Intermediate microeconomics

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Question 1 Donald and Joe have the following initial endowments of apples (A) and oranges (O): AD = 6, 0D = 6, A, = 6,0, =6 Donald's preferences are represented by the following utility function: Up (AD, OD) = AD3OD3 Joe's preferences are represented by this utility function: u, (A,, 0,) = A,30,3. a) Draw an Edgeworth box diagram with Donald in the lower-left corner and Joe in the upper-right corner, where consumption of oranges is measured on the horizontal axis and consumption of apples is measured on the vertical axis. Identify the initial endowments and draw the indifference curves of Donald and Joe consistent with these endowments. (5 points) b) Let PA and Po denote the prices of apples and oranges respectively. Calculate a competitive equilibrium when Donald and Joe decide to trade with each other. That is, find the equilibrium prices and the final (optimal) allocation of apples and oranges. Show your calculations. (15 points) c) Show graphically the Pareto dominating space given the initial endowments and show that the competitive equilibrium is Pareto-efficient. Explain what a Pareto-efficient allocation means for Donald and Joe. (5 points)