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# Incentives Q&A

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Topics: Employment, Salary, Law
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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