# Exercise 4 of Microeconomics I

Universitat Pompeu Fabra, 1998/1999

Due October 28, 1998

The midterm exam is scheduled for October 28, 1998, 13:30.

1. Consider the problem of rationing in a credit market. Instead of assuming that the bank can't get anything in case the project fails, assume that it may have the apartment of the firm's manager as a collateral. The apartment's value is C.

1. How would the result change in comparison to the case discussed in class?
2. In case that C>I, one may think that the firm's manager does not need the bank at all. He may sell his apartment instead. Do you think that there may be reasons to take a loan from the bank also in this case?

2. Consider the problem of moral hazard with the following modification: The agent is choosing two continuous effort variables e1, e2. The principal is risk neutral. The agent is risk averse and has the expected utility function EUA=E(w)-(1/2)Var(w)-v(e1,e2). His reservation utility level is zero. The firm's sales of two variables (x1, x2) are proportional to the effort levels: x1=A×e1+H1; x2=B×e2+H2, where A, B are two different constants and H1, H2 are random variables with mean equal zero and variance equal 1. H1 and H2 are correlated and their covariance Cov(x,y) is equal to R12.

1. Assume that the contract that the principal proposes should have the form w(x1,x2)=A+x1×B1+x2×B2, and that the agent's disutility (or cost) from effort is v(e1,e2)=(1/2)(e1+e2)2. What is the optimal contract? Note that for any two random variables x,y and for any three constants a,b,c, we have: V(a+bx+cy)=b2V(x)+c2V(y)+2Cov(x,y).)
2. Find the optimal contract when the cost of the effort is v(e1,e2)=(1/2)(e12+e22).

3. In most countries unemployment insurance payments decrease the longer the unemployment period is.

1. May you explain that with the theory of moral hazard?
2. Can you propose an empirical test that may test whether the above mentioned theory is the correct explanation?