Incentives Q&A

MN404: Incentives and Governance in Organizations

Analytical Exercises
Sesssion 5
Question 1
Consider a problem in which a principal (P ) must delegate one task to a risk-neutral agent (A).
There are two effort levels e ∈ {0, 1}; and two possible outcomes (output or revenue levels): S ∈
0, S . The principal can offer a contract t, t in which t is a monetary transfer from the principal to the agent in case S happens, and t is a monetary transfer from the principal to the agent in case
S = 0. The agent’s utility is U − ψ(e), where effort disutility is given by ψ(0) = 0; and ψ(1) = 3.
The probability of S when effort is low is given by π0 = 0.3 and the probability of S when effort is high is given by π1 = 0.6.
For parts (1) and (2) of this question, suppose that P wants to induce A to pick e = 1.
1. Find the optimal contract, assuming no limited liability. Explain the intuition behind the optimal contract.
2. Now assume that there is limited liability, so that negative transfers are not allowed by law.
Find the optimal contract under this additional constraint.
3. (Harder) Discuss the conditions under which the principal would decide to induce e = 1, with and without limited liability.

Question 2
You have been hired to help start up a new, innovative, legal partnership in the City of London.
The head partner wants to design the compensation packages for his employees to ensure that the associates employed by the firm work hard. There is an effort cost of 10 in this firm, incurred by each associate when she works hard.
The firm consists of a group of partners and a group of new associates. Start by focusing on the wage levels and trajectory of the new associates: To simplify, we will assume that there are only
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two employment periods.
You want to design a 2-period contract that specifies the fixed wage that you will pay the new associates in the first stage of their employment and then the fixed salary they can expect to receive if they are promoted to partner at the end of that first stage. Partners do not exert effort. The two salary levels are denoted (Wt , Wt+1 ).
The outside alternative payoff (wage less effort cost) for the type of lawyers you want to hire is
Vt in the first stage of their career and Vt+1 in the second stage (irrespective of where they work in the first period). If an associate works hard in this new firm, she will be promoted to partner at the end of the first period. If she does not work hard, there is some probability that she will be lucky and still get promoted but, with probability p, the partners will realize she is a lazy lawyer and fire her.

a) First, assume the lawyer has signed the contract, how much does his expected wage as partner have to be in order to induce him to exert effort in his first period as an associate?

b) In order for a new lawyer to sign the employment contract as an associate in this firm, what condition must hold for his career payoffs? That is, find his individual rationality constraint, which, if satisfied, means he will join the firm. (Note: the lawyer will not exert costly effort if he is promoted to partner, only receive the payment Wt+1 that you found in part (a)).

c) Having discussed extensively with the partners, you are convinced that the outside option of each new lawyer they want to hire is constant over time (so Vt+1 = Vt ). Write down the wage contract for a new associate in the firm. Be sure to specify Wt and Wt+1 and the promotion rule.

d) Having successfully implemented this compensation structure in the new law firm, you are contacted by a second new law firm. The expected outside options of lawyers in each stage of their careers are the same as in part (c), but this firm is in a slightly different area of law. In this area, partners work much more closely with associates than in the first firm. This means that if an associate is not working hard, it is much easier for the partners to be able to tell. And, if the

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associate is being lazy, the partners will fire him, so p is much higher in this firm.
How does this difference in the nature in the work across the two firms affect the optimal wage trajectory of lawyers in each firm? Which associates see a larger raise when they are promoted?
Which associates have a higher entry-level salary?

e) In this second new law firm, the partners also need to hire some specialized lawyers who have expertise in offshore tax law. These lawyers have the same outside option as the regular new lawyers, of Vt , in the first stage of their careers, but can earn enormous salaries in the Cayman
Islands in the second stage of their careers (independent of where they work in the first stage).
Does this affect how much these lawyers need to be paid as associates in order to ensure that the tax specialists work hard in this stage?

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