6. Suppose two individuals, A and B, each have 10 hours of labour (one input only, no capital) to devote to producing two goods x and y. The production functions are 2 = 2L, and y = 3L,, utility functions are UA = 2%*%' and UB = xys5 and initial endowments, as mentioned above, are L A = 10 and LB = 10. (a) Find the production possibilities frontier (PPF) in the format of y = f(x) when the resource (labour) is used efficiently (3 points) (b) Solve for the market clearing prices Pz and P, assuming labour price (wage rate) W = 1 dollar per hour (normalized price, note that only one price can be normalized) that would balance the aggregate demand equal to the aggregate supply of the two goods x and y (5 points) (C) How should the resource (labour) be allocated (L, and Ly) for production of x and y to satisfy the demand calculated in (b)? (2 points) 6. Suppose two individuals, A and B, each have 10 hours of labour (one input only, no capital) to devote to producing two goods x and y. The production functions are 2 = 2L, and y = 3L,, utility functions are UA = 2%*%' and UB = xys5 and initial endowments, as mentioned above, are L A = 10 and LB = 10. (a) Find the production possibilities frontier (PPF) in the format of y = f(x) when the resource (labour) is used efficiently (3 points) (b) Solve for the market clearing prices Pz and P, assuming labour price (wage rate) W = 1 dollar per hour (normalized price, note that only one price can be normalized) that would balance the aggregate demand equal to the aggregate supply of the two goods x and y (5 points) (C) How should the resource (labour) be allocated (L, and Ly) for production of x and y to satisfy the demand calculated in (b)? (2 points)