Problem 3 In a twdgood economy where consumption of a good must be nonnegative= Bob's preferences are represented by a CobbDouglas utility function 1.r.(::::1= 1:2) 2 1:12:32. Let p = (1= 1) be the initial price vector. I am introducing you to the concept of an endowment economy in this problem. Suppose that Bob has an endowment of e = (23 4). Bob can potentially trade parts of his endowment towards buying more of the other good. Bob's budget line is therefore given by mm + p232 2 13181 + 11282: where e 2 (e1: a2) is the endowment bundle. (1) Solve for the optimal consumption bundle. Denote this as point A. Is Bob a net buyer or net seller of 1:1? Is Bob a net buyer or net seller of :52? (2) Now suppose that prices change to p' = (4:1). Denote the new optimal consumption bundle by C. How will your answers about net buyer and net seller status in (1) change? Why? Graph bundles A and C in a graph with the two budget lines and the indifference curves associated with bundles A and C. In the following= we are going to decompose this change in the optimal consumption bundle into three effects substitution effect= ordinary income effect: and endowment income effect. (3) First calculate the substitution effect. From part (1)= the optimal consumption utility under price 'p = (1= 1) is u(3,3) = 9. We hold as constant the utility level 1:. = 9: and solve the expenditure minimization using the new price p' = (:515 1). Denote this consumption bundle as point B. Add it to your graph in part 2. The difference between consumption points A and B is the substitution effect. The difference between consumption points B and C is the total income effect. To decompose this income effect5 we solve for the endowment income effect. (4) In part (1) the endowment e = (25 4) along with prices p = (15 1) give an income of 2 + 4 = 6. Suppose that Bob's income is xed at I35 and change prices to p' = (4:1). Solve for the optimal consumption bundle. Denote this as point D. Add it to the graph in part 2. The difference between consumption points B and D is the ordinary income effect= and the difference between D and C is the endowment income effect