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3. (14 points) Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 6 units of good X and 1 units of good Y. Consumer B is given an initial endowment of 2 units of good X and 7 units of good Y. Consumer A 's utility function is given by: UA(X,Y)=XY And consumer B's utility function is given by UB(X,Y)=XY3 Therefore, consumer A's marginal utilities for each good are given by: MUX=YMUY=X Also, consumer B's marginal utilities for each good are given by: MUX=Y3MUY=3XY2 a) (6 points) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium. PX= b) (8 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 : 3. (14 points) Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 6 units of good X and 1 units of good Y. Consumer B is given an initial endowment of 2 units of good X and 7 units of good Y. Consumer A 's utility function is given by: UA(X,Y)=XY And consumer B's utility function is given by UB(X,Y)=XY3 Therefore, consumer A's marginal utilities for each good are given by: MUX=YMUY=X Also, consumer B's marginal utilities for each good are given by: MUX=Y3MUY=3XY2 a) (6 points) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium. PX= b) (8 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

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