8. Consider a two-date (one-period) economy and an agent with utility function in each period u(c)...

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8. Consider a two-date (one-period) economy and an agent with utility function in each period u(c) so that u'(c) > 0 and u"(c) <0. Define the objective function as V(C₁, C₂) = u(c₁) + u(c₂). Show that the agent will always prefer a smooth consumption stream to a more variable one with the same mean, that is, u(e) + u(e) > u(c₁) + u(c₂), where = (₁+₂). 8. Consider a two-date (one-period) economy and an agent with utility function in each period u(c) so that u'(c) > 0 and u"(c) <0. Define the objective function as V(C₁, C₂) = u(c₁) + u(c₂). Show that the agent will always prefer a smooth consumption stream to a more variable one with the same mean, that is, u(e) + u(e) > u(c₁) + u(c₂), where = (₁+₂).