We analyze a Principal-Agent model of an insurer who faces an adverse selection problem. He is unable to observe if his client has a high risk or a low risk of having an accident. At the underwriting of the contract, the insurer requests the client to declare his risk. After that, the former can costly audit the truthfulness of this announcement. If the audit confirms a false declaration, the insurer is legally allowed to punish the defrauder. We characterize the e¢cient contracts when this punishment is bounded from above by a legal restriction. Then, we do some comparative statics on the efficient contracts and on the agent’s utility. The most important result of this paper concerns the legal limit to a defrauder’s punishment. We prove that there exists a unique value of this legal limit that maximizes the expected utility of a high risk type. Facing this particular value of the legal limit to a defrauder’s punishment, the insurer will effectively audit a low risk report. We also show that this particular value increases with the probability of facing a high risk policy- holder. Therefore, when this probability is su¢ciently high, the nullity of the contract is not enough. From the point of view of a potential defrauder, the law should allow harder sanctions. This is an striking result because the nullity of the contract is a common sanction for this kind of fraud in the USA and in some European countries.
