Exercise 1

Consider the following instances of asymmetric-information

1. The owner of a company wants to hire a manager. He is considering various candidates but is unable to perfectly observe their ability.
2. The owner of a company has hired a manager. He is unable to observe whether the manager is working or shirking.
3. A bank is considering lending money to a firm but is unable to perfectly asses the firm’s risk profile.
4. A bank has lent money to a firm but is unable to observe whether the firm is investing in risky projects or safe projects.
5. A bank has lent money to a firm but is unable to observe whether the firm has invested in risky or safe projects. The bank is now considering whether to renew the loan.
6. A trader cannot observe whether, at the current price, the shares that her coun- terparty is trying to sell her are overvalued or undervalued.

Discuss whether each of these cases qualifies as a problem of moral hazard or adverse selection.

Exercise 2

A publisher wants to launch a new series of classics. The necessary initial investment is £1,000. If the series is successful it will provide a cash flow of £2,000 next year. If it is unsuccessful it will yield £0. The publisher can invest at most £200 in the project and therefore needs to raise the rest (£800) on the market. If the project is undertaken, the publisher must choose whether to assign it to its top editor or to a

junior editor. If the project is supervised by the top editor, it will be successful with probability 0.8. If it is assigned to a junior editor it will be successful with probability 0.3, but the publisher will be able to save £200 in editorial fees. Whether the top editor is in charge of the series or not is not observable by outside investors. All other assumptions are as in lecture 2. In particular, consider a contract paying a share R_I of the proceeds to outside investors and a share R_E to the publisher.

1. Write down the publisher’s incentive compatibility constraint as a function of

R_E. Discuss.

• Determine the pledgeable income and the expected pledgeable income.
• Compare the expected pledgeable income with the initial investment that outside investors are required to make. Will the project be funded? Discuss.
• Does your answer change if, by assigning the project to a junior editor, the publisher is able to save more than £500?
• Does your answer change if, by assigning the project to a junior editor, the publisher is able to save £600, but he is also able to invest £400 (rather than only £200) upfront?

Exercise 3

The financial press often mentions that implicit or explicit government guarantees to financial institutions may induce these institutions to take excessive risk, thus creating a “moral hazard problem”. How would you reconcile this view of moral hazard with the analysis in the lecture? Discuss.

Exercise 4

Provide two examples, beside those discussed in the lecture, of market interactions (or other types of interactions) that are affected by adverse selection.

Exercise 5

In the adverse selection model seen in Lecture 4

1. Find an explicit expression for the critical value a^∗ of the share of good projects.
   1. Describe what happens in equilibrium when a > a^∗ and when a < a^∗, providing economic intuitions.
   1. Determine how a^∗ depends on each of the parameters of the model (I, R, p, q).

Exercise 6

In the moral hazard model seen in the lecture, assume that the entrepreneur has no cash to invest in the project (A = 0). However, E is able to pledge collateral that could be repossessed by investors if the project is unsuccessful. Assume for simplicity that the contract is such that, if the project turns out to yield zero return, E makes a fixed transfer D > 0 to the investors. [If the project yields R > 0 then R_I is paid to the investors and R_E = R − R_I to E as in the lecture notes]. All other assumptions are as in the lecture notes. In particular, p_HR > I and p_LR + B < I.

1. Show that, if incentives are such that E exerts low effort in equilibrium, the project will not be funded.

Assume that p_H (R R_I) (1 p_H )D 0 (can you say why we need to assume this?). Write down E’s incentive compatibility constraint and show that the pledgeable income is now RI∗ ≡ R + D − B/(p_H − p_L).

• What is the effect of an increase in D on pledgeable income? What is the intuition for this effect? (Hint: an increase in D essentially relaxes the limited liability constraint).