# MORAL HAZARD IN THE CONTEXT OF PROBABILITY OF SURVIVAL

In the moral hazard model we again assume only two entities — a principal and a single agent. We consider the accident probability π to be an endogenous variable here. The agent can (but need not) spend money to reduce this probability. He will do so if it will increase his probability of economic survival. Let us denote the cost of reducing the risk by c. When the agent spends c > 0, the original (unreduced) accident probability π(0) = π0 decreases to π(c) Î (0,π0).

We again assume that the agent cannot exist independently — if the principal perishes, the agent perishes as well:

The principal maximizes his expected income:

The probability of economic survival of the principal is:

Expenditure on reducing the accident probability will increase the principal's probability of survival:

For the agent, expenditure on reducing the accident probability reduces the first multiplicand in (**). The second multiplicand increases, so the effect of spending c on the agent's utility (i.e. on his probability of survival) is given by the difference:

The sign of the difference va(c) - va(0) is driven by the relation of the extent of the threat to the agent and the principal. If the agent regards the principal as "indestructible”, he will not spend the cost and will transfer his risk fully onto the shoulders of the principal. The agent will thus pay va(c) – va(0) < 0. The more endangered the principal is in the eyes of the agent, the bigger is the difference va(c) - va(0). For an extremely threatened principal it certainly holds that va(c) – va(0) > 0. Hence, there is definitely some threshold above which the agent will not voluntarily practice moral hazard and will spend to reduce the accident probability in the interests of both parties.

# COMPARISON OF THE STANDARD HOMO ECONOMICUS WITH A SURVIVAL-PROBABILITY-MAXIMIZING AGENT

The above analysis has demonstrated that the problem of information asymmetry (specifically, the problems of adverse selection and moral hazard) is much weaker in a model economy where agents maximize their probability of economic survival than in the standard economic climate of agents maximizing their expected profit, where the utility of the agent is in an antagonistic relationship with that of the principal.

We have shown that the adverse selection problem — where contracts are signed by the most risky agents — disappears if the survival of the agent is contingent on the survival of the principal. In fact, the opposite applies — the most risky agents do not enter into the contract because paying the premium increases their probability of economic extinction even if no accident occurs. Under these conditions (in contrast to the standard adverse selection model) a competitive-equilibrium and Pareto-efficient pooling contract can exist where the insurance company offers one contract to all. If the survival of the agent is only partially contingent on the survival of the principal, the adverse selection problem reappears, albeit to a lesser extent than in the case of maximization of expected income.

The moral hazard problem — where the principal is unable to verify whether the agent has spent money to reduce his accident probability — also disappears to some extent. If the threat to the principal relative to the threat to the agent (in the assessment of the agent) is above a certain threshold, the agent will voluntarily spend to reduce his accident probability and will therefore not practice moral hazard.

For both models analysed (adverse selection and moral hazard) the assumed maximization of the probability of economic survival by agents implies that a Pareto-optimal equilibrium can exist with a pooling contract with full accident cover provided by the principal. This is the main difference from the standard model with decision-takers maximizing their expected income.