1. Consider the following setup. Suppose that there are two agents A and B each holding 6 units of apples and 6 units of oranges as initial endowments. The utility functions of agents A and B are given by u (xA, yA) = xby and UB(XB, VB) = XB YB 1/5 where XA, YA, XB, VB have the same meaning as in the lecture. Let p, be the price of apples and py be the price of oranges. (a) Write down the budget constraint for each agent in terms of XA, YA, P,, Py for agent A and XB, VB, Px, Py for agent B. (b) Show that the demand functions for each agent are given by the expressions below. (c) Using the demand functions in (b), find the price p, of apples such that when the price of oranges py = 2, the market for both apples and oranges clear. (d) Using the prices in (c), calculate the amount of apples and oranges demanded by each agent. Also, calculate the amount of apples and oranges traded between agents A and B