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Insurance Model: Competitive Contracts - Essay Example

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We consider a model with a large number of firms and a large number of rational risk-averse consumers with standard preferences. The consumers have an initial wealth W and there is a possibility of an accident that causes damage D. We shall set up the insurance model as one of trade where the firm offers the consumers state contingent claims in return for their initial endowments…
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Insurance Model: Competitive Contracts
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Download file to see previous pages 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 competitive firms The representative competitive firm’s objective is to maximize its expected profits or alternatively minimize its expected costs by trading with the consumer. Each firm 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. If P is the probability of a claim, then the expected costs of the firm 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. Competitive equilibrium A crucial point to note is that because the market is competitive, the firm can make only zero profits in equilibrium. Therefore, the equilibrium contract will ensure that the cost is equal to the value of the consumer’s endowment such that revenue equals cost. We start off by considering the possibility of pooled and separating equilibriums under asymmetric information. Competitive pooling 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 context 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 firms are perfectly aware of the exact probability distribution of consumer types. A pooling contract will offer the same good state bad state consumption claims to both types of consumers. That is, a single contract will be available for both types. There are three participation constraints that must be satisfied, two for either type of consumers and one for the firm. 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 initial endowment ...Download file to see next pagesRead More
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