ABSTRACT
These assumptions imply that all agents will make investments in T = 0, but type 1 agents will want to liquidate their investments in T = I while type 2 agents will consume their investments when they mature in T = 2. If agents decide to invest autarkically, they are guaranteed returns of 1 if they turn out to be type 1 and choose to liquidate their investments in T = I, and R if they turn out to be type 2 and keep their investments until T = 2. However, since they are risk-averse and know the proportion of types, there is presumably some scope for mutually beneficial risk-sharing against the 'unlucky' event of turning out to be type 1. If we let Cj,i represent the consumption of a type i agent in period j, this 'insurance' would involve CI,I > 1 and C2,2 < R, and Diamond and Dybvig show that an optimal insurance contract exists and satisfies
(where the * denotes optimality). The first condition comes from noting that type 1 households derive no utility from consumption in period 2, and vice versa; the second indicates that marginal utility is in line with marginal productivity, and the third is the resource constraint. Note that pR > 1 and the second condition in (3) imply that CI,I* < C2,2*' It follows, then, that the optimal outcome satisfies the self-selection constraint that no agent has an incentive to misrepresent his type - type Is have no incentive to represent themselves as type 2s, since CI,I* > 1 > CI,2* = 0, and type 2s have no incentive to misrepresent themselves, since C2,2* > CI,I*'
V2(f,rl) = max [R(I-rJ)/(I-f), 0] (see Diamond and Dybvig 1983: 408).7
