Question 1. The cost of an information producer (i.p.) to produce information is 10, which is non-monetary. The i.p. is risk averse with a utility function, √x, defined over monetary wealth, x. The i.p. demands a minimum expected utility level of 20; otherwise, he/she will work elsewhere.
A firm that wishes to attract capital has to hire the i.p. to release information to the capital market. The firm can monitor the i.p.'s effort. This monitoring produces a noisy signal. If the i.p. produced information, the signal says that he/she did only with probability 0.8 and is erroneous with probability 0.2. If the i.p. did not produce information, the signal says that he/she did only with probability 0.2 and that he/she did not with probability 0.8.
(a) What would be the best way for the firm to compensate the i.p. so as to induce information production?
(b) Now, there are three identical i.p.s, each of them deals with a separate firm. The three i.p.s pool their payoffs that are shared equally among themselves. The three i.p.s are cooperating in that they either all produce information or all do nothing. Signals across the three firms are mutually independent. Show that the i.p.s in this case can be made better off as compared to the case in part (a).
Question 2. Consider a borrower who needs $100 at t = 0 to invest in a project that will pay off at t = 1. The borrower can choose between two mutually exclusive projects, S and R. Project S will yield a payoff of $300 with probability 0.9 and nothing with probability 0.1. Project R will yield a payoff of $400 with probability 0.6 and nothing with probability 0.4. The borrower has sufficient personal assets that can be used as collateral. However, liquidating the assets at t = 0 to finance the project is prohibitively costly. As such, the borrower has to solicit the entire amount of $100 from a bank at t = 0. Assume that collateral worth $1 to the borrower is worth only 80 cents to the bank. There are no taxes and no bankruptcy costs. Everybody is risk neutral and the riskless rate of interest is 10%. The bank is competitive in that it earns zero expected profits.
(a) Suppose that the bank is able to directly control the borrower's choice of project. Which project will the borrower choose? Why?
(b) Suppose that the bank is unable to directly control the borrower's choice of project. Which project will the borrower choose if the bank loan contract consists of the interest rate only? How large is the agency cost due to the asset substitution problem in this case?
(c) Suppose that the bank is unable to directly control the borrower's choice of project. Which project will the borrower choose if the bank loan contract consists of not only the interest rate but also the collateral requirement? How much should the borrower pledge as collateral? How large is the agency cost due to the asset substitution problem in this case?
(d) Comparing parts (b) and (c), why is there a reduction in the agency cost due to the asset substitution problem when collateral is used?