5. [Exchange Economy] Consider an economy with two people, Alice and Bob, and two goods, and x2. Alice's utility function is u (x1, x) = x (x) and Bob's utility function is u(x, x) = (x3) x. Assume that Alice is endowed with one unit of good 1 and no good 2, i.e., (w = 1, w = 0) and Bob with one unit of good 2 and no good 1, i.e., (w = 0, w = 1). (a) Find the competitive equilibrium for this exchange economy (let good 1 be the numeraire so that P = 1). =2), (b) Now suppose that Bob's endowment of good 2 doubles, from one unit to two units, i.e., (B = 0, B = and Alice's endowment is the same as before (w = 1, w = 0). We would certainly expect this to make Bob better off. What effect does it have on Alice's utility? (c) Now suppose instead that Alice's endowment of good 1 doubles, to two units, i.e., ( = 2, = 0), and Bob's endowment is the same as before (w = 0, w = 1). What effect does it have on Alice's utility? How does this compare to your answer to part (b)? (d) Now think of Alice and Bob as countries rather than individuals, and think of an increase in endowment as a resource discovery, such as the discovery of oil or natural gas. Use your answers to part (b) and part (c) to discuss the circumstances under which you would rather have such a discovery in your own country, and those in which you would rather have it in another country. Keep your answer briefly and to the point.