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Econ 452, 2005
Midterm exam.
Economics 452
Midterm examination
Dr. L. Welling
February 23, 2005
Time: 50 minutes
Total value: 45 marks
DO ALL QUESTIONS. Please double-space all written answers, and use
one-half page for each diagram you want marked. Be sure to label all
diagrams.
1. (15 marks) Sharda has a utility of wealth function given by u(w)=w½ . Her
current wealth is 100,000, and she knows that with probability 0.5 she will lose
51,000.
a) (5) In a state space diagram, label Sharda’s endowment point E,
and sketch her indifference curve through this point.
b) (5) Briefly explain what the “indifference curve” you drew means.
Ans: joins up all pairs of wealth - one level if loss occurs, one if no loss - which
leave her with same expected utility ex ante.
c) (5) Calculate the maximum amount Sharda is willing to pay for full
insurance against her loss, and indicate this amount in your
diagram.
0.5 100000  0.5 49000
Ans: Sharda's EU is =
. If she
buys full insurance, she would have the same wealth in either state. The max
she is willing to pay for full insurance is the difference between her current wealth
and the level of wealth received, for certain, which yields the same utility as the
w defined by
2 w  100,000  49,000
In the diagram w is the horizontal (=vertical) coordinate of the point at which
EU she has initially: that is
Sarda's indifference curve through E intersects the certainty line (where
w1  w2 .
2. (30 marks) Jason is seeking a producer for his new line of glow-in-the-dark
nunchucks. The nunchucks have a value to him of S(n)=10ln(n), where n is the
number of nunchucks and S’(n)>0>S”(n). There are two possible types of
producers in town, who differ in their marginal cost of production; assume that
each producer knows their own marginal cost. Efficient producers can provide
nunchucks at a marginal cost of 1, whereas inefficient producers can provide
them at marginal cost equal to 2. All producers have a reservation utility of zero.
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Econ 452, 2005
Midterm exam.
a) (5) If Jason were to contract with someone he knew to be an efficient
producer, how many nunchucks would he order, and what would he
pay for them?
Ans: Let's assume that Jason has all the bargaining power here - so he will
extract any surplus generated in the market. Then he will pay the producer their
opportunity cost - the cost of production - and will choose to buy the number of
nunchucks which maximizes total surplus: that is, he will choose n to max
S (n)  n  10ln n  n . Solving this max'm problem for n yields
n=10; the cost of production would be 10 - which would be the price he would
pay the producer.
Suppose now that Jason cannot costlessly identify the efficiency of any
given producer.
b) (6) In this situation, should Jason be more suspicious of someone who
claims to be efficient, or inefficient? Explain briefly.
Answer: depends on who has the incentive to cheat here. Suppose he offers the
contract {n,p}={10,10}. Then an efficient producer would accept the contract,
since it yields the reservation utility. Would an inefficient producer be wlling to
accept this contract? For an inefficient producer, the total production cost of 10
nunchucks = 2x10=20>10, so this type of producer would rather not.
However: if Jason were to contract with an inefficient producer, the optimal
10 ln n  2n
contract would have p=2n, and n would solve max
, so n=5,
and p=10. The efficient producer, if offered this contract, would make positive
surplus of 5 (since it would cost the efficient producer only 5 to produce 5
nunchucks). Since the efficient producer would gain by overstating his cost,
Jason should be suspicious of anyone claiming to be an inefficient producer.
c) (7) Using subscripts “e” and “i” for efficient and inefficient producers
respectively, write down the constraints on the quantity-price contracts
that will ensure that a producer who accepts a contract will be the type
they claim to be.
{ne , pe } be the contract designed for an efficient producer, and
{ni , pi } the one designed for an inefficient producer. Then the selfAns: let
selection constraints are:
pe  ne  pi  ni
Inefficient producer: p  2n  p  2n
1
i
e
e
Efficient producer:
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Econ 452, 2005
Midterm exam.
d) (5) Explain what is meant by the term “information rents” in this context.
Ans: "information rents" refers to the surplus which must be transferred to the
efficient producer to induce him to not misrepresent himself as inefficient. This is
surplus which Jason would be able to capture if information on type were
costless to acquire; since this info is not costless, the efficient producer, who
benefits from the private info on type, must be paid to impart the full info.
e) (7) Suppose now that the marginal cost of efficient producers
decreases, while that for inefficient producers was unchanged. Would
this increase or decrease the problem caused for Jason by the
asymmetric information? Explain.
Ans: the greater the difference in the marginal costs, the greater the profit an
efficient producer would receive from misrepresenting themselves as ineffcient.
Thus the greater the surplus which the efficient producer receive under
asymmetric information. Since, in this setting, Jason is the only other agent who
receives any surplus, greater surplus for the efficient producer must mean less
surplus for Jason.
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