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1 Insurance
Pete’s utility function is given by U(M;C) = pM 􀀀 C, where M is Pete’s income and C are the
personal/psychological costs he has to bear when he goes to work. His monthly income is M = 40,000
euros. Pete does not like his job. If he does not go to work, C = 0. If he goes, then C = 20. There is
a   0.2 chance that Pete loses his job, which implies his income drops to 0. An insurance company
o¤ers Pete an unemployment insurance. If Pete buys the insurance, he gets in case he loses his job an
unemployment bene…t of 25,600 euros. The price of the insurance is P. This price he pays only if he
loses his job (this is thus NOT a standard insurance premium).
1. What is the maximum price Pete is willing to pay for the insurance? Call this price pmax.
2. Suppose the insurance company requires to be paid a price p < pmax. Of course, because of problems
of moral hazard, Pete could always behave in such a way that he gets …red from his current job and
still gets the unemployment bene…t from the insurance company because they do not discover his
misbehavior. Assuming that this can indeed happen, show that this moral hazard issue can have
consequences for the relationship that exists between p and the maximum unemployment bene…t
the insurance company is willing to pay to Pete.

还有一题
2 Search
Leslie is looking for a smart, intelligent and clever partner (who cares about beauty and wealth nowadays
anyway, right?). Suppose that the IQ of potential partners he could be interested in going out with is
uniformly distributed over the interval 100 to 150. One IQ point is worth 2 euros to Leslie. Leslie learns
the IQ of potential partners by going out with them. Going out costs him x^2, where x is the number of
times Leslie has gone out (thus for the …rst partner, the cost is 1, for the …fth, the cost is 52 = 25 and so
on).
Assume partners are not jealous (it’s a micro exercise after all, we are allowed to make silly as-
sumptions). Thus Leslie can always go back and continue dating a partner Leslie went out with in the
past.
1. After how many rounds of search will Leslie stop searching? In your analysis, assume that, at the
beginning of each possible new round, the IQ of Leslie’s current partner is equal to what Leslie
expected that IQ to be.
2. Compute, for each date (the …rst, the second and so on up to the nth maximal date you identi…ed
in the previous question) what is the IQ of that date that would make Leslie stop searching.
Assume now, realistically, that partners are jealous. Thus previously ’tested’ partners are NOT
available to Leslie anymore.
1. After how many rounds of search will Leslie stop searching? In your analysis, assume that, at the
beginning of each possible new round, the IQ of Leslie’s current partner is equal to what Leslie
expected that IQ to be.
2. Compute, for each date (the …rst, the second and so on up to the nth maximal date you identi…ed
in the previous question) what is the IQ of that date that would make Leslie stop searching.

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关键词：紧急求教 unemployment MORAL HAZARD relationship Consequences 求教

哎，第一题又是乱码，Pete的效用函数是U=SQRT（M）-C.