By Elhanan Helpman

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DECISION MAKING UNDER UNCERTAINTY Note that only holdings of security a provide income in state a. ,ρΝ(χ);ΑΗ(<χ)]. Turning to portfolio decisions, individual /? 8) choose Ah(\\Ah(2\ . . ,Ah(S) to maximize a=1 subject to s Σ Φ)ΑΗ(*) < Σ <*(« Σ Σ P>)*/*(a) a= 1 where JJ= ι pMeih^) is ^'s endowment of security a, and it equals the value of his commodity endowment in state a. In equilibrium the demand for good / in state a equals its supply. 9) Σ ? » = Σ h = 1 Λ= 1 */W / = 1,2 TV, oc= 1 , 2 , . .

The nature of these results can be described as follows. Consider the home country which has an endowment of e{a) units of the single good in state a, a = 1,2. 20) choose c(l), c(2) > 0 to maximize W[c(l),c(2)] = π(1)ιι|>(1)] + TC(2)U[C(2)] subject to c(l) + gc(2) < e(l) + ge(2) where g = g(2)/g(l) is the relative price of state-2 contingent goods, and π(α) is the subjective probability assessment of state a. 20) occurs at a point at which g equals MRS^ on the budget line. This is a standard result in consumer theory, and we can represent the present solution by means of indifference curves and budget lines.

The amount of money paid by a security depends on the state of nature that realizes. Security a pays 1 dollar if state a occurs or zero if a different state occurs. There are precisely S such securities. Trade in securities takes place at the beginning of the period. Then, when a state a occurs, trade in commodities takes place. Let q(oc) be the price of security a, and pf (a) the price of commodity i in state a. Consumer h solves a two-stage decision-making problem. In the first stage, before the resolution of uncertainty, he determines his portfolio; in the second stage, after the resolution of uncertainty, he uses portfolio returns to purchase commodities.

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