## Info

Excellent

From 85% on

100 Rs

From 5.5 on

A working hour for financially oriented activities costs the agent 7Rs, and working for alleviating poverty costs 5Rs. Compute the optimal time allocation for the manager of the MFI, and for the agent. Explain your answer.

9. Consider two financial institutions. Each institution employs two loan officers (henceforth: agents), and both institutions have the same objectives: financial self-sustainability and poverty alleviation. Assume that the agents are identical and risk-neutral and that they work eight hours per day. Each working hour costs four rupees. Institution A applies a balanced incentive scheme: Agents are rewarded for meeting both objectives. Suppose the agents' evaluations take the following form:

Evaluation

Working time division by the manager

Salary/day (rupees)

Good

Excellent

If the agent spent less than two hours working for at least one of the two objectives

If the agent spent 3-3.5 hours working for both objectives

If the agent spent four or more hours working for both objectives

20 Rs (the minimum level of salary)

### 6ORs lOORs

Institution B, on the other hand, applies a different incentive scheme: One agent will specialize in obtaining financial self-sustainability, and the other in alleviating poverty:

Evaluation levels

Working time division by the agent

Salary/day (rupees)

Good

Excellent

If the agent spent less than or equal to four hours working for the objective required

If the agent spent more than or equal to six hours working for the objective required

If the agent spent more than or equal to eight hours working for the objective required

20 Rs (the minimum level of salary)

### 6ORs lOORs

The production function (also the utility function for the two institutions) is q = x2 + y2 where x and y are, respectively, the time spent on financially oriented activities and in poverty alleviation. Show that this production function indicates that specialization will make the agent more effective. Draw the function. Compute the optimal choice for the agent in institutions A and B, and compute the maximum utility for each institution.

10. Consider a model with competitive and risk-neutral principals and a risk-neutral agent. The agent may be of two possible types (abilities) 6e {1; 0.5} with respective probability v = -and 1 - v = There are two periods t = 1 and t = 2 and no discounting. The agent's output q in each period may take two possible values, zero and ten, with respective probabilities (1 - 6p); 6p where p = 1 if he exerts effort and p = 0.6 otherwise (effort is unobservable). The cost of effort for the agent is e = 1. We assume that there is perfect competition between alternative principals in order to attract the agent in period 2. Also, neither the agent nor the principals are informed of the ability of the manager. In addition, the principal cannot write contracts conditional on the production level (the production level is observed but not verifiable). The first-period wage is a fixed wage t1, while the second-period wage may depend on past observation t2(q). The timing of the model is as follows:

Compute the posterior belief held by the market on the agent's ability after the first period has been observed. Compute the fixed wage t2 offered to him in the labor market. By comparing the expected payoff when the agent puts forth effort and when he does not put in effort, state whether it pays to put in effort. If the agent lives for one period only, will he put forth any effort?

11. Consider the same scenario as in exercise 10. But in this case, 6 e Q = {6; 6} where 6 = 1; 6 < 1 and the probabilities of being a high type and low type are respectively v;(1 - v). The output can take two possible values q or 0. And p can be 6, p and 6 = 1. The cost of effort is e. Write the incentive constraint of the agent that needs to be satisfied in order to elicit a high level of effort from him.

12. Again, consider a similar problem to the one spelled out in exercise 11, but in this case the agent's effort in each period is observable. His ability remains unknown, however, for both the market and the agent. Compute the explicit incentive constraint that needs to be satisfied in order for the agent to put an adequate effort level. Show that implicit incentives can only be imperfect substitutes to the explicit monetary incentives obtained via a wage that is linked to performance.