tangent to the budget line. As the buyer obtains full insurance, also lies on the 45-degree line. This scenario is referred to as the (high effort, low insurance) outcome in what follows. What happens for a lower probability of the good state is indicated by a flatter in Figure 1. The budget line is also a decrease in probabilities. ‘flattened’ reflecting The equilibrium is represented by the point labelled where the new iso-expected-utility is tangent to the budget line . Note that the flattening of the budget line is the consequence of increased Arrow price indicating that the price of insurance will accordingly be more ‘expensive’. 2.2 Pareto efficient AD equilibrium with contractible effort So far, state probabilities have been treated as exogenous: what if they depend on the effort of the buyer? So long as the effort levels are contractible, the same equilibria can emerge, with the seller offering a of prices conditional on the observable effort of the buyer, where ‘menu’ the subscript and would now refer to High and Low levels of effort by the buyer as attached to prices on the menu. Which of the equilibria will emerge depends on the cost of effort to the buyer: in the example below, we find that, were it fully contractible, the buyer would choose High effort, with as the AD equilibrium. For analytical tractability we assume that effort level by the buyer is discrete, either zero or 1, with zero effort having no utility cost and the effort level of 1 having a utility cost of .The effort level of 1 generates a probability of good state to be and the effort level of zero generates where . If effort is fully contractible and , the equilibrium is (high effort, cheap Proposition 1. insurance). When effort is fully contractible, the only possible outcome would be either or in Proof: Figure 1. Since , buyer will choose high effort given the menu and the seller is indifferent. It is clear that this equilibrium is Pareto efficient. 2.3 Non-existence of AD equilibrium with non-contractible effort Specifically, the effort cost is assumed as
tangent to the budget line. As the buyer obtains full insurance, also lies on the 45-degree line. This scenario is referred to as the (high effort, low insurance) outcome in what follows. What happens for a lower probability of the good state is indicated by a flatter in Figure 1. The budget line is also ‘flattened’ reflecting a decrease in probabilities. The equilibrium is represented by the point labelled where the new iso-expected-utility is tangent to the budget line . Note that the flattening of the budget line is the consequence of increased Arrow price indicating that the price of insurance will accordingly be more ‘expensive’. 2.2 Pareto efficient AD equilibrium with contractible effort So far, state probabilities have been treated as exogenous: what if they depend on the effort of the buyer? So long as the effort levels are contractible, the same equilibria can emerge, with the seller offering a ‘menu’ of prices conditional on the observable effort of the buyer, where the subscript and would now refer to High and Low levels of effort by the buyer as attached to prices on the menu. Which of the equilibria will emerge depends on the cost of effort to the buyer: in the example below, we find that, were it fully contractible, the buyer would choose High effort, with as the AD equilibrium. For analytical tractability we assume that effort level by the buyer is discrete, either zero or 1, with zero effort having no utility cost and the effort level of 1 having a utility cost of .The effort level of 1 generates a probability of good state to be and the effort level of zero generates where . Proposition 1. If effort is fully contractible and , the equilibrium is (high effort, cheap insurance). Proof: When effort is fully contractible, the only possible outcome would be either or in Figure 1. Since , buyer will choose high effort given the menu and the seller is indifferent. It is clear that this equilibrium is Pareto efficient. 2.3 Non-existence of AD equilibrium with non-contractible effort Specifically, the effort cost is assumed as
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