[30 points] Consider a two-period economy populated by two agents. Both agents have lifetime utility given by: log c i 1 + log c i 2 , 0 < < 1 (1) where c i 1 and c i 2 denote agent is consumption in periods one and two, respectively. Agent 1 is endowed with one unit of goods in period one but receives no endowment in period two. Agent 2 is endowed with one unit of goods in period two but receives no endowment in period one. Consumption has a unit price in both periods. The agents can borrow or lend at gross interest rate 1 + r. (a) Define a competitive equilibrium for this economy. (b) Solve for the competitive equilibrium in this economy. (c) Is there any savings in this economy? Why or why not? (d) Plot the equilibrium consumption bundles over the domain of . Interpret your figures.