Question

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^{B}\left(X_{B} Y_{B}\right)=3\left(X_{B}\right)^{2} Y_{B} a. Suppose that initially consumer A has 10 units of X and 10 units of Y, while consumer Bhas 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] U^{A}\left(X_{A} Y_{A}\right)=X_{A}+2 Y_{A}

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