2. (40 points) Consider an economy with a unique good and three datesdates 0, 1, and 2with a storage technology that yields a zero net interest and a long-run technology that yields R = 1.2 units with certainty at date 2 but yields only 3 = % if prematurely liquidated at date 1. Both technologies are available to any agent. A continuum of agents of unit mass is endowed with 1 unit at date 0. Of these agents, a proportion 7T1 = % will prefer to consume at date 1 (and nothing at date 2; they are labeled 'early consumers'), and the complementary proportion W2 2 % will prefer to consume at date 2 (and nothing at date 1; they are labeled 'late consumers'). The agents' utility function is u(c) = c'1. (a) (10 points) Find the Pareto optimal allocationconsumption of early and late types, and optimal investment into the long-run technologyand the ex ante utility of agents under this allocation. (b) (2 points) In this setup, we have shown that the market allocation will result in the optimal consumption of early types below the Pareto-optimal level, and con- sumption of late types above the Pareto-optimal level if the coefcient of relative risk aversion for an individual's utility function is above 1, i.e., if i[cu'(c)]