Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B. There are 20 units of X and 20 units of Y in the economy. The preferences of the consumers are represented by the following utility functions: U(X Y )= X + 2Y U' ( X Y ) = 3(X )Y, a. Suppose that initially consumer A has 10 units of X and 10 units of Y, while consumer B has all the remaining units of the two goods. Is this allocation Pareto efficient? [7 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. [8 marks] c. Now suppose initially A has all the available units of X and B has all the units of good Y. The price of X is 1 and the price of good Y is 1 as well. Write down expressions for the budget constraints for A and B. How much X and Y will be demanded at these prices? Do these prices and quantities form a general competitive equilibrium? [10 marks]