Assume the investors have time-additive utility and the date1 allocation solves the social planners problem (4.1). Using

Question:

Assume the investors have time-additive utility and the date–1 allocation solves the social planner’s problem (4.1). Using the first-order condition (3.9), show that the equilibrium allocation is Pareto optimal. Hint: Using the first-order condition

(4.4) with η˜ = ˜η1, show that

(∀h) λhu

h0(ch0) = RfE[ ˜η1].

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