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1. Suppose there are two consumers, A and B. The utility functions of each consumer are...

1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = X*Y UB(X,Y) = X*Y3 Therefore: • For consumer A: MUX = Y; MUY = X • For consumer B: MUX = Y3; MUY = 3XY2 The initial endowments are: A: X = 10; Y = 6 B: X = 14; Y = 19 a) (40 points) Suppose the price of Y, PY = 1. Calculate the price of X, PX that will lead to a competitive equilibrium. b) (16 points) How much of each good does each consumer demand in equilibrium? Consumer A’s Demand for X: Consumer A’s Demand for Y Consumer B’s demand for X Consumer B’s demand for Y c) (8 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium?

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