Consider the portfolio choice problem with only a risk-free asset and with consumption at both the beginning and end of the period. Suppose the investor has time additive utility with u₀ = u and u₁ = u for a common function u and discount factor . Suppose the investor has a random endowment at the end of the period, so he chooses c₀ to maximize:

u(c₀) + E[u((w₀ - c₀)R_f + )]

Suppose the investor has convex marginal utility(u''' > 0) and suppose that E[] = 0. Show that the optimal c₀ is smaller than if = 0