13.1 Observable Actions and Risk Neutrality

In the previous chapter, we analyzed adverse selection, a problem of asymmetric information that arises when a characteristic relevant to the payoffs — such as an individual’s risk level or a worker’s ability — is not observable by the other side of the market. While in our discussion of adverse selection we examined both the insurance and labor markets, in this chapter we will focus exclusively on the latter. Moral hazard is a relevant issue in both contexts and, in fact, originally emerged in the study of insurance markets. We develop the analysis in the labor market only to avoid making the exposition too heavy. In this chapter, we examine moral hazard, which arises when the unobservable variable is an action taken by one of the parties after the contract is signed. In our case, the hidden action is the worker’s level of effort, which affects the probability of success of a project undertaken by the hiring firm.

Consider a firm that must decide whether to continue offering its current product line, obtaining a certain profit equal to $\underline\Pi$ euros per week, We are therefore assuming that $\underline\Pi$ is the firm’s reservation profit, that is, the cost to the firm of foregoing its first alternative (keeping its line unchanged). For reasons we will explain shortly, we assume that $\underline\Pi<1875$. or hire a product design manager tasked with redesigning the line. The new project can succeed and generate revenues equal to 3000 euros per week, or fail and generate only 1000. The probability of success depends on the manager’s effort, denoted by $e$, which we assume is unobservable by the principal. If the manager exerts effort ($e=1$), the probability of success is $0.75$ and that of failure $0.25$. If instead the manager does not exert effort ($e=0$), the probability of success is $0.25$ and that of failure $0.75$.

We will assume that the principal is risk-neutral and therefore interested in maximizing expected profit. As for the manager, we will assume that he derives utility from his salary, that effort is costly, and that his best alternative employment guarantees him, without exerting effort, a certain wage equal to 225 euros per week, corresponding to a reservation utility equal to $\underline{U}$.

We will consider two cases:

• Risk-neutral agent. The manager's utility is his wage, net of the possible disutility of effort, which we assume to be 400. If he does not work for the firm, his utility is therefore $\underline{U}=225$. If he works for the firm receiving a wage $W$ his utility is $$U=W-400\times e$$

• Risk-averse agent. The manager's utility is the square root of his wage, and we assume the disutility of effort is 10. If he does not work for the firm, the manager obtains $\underline{U}=\sqrt{225}=15$, while if he works for the firm receiving a wage $W$ he obtains $$U=\sqrt{W}-10\times e$$

To make the problem interesting, we chose numbers such that it is socially efficient It is easy to see that, both in the risk-neutral and risk-averse cases, the agent is indifferent between (i) not working for the firm, (ii) working for the firm without exerting effort and earning a certain wage of $225$, and (iii) working for the firm exerting effort and earning a certain wage of $625$. Therefore, 225 and 625 measure, in euros, the cost to the manager of working for the firm without and with effort respectively. for the firm to hire the manager and for the manager to exert effort. This indeed produces a benefit (expected revenue) equal to $0.75\times3000+0.25\times1000=2500$ and a cost equal to $\underline\Pi+625$, thus a total surplus equal to $1875-\underline\Pi$, which is greater than zero (total surplus if the manager is not hired) by assumption. Moreover, hiring a manager who does not exert effort creates a smaller surplus: the benefit is $0.25\times3000+0.75\times1000=1500$ and the cost $\underline\Pi+225$, so the total surplus is $1275-\underline\Pi$.

Observable Actions

Will the two parties be able to generate the maximum total surplus possible? And whatever surplus they end up generating, how will they split it? Before addressing the first (and more important) question, let us answer the second. For simplicity, we assume that the firm captures all the surplus generated by the trade. How? By offering the manager a contract that the manager can only accept or reject. The contract specifies

• a base salary, denoted by $W_0$, which the firm pays the manager in any case;
• a performance bonus, denoted by $B$, which the firm pays the manager only in case of high revenues (success of the new line).

If the manager accepts, he will work for the firm: he will choose whether to exert effort or not, and once the results of his management are observed (success or failure of the project), the firm will pay him the agreed salary ($W=W_0$ or $W=W_0+B$). If the manager refuses, he will not work for the firm; he will then obtain his reservation utility $\underline U$, while the firm’s profit will be $\underline\Pi$.

Now, let us address the first question we posed. As we will see, the answer is generally negative. The problem lies in the fact that a crucial variable affecting the welfare of both parties, the manager’s effort, is not observable and therefore cannot be specified in the contract. This obstacle to contracting between the parties may prevent them from fully realizing the potential gains from the exchange.

To understand exactly when, how, and why such inefficiency arises, it is useful to take as a benchmark the ideal situation in which the firm can observe the manager’s level of effort and specify it in the contract. In particular, we will suppose for a moment that, in addition to base salary and bonus, the contract can include a minimum effort level: if the manager signs the contract, he cannot choose to exert less effort than stated in the contract. We call this situation first best because, as we illustrate below, it allows for the realization of the maximum total surplus through a contract that we will call first best contract.

From the figure, we can observe the following:

• In the case of a risk-neutral manager, any contract that specifies (i) a high level of effort and (ii) wages such that the expected salary equals 625, is a first best contract. By offering a contract with these characteristics, the firm obtains a profit equal to 1875 and therefore a surplus equal to $1875-\underline\Pi$, which is indeed the maximum total surplus.

• In the case of a risk-averse manager, there is only one first-best contract: the one that specifies (i) a high level of effort and (ii) a fixed wage equal to 625. This result should sound familiar. In Chapter 11, we saw that a risk-averse individual, being unwilling to tolerate variability in payoffs, is willing to accept a relatively low amount in exchange for certainty. This amount represents a cost for the firm, which will therefore aim to minimize it by offering a fixed rather than a variable payment.

Unobservable Actions and Risk Neutrality

When the manager’s effort is not observable, the contract cannot directly specify that variable. However, the firm can still try to incentivize effort through the wage structure: by using an appropriate bonus that encourages the manager to exert effort. The goal is therefore to design a contract that induces the manager to voluntarily choose to exert effort.

As we will now see, if the manager is risk-neutral, it is possible to design a contract that achieves the first-best allocation even in the absence of observability of effort. The contract must satisfy two properties:

• The participation constraint (also known as the individual rationality constraint): the manager must prefer accepting the contract over the outside option, that is, must obtain expected utility at least equal to $\underline{U} = 225$.
• The incentive compatibility constraint: the manager must prefer to exert effort rather than shirk, given the contract’s wage structure.

In the graph below, we can identify a contract that satisfies both constraints and allows the firm to achieve the first-best outcome. The curves $U_H$ and $U_L$ represent, respectively, the manager’s utility when exerting effort and when shirking. To ensure participation, the contract must be such that the points $L$ and $H$ do not both lie below the horizontal green line. To satisfy incentive compatibility, point $H$ must lie at a height at least equal to that of point $L$.

The contract identified allows the firm to obtain an expected profit of $2500 - 625 = 1875$, exactly as in the first-best case. With a risk-neutral agent, moral hazard entails no efficiency loss.