3. (25\%) Consider an exchange economy with two agents, Dan and Eve, and two goods, x and y. The utility function of Dan is UD(xD,yD)= xD(yD+80), and that of Eve is UE(xE,yE)=xE+2yE, where (xD,yD) and (xE,yE) are the bundles that Dan and Eve consume, respectively. 3 Each agent has an initial endowment of 100 unit of x and 100 unit of y. (1) Draw the Edgeworth box for Dan and Eve. Label their initial endowment point. Draw the indifference curve for each agent that passes through the initial endowment point. Is the initial endowment a Pareto optimal allocation? Explain. (2) Draw and describe clearly the contract curve and the core. (3) Find the competitive equilibrium price ratio and allocation. (4) If Eve can dictate the price ratio, what price ratio will she choose? Is the resulting allocation Pareto efficient