In the other basic principal-agent model — the "moral hazard” model^{[1]} — the agent takes his decision e be for e he knows the value of the random variable θ, and the principal can observe neither the agent's decision e, nor the value of the random variable θ, but only the outcome of the agent's activity x. In this case the principal cannot force the agent to choose the decision e which would be the best from the principal's point of view. Consequently, the principal will enforce a contract rewarding the agent according to the outcome x. This results in a situation (as in the adverse selection model] where a competitive equilibrium either does not exist or is Pareto inefficient

Let us describe this model in greater detail for the case of one agent (and one principal, i.e. as assumed throughout this chapter).

Let us assume again that the principal is risk neutral and competitive (i.e. he is satisfied with zero expected profit as he does not want to lose a customer]. Contrary to the model in the previous section the expected loss is endogenous to the model (i.e. it is affected by the decision of the agent).

We assume that the agent (let's say an insured party) can — but does not have to — spend c money units to reduce the risk of loss. We also assume that the agent (unlike the principal] has information that:

• if he spends nothing (i.e. if c = 0), the probability of loss is π0 Î (0,1),

• if he spends c = c1, the probability of loss is π1 Î (0,π0),

As in the previous section we will denote the insurance premium by p, the level of cover provided by the insurance company by q (where, of course, q < L) and the initial level of income by y. The expected income of a prudent agent who has bought cover and spent cx to reduce the risk is:

If insurance companies have the same information as the insured (i.e. if they can check whether the customer has really spent money to reduce the risk of loss), a competitive market will lead to the Pareto optimal contract with full cover (q = L) and with a premium of p0 = L • π0 for imprudent customers and p1 = L•π1 for prudent customers. The expected profit of the insurance company will be zero.

If the insurance company is unin formed and credulous, it will offer the contract (L • π1, L). For the customer it is optimal to accept this contract and to spend no money on reducing the risk, i.e. c = 0. The expected profit of the insurance company is negative in this case — the insurance company creates losses due to its naivety.

As unin formed but suspicious insurance company will proceed similarly as in the adverse selection model — it will offer an insurance contract with partial coverage. Less risk-averse customers will not spend money to reduce the risk and will accept a contract with full cover and a higher premium, whereas customers with high risk aversion will pay such costs and will accept a contract with partial cover. The expected profit of the insurance company is zero (as in the case of fully in formed insurance companies).

By contrast, the insured is worse off than in the case of fully in formed insurance companies — he has either lower cover with the same expected income, or lower expected income with full cover. As in the adverse selection model, therefore, this equilibrium is not Pareto optimal.

This model represents a kind of market failure. The state can try to rectify this failure by means of tax policy. For example, in the health insurance area it can impose higher taxes on cigarettes to stimulate spending on reducing the risk (spending on nicotine addiction therapy), or in the property insurance area it can reduce indirect taxes on alarms or locks. This can lead to an improvement in Pareto efficiency. The problem, however, is that the government needs a lot of information about the preferences and the sets of feasible solutions for the decision-making problems of economic agents in order to set the optimal tax policy. But if the principal does not have this information, the state will not have it either.

A common problem of the moral hazard and adverse selection models, then, is that it is impossible to achieve an Pareto-efficient equilibrium and even impossible to achieve a contract that is beneficial for both sides. Hence, even if a market equilibrium exists, it is not Pareto optimal.

The assumed decision-making criterion of economic agents — namely maximization of the utility of expected income — is of course crucial to these conclusions. We will show that the generalization of agents' decision-making criterion to maximization of the probability of survival, together with the survival of the agent [conditional on the survival of the principal], can under some conditions guarantee the existence of a market equilibrium even in cases where such equilibrium does not exist if we use the criterion of maximization of the utility of expected income.

We will go on to show that the generalization of the profit-maximization criterion to maximization of the probability of survival for agents enables us to usefully model some situations characterized by two criteria per decisionmaking problem and imperfect information of one of the economic agents, with the interests of the principal and the agent being at least partially jointly satisfied.

[1] See Mirrlees, J. A.: The Theory of Moral Hazard and Unobservable Behaviour. Part I. Mimeo. Oxford: Nuffield College, Oxford University, 1975, or Holmstrom, B.: Moral Hazard and Observability. Bell Journal of Economics 10, 1(1979): 74–91.

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