WCAS - Economics of Banking and Insurance Asymmetric Information

Asymmetric Information

These questions are due by the end of the week. As usual, upload your answers to Canvas. Do not hesitate emailing me if you have any questions about the assignment.

Question 1:  Adverse selection and Signaling

In the class, we have covered the adverse selection problem and we went over the concept of signaling through self-inancing.  As we discussed, the cost of capital is increasing in the share of self-inancing, α . This means that the signal is costly.

  Explain in your own words the concept of the cost of capital being increasing in α and

derive (for the parameterization explored in class) how capital costs change with α .

  When a major league baseball players contract has expired, he can either sign a new contract

with his current team or become a free agent and sign a contract to play with a diferent team.  If adverse selection is a problem in the market for major league ball players, who do you think are more likely to be injured the season after they sign a new contract:  players who re-sign with their current team or players who sign with a new team?  Explain.  How can the player signal his type? What kind of incentive compatible contract can be written to mitigate adverse selection?

Question 2:  Holmstrom and Tirole 1997

The objective of this question is to derive the conclusions of the model that we didn’t cover in the last slides of Lecture 4. We will cover the material next class, so this will help you understand the theory underlying the moral hazard problem beforehand.  These models are highly stylized, but the real value is in understanding how from a simple set up, robust conclusions can be derived and have policy implications. You can also follow this in the textbook, section 2.5.3.

There are three types of agents: irms, represented by the index f, banks, represented by the index m, and depositors, represented by the index u.  Each industrial project owned by the irms has the same cost, I, and returns y, which are veriiable, in case of success and nothing in case of failure. There are good projects, with probability of success pH , and bad projects, with probability of success pL . Bad projects give a private beneit to the borrowing irms, B . If the bank monitors, at cost C, the beneit is reduced from B to b. Investors are risk-neutral, uninformed, and cannot monitor the irms. There is a risk free asset that pays 1+ r . Only good projects have positive NPV (like in the slides, pH y > 1 + r > pLy + B .

Firms difer in their capital A, which is public information. The distribution of capital among the continuum of irms is represented by a generic cumulative distribution function G(A). Bank’s aggregate capital is exogenous, Km .

  In the case of direct inancing (depositor-irm): Derive the minimum amount that irms need

to promise investors. What is hte maximum amount a irm can directly borrow as a function of its initial capital A?