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Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B

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Consider a pure exchange economy with two consumption goods, X and Y, and two consumers, A and B. There are 20 units of Xand 20 units of Y in the economy. The preferences of the consumers are represented by the following utility functions: UAXXA) = Xx + 2YA UB (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? 17 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] ? 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 Yis1 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?