Insurance Model Essay Example | Topics and Well Written Essays - 1000 words

Insurance Model - Essay Example The consumers have standard preferences defined over consumption. If P is the probability of the loss, then the consumers expected utility is: Thus, we can have the following indifference curve: It is simple to show that this leads to negatively sloped convex indifference curves. The slope of the indifference curves are: The high risk and low risk groups differ in their probabilities of incurring the loss. The probability of accident of an individual consumer belonging to the high risk group is PH and that of one belonging to the low risk group is PL, where PH> PL. Figure 1 below shows the indifference curves for a particular utility level for representative agents from the two groups. Observe that since PH> PL the indifference curves for the high risk type will have flatter slopes (less negative). Figure 1: Indifference curves for the high risk and the low risk consumers The monopolist The monopolist’s objective is to maximize its expected profits or alternatively minimize it s expected costs by trading with the consumer. The monopolist offers a pair of contingent claims (G,B) which realize in the good (No loss) and bad (loss) states in return for the consumers initial endowment. The expected costs of the monopolist are equal to: We can form the Iso-cost function for the monopolist as follows: Evidently, these are straight lines with a slope of . Observe that since PH> PL the Iso-cost line for the high risk type will have a flatter slope (less negative). Thus, the iso-cost lines for the High risk type and the low risk type can be drawn as follows: Figure 2: The iso-cost lines for the monopolist insurer for high risk and low risk contracts – C(H) represents the iso cost line for the high risk types and C(L) represents the isocost line for the low risk type. The separating equilibrium under asymmetric information Recall that asymmetric information is a situation where one or some of the players of the game have private information. In the present co ntext the asymmetric information is manifested in the form of consumers having private information since they know whether they belong to high risk or low risk groups. The firm does not know any particular agents type. However, the monopolist is perfectly aware of the exact probability distribution of consumer types. A separating equilibrium in the present context would be one where the high risk types choose a contract that is different from the contract chosen by the low risk types. The monopolist firm’s objective is to minimize its costs subject to the participation constraint or the individual rationality constraint and the incentive compatibility constraint of the consumer. The participation constraint requires that the contract offered by the firm provides him at least as much expected utility as the consumer’s initial endowment. This implies that for any consumer to accept the firms offer, the contract has to lie on or above the indifference curve through the in itial endowment. The incentive compatibility constraint on the other hand requires that consumers of either type do not find it beneficial to accept the contract devised for the other type. It is essentially the satisfaction of this constraint that leads to the separating equilibrium. In terms of indifference curves, the incentive compatibility constraint requires that the contract for the high type lies on or below the low types indifference curve