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Exercise 28.3 Consider a two good, two individual endowment economy. Suppose that indi- vidual i 's endowment is given by: Hi = (0);, Ni) and individual 2's, endowment is given by: \"j = (\"41%) 3 where we assume that w; > oi. and or; > mg. Also assume individual 1's preferences are given by: U (my) = 0105(3) + (1 a) 105 (y) and individual 2's preferences are given by: Way) =iloe(a=) + (1 - 7) 103(9)- Finally, let the absolute prices of good 2 and good y be given by p: and py. a. Dene the competitive equilibrium of the endowment ec0nomy. b. Write down each individual's maximization problem. c. Solve each individual's maximization problem. You should obtain x3', yi', and n; for ' = 1. 2 where n; denotes the Lagrange multiplier on individual i's budget constraint. d. Find X " and Y', the aggregate demands for the two goods. e. What are the equilibrium conditions for this economy? E. Find the market clearing relative price for the a: market. 5. Now use the market clearing condition in the y market to nd the equilibrium price. How much of good 3; does each individual consume? h. Determine the equilibrium values of 17;. Can you obtain a value for 17;? Discuss your answer in light of the importance of normalizing an absolute price. What quantity are you able to compute? What is its interpretation? How does this relate to the fact that we have analyzed a real model (one in which there is no money)