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PRELIM 1- ECON 3350 - Cornell University - J. Wissink – Fall 2011 – Oct 6
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.
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WHO DO YOU THINK WILL WIN THE NOBEL PRIZE FOR ECONOMICS THIS YEAR?
533563139
1. Consider the basics of welfare economics.
a) Write down the definition of what it means for an allocation to be Pareto Efficient.
b) Write down the 1st Fundamental Theorem of Welfare Economics which includes the set of "if"
assumptions made to get the stated “then” result.
c) What are the three conditions that will characterize a Pareto Efficient allocations in a 2-person; 2-output;
2-input model of an economy - assuming all the relevant fundamentals of the economy are "very nicely
behaved."
d) Using one of the conditions you described above, construct an argument (or mini-proof) to demonstrate
that the condition you chose would be satisfied at a Walrasian equilibrium allocation under the
assumptions of the 1st Fundamental Theorem.
e) What does the 1st Fundamental Theorem suggest about the role of the government in a market oriented
Walrasian economy?
ANSWER SPACE:
2
ANSWER SPACE:
3
2. Consider the two graphs below.
a) The aggregate point "E" with division of goods as represented by 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). Explain what conditions that characterize Pareto
Efficient allocations are and are not being met?
b) Construct a brief argument to demonstrate to me that “E/e” is NOT Pareto Efficient.
c) On the efficient grand utility possibility frontier illustrated below, indicate loosely where
uI and uJ would be when the economy is at E/e.
d) On the efficient grand utility possibility frontier illustrated below, indicate where a
Benthamite/Utilitarian social welfare optimum would be and why.
e) On the efficient grand utility possibility frontier illustrated below, indicate where the
Rawlsian social welfare optimum would be and why.
f) Suppose the omnipotent benevolent social planner named Zeus, is a COMMODITY
egalitarian. Would Zeus’
social optimum necessarily
be on the grand utility
possibility frontier?
Briefly defend your
position.
Key
PP=Production Possibilities Frontier
OV=total production of food
OT=total production of clothing
UI=I's indifference curve
UJ=J's indifference curve
OU=I's consumption of F
UV=J's consumption of F
OS=I's consumption of C
ST=J's consumption of C
4
ANSWER SPACE:
5
3. Consider Felix and Oscar and suppose: uFelix = 2X + 2Y and uOscar = 2X + 1Y. Assume there is no
production in this "economy". Assume the total amount of X is 300 and the total amount of Y is 150.
Felix and Oscar are endowed with half of each commodity. Put X on the horizontal axis and Y on the
vertical axis, and Felix at the “bottom-left” and Oscar at the “top-right” for all your answers.
a) Is the endowment point Pareto Efficient? Briefly, illustrate why or why not in an Edgeworth-Bowley
box.
b) Illustrate the contract curve on your carefully labeled Edgeworth-Bowley box diagram using these
particular preferences.
c) Identify the CORE of this particular 2 person pure exchange economy.
d) Derive the utility possibilities frontier (u.p.f) for this economy and describe its slope.
ANSWER SPACE:
6
4. 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 the market, how much G
would be purchased by each person in a Walrasian/market solution?
b) Suppose we recognize the collective consumption nature of this good. What is the Pareto Efficient
amount of G?
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 Bowen-style
method of majority rule to determine G, and will this result in a Pareto Efficient amount of public good
being provided?
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:
7
ANSWER SPACE:
8
5. Suppose Abe, Betty and Charlie are asked for their personal 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 we build the lighthouse? 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 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? What must be done with this revenue?
d) What is Abe’s payoff (payoff would be defined as $v-$tax) from playing the Clarke 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 vA when confronted with the Clarke mechanism.
ANSWER SPACE:
9
ANSWER SPACE:
10