Answer all parts Consider a two-state model insurance-purchase decision of a risk-averse individual with income endowment y. The income endowment available for spending on consumption (i.e. prior to the incurring of any loss, or expenditure on accident prevention costs and / or insurance purchase) is denoted y. Income net of any accident prevention and/or insurance prevention costs is y1 in the good state of the world (i.e. when there occurs no loss) and y2 in the bad state (i.e. when a loss of amount L occurs). The probability of an accident which results in loss of amount L occurring is denoted ? and is a monotonically decreasing function of ai, the amount spent by the individual on care (accident prevention), i.e. ? = f(ai), and ?? / ?ai ? f ? (ai) < 0. For each of the parts below, diagrams should be drawn so that y1 (income in the good state) is measured on the vertical axis, while y2 (income in the bad state) is measured on the horizontal axis, so that the initial endowment point (i.e. that for ai = 0) is situated above the certainty line. Given this information: (a) Assuming a competitive insurance market, and that insurers are able to observe fully each individual customer’s volitional choice of ai, provide a diagrammatic analysis with accompanying discussion of how the value of ai affects the equilibrium. (25%) (b) Again assuming a competitive insurance market, and full observability of each individual’s expenditure on care, depict and discuss the equilibrium that would arise when the government compels individuals to spend a specific amount aˆ on care, such that the individual’s expected utility is lower in equilibrium, in spite of any insurance cover purchase, than it would have been had the individual not been compelled to spend aˆ on care. Describe and explain also how the representation of the equilibrium would differ if the government’s requirement that aˆ be spent on care were to lead to the individual’s expected utility in equilibrium being higher than when there is no such requirement. (25%) (c) Assuming once again that the individual is free to choose their level of care (ai), which must now take either one of two values, a0 (low) or a1 (high), where 0 ? a0 < a1, analyse with appropriate diagrams the competitive equilibrium when insurers cannot observe each individual’s choice of ai. Your accompanying discussion should explain, inter alia, the optimal design of the insurance contract and the welfare implications of the non- observability of actions. Proceed to discuss, explain and depict the potential welfare impact in this situation of a policy consisting of both a lump-sum tax and a subsidy. (50%) Guidance Note (i) You are neither required nor expected to make use of the Kuhn-Tucker optimization procedure in preparing their answers.
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