where I’s and J’s indifference curves are tangent when the economy produces aggregate point “F”.
Indifference curves are drawn and labeled for person I. (Feel free to draw in the
indifference curves for J, if you’d like to.)
a. Consider the allocations a, b, and c. Which of these three allocations are Pareto Efficient in this
two-by-two-by-two production economy?
b. What marginal conditions characterizing Pareto Efficiency are and are not met at each allocation
a, b, and c?
c. Out of allocations a, b, and c, which one is socially best?
Extra credit(only do once you have completed the REST of the exam): Putting person I on the
horizontal axis and person J on the vertical axis, sketch out the grand utility
possibilities frontier correcting locating the analogues of allocations a, b and c on your
diagram to the best of your ability.
E
F
6
ANSWER SPACE:
7
4. Suppose Abe, Betty, Charlie and Dave are asked for their personal evaluations for a new lighthouse
on Cayuga Lake. From their points of view the cost of the lighthouse is not an issue. It is being
financed by “outside” money. If the lighthouse is built, their true $values are:
vAbe=$200, vBetty=$-145, vCharlie=$-70, vDave=$30. If the lighthouse is not built, each person has a
value of vi=$0.
a. Should we build the lighthouse?
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 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 Clarke
mechanism?
e. Assuming that Betty, Charlie and Dave tell the truth, demonstrate to me (by numerical example)
that Abe has no incentive to lie about his true value and announce a value other than vA when
confronted with the Clarke mechanism.
ANSWER SPACE:
8
ANSWER SPACE:
9
Abe
Betty
Charlie
W
X
Y
X
Z
X
Y
W
W
Z
Y
Z
5. Suppose that three people, Abe, Betty and Charlie rank alternatives W, X, Y and Z as follows:
a. What are the axioms that Arrow considered necessary for a “good” rule which will aggregate
individual preferences into a social preference ordering? (Feel free to use either the conventional
“social choice theory” terms or the “laymen” terms invented by Blair and Pollak.)
b. Given the chart above, what is this society’s preference ordering over each pair of alternatives if
we use the method of majority voting to create this ranking?
c. Given this particular social preference profile, which of Arrow’s axioms are, or are not,
satisfied?
d. Considering all possible social preference profiles, which of Arrow’s axioms are always, or are
not always, satisfied when using the method of majority rule to aggregate a list of individual
preferences into one social preference?
ANSWER SPACE:
10
ANSWER SPACE:
11