This is a scenario where a Principal has different options of setting wages and

Question

This is a scenario where a Principal has different options of setting wages and the Agent has different levels of work. Consider this model with the following special values:

u(2w); dH=15, dL=0, g=300, m=200, b=100, wb=wage base=0

eH results in a probability of profit levels g, m, b as 0.5, 0.3, 0.2

eL results in a probability of profit levels g, m, b as 0.2, 0.3, 0.5

Assuming the Principal chooses a pure wage scheme, what would be the expected payoffs for the Principal and the Agent?

Assuming the Principal chooses a pure franchise scheme, what would be the maximum franchise fee? What would be the expected payoffs for the Principal and the Agent?

Assuming the Principal chose a wage plus bonus scheme, what is the minimum bonus to induce eH? What would be the expected payoffs for the Principal and the Agent?

In this scenario, what should the Principal choose to do?

Explanation / Answer

In their model the shareholders’ problem is to design a wage contract or mechanism that induces the manager to maximize stock value. This problem have become classic in the principal-agency literature.

Hart and Holmström consider four cases. In all cases the agents and the principals are perfectly rational and they pursue utility maximization (full opportunism). The shareholders are assumed to be risk neutral. Normally, this is a terribly unrealistic assumption, but not in this case. It is reasonable to believe that the introduction of risk averse stockholders would not change the implications of the models as long as the risk aversion by the stockholders are significantly less than the risk aversion by the manager. Furthermore, it is realistic to expect that shareholders are less risk averse than managers because they are more capable of diversifying their portfolios and/or because managers may have a large portion of their wealth in the firm they manage (risk aversion normally increases by the share of ones wealth at risk). The assumption of risk neutral shareholders is therefore unimportant for the economics of the models.

CASE 1: The shareholders have full information (perfect monitoring) about management effort. This case is trivial. The shareholders can implement the profit maximizing optimum by threatening with severe punishment, should the manager not render the efficient level of effort. Furthermore, because the manager is risk averse the optimal wage contract will have to pay the manager at a fixed salary (full insurance) equal to his reservation salary evaluated at the optimal level of effort.

CASE 2: Now, the manager is risk neutral, but the shareholders only observe profit. They cannot observe the manager’s effort level. This is, asymmetric information. The optimal solution is to design a wage contract that pays the manager the entire profit, less a fixed amount equal to the expected total profit, less the manager’s reservation salary. In effect, the manager is made the residual claimant of the firm’s profit, as if he was the sole owner of the firm (no insurance). On average, the manager gets his reservation salary only if he chooses the efficient level of effort. Therefore, the solution is first best like it was in case 1.

CASE 3: Now, the manager is assumed to be infinitely risk averse, and the shareholders remain unable to observe manager effort (asymmetric information). An implication of infinite risk aversion is that the manager will avoid any risk at any cost in mean return. This outlaw wage contracts that tries to induce higher effort by higher pay for higher profit. Therefore, the principal can do no better than paying the manager a constant salary (full insurance) equal to the reservation salary evaluated at the minimum effort level. Note that the agent always chooses the minimum effort level because he knows that the principal cannot observe it. The outcome of this model is clearly second best.

CASE 4: Now, the manager is assumed to be normally risk averse and the shareholders can still not observe manager effort, only profit (asymmetric information). These are very sensible assumptions why this case is the most interesting from an economic point of view. The best possible solution is to make the wage an increasing function of profit in order to induce profitable effort levels. Unfortunately, this makes the salary risky, and the agent will suffer a utility loss by not being fully insured. The wage contract will have to compensate the agent for this loss.

Comparing the models with asymmetric information (case 2,3, and 4), it can be proved that case 4 is the situation between the to extremes; case 3 (infinite risk aversion, constant salary, minimum effort) and case 2 (risk neutrality, residual payment, social efficient effort). Case 4 has medium risk aversion, a profit dependent salary, and the manager exert an effort below the socially efficient but above the minimum level. Furthermore, case 1 and

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