1. Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B. There are 20 units ofX and 20 units on in the economy. The preferences of the consumers are represented by the following utility functions: UA(XA, YA) = XA + YA UB (X3, Y3) = (YB)2 X3 a) Suppose that initially consumer A has 4 units of X and 16 units of Y; and that consumer B has 16 units of X and 4 units of Y. Is this allocation Pareto efficient? What are the utility levels of A and B at this allocation? [5 marks] b) Sketch the indifference curves and the initial allocation on an appropriate diagram. In your diagram identify the area where there is scope for a Pareto improvement and explain why this is the case. [5 marks] c) Explain what the contract curve is and derive its formula in this example. Sketch it into your figure from part (b). What is the marginal rate of substitution on the contract curve? [8 marks] d) The general competitive equilibrium in this economy is (XA = 13.333, YA = 6.667). Locate this point on your diagram and describe the trade that achieves it. Explain intuitively why individual A does not gain from trade in this case. [7 marks]