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General equilibrium and externalities/public goods [25 points] [Note that parts (a) - (b) are separate from parts (c) - (e).] Consider a two-good/two-person pure-exchange economy. The respective utility functions for each individual consumer (agent) are given by U() = x+ 3y , U(2) = xty . where x and y denote quantities of consumption goods. The first agent holds an initial allocation of w(): (x = 6; y = 5} and the second an initial allocation of w(2): {x = 7;y = 4). Assume that the agents can exchange x and y with one another. (a) Draw the Edgeworth box for this economy clearly indicating where the initial allocation lies and what the sides of the box measure. Then, indicate the set of points in the Edgeworth box that are a Pareto improvement with respect to the endowment point. (b) In another Edgeworth box, indicate the possible Pareto optimal allocations of x and y after trade has taken place. Explain the intuition for your solution. Now consider externalities. (c) Suppose that the (inverse) market demand curve for good X is given by P(X) = X-2, X > 0. The marginal social cost of producing it is MSC(X) = 8X, whereas the marginal private cost of producing good X is MPC(X) = X. Based on this information, and assuming that X is produced in an (unregulated) competitive market, carefully explain why the quantity of the commodity produced would not be socially efficient. Then, provide a "real world" example of a commodity that good X might represent and its implications for third-party consumers or producers.Consider a pine exchange economyr that consists of two consumers, A and B and two goods X and Y. Consumer A's utilityF mction is U A = xfyj'\" and consumer B's utility fimction is ll}r = xgyg-B. Suppose the total amount of good X available to both is 10!] and the total amount of good '1' is 50. Suppose consumer A has 26 units of good X and consumerB has 10 units ofgoodY. Let cr = 13'2 and!)I = 4.5. Assume there is no production of X and Y, but the two consumers can exchange one good for another. Starting from the initial altocation of goods X and '1' for each consumer, is it possible for consumer A and consumer B to trade with each other so that both consumers are better off? If so, explain how they should trade. if not, explain why:r not? Draw a graph illustrating your answers Consider a twoperiod model of a small open economy with a single good each period and no investment. Let preferences of the representative household be described by the utility function U{C1, C2} = p C1 + [5 p C2 The parameter [3 is known as the subjective discount factor. It measures the consumer's degree of impatience in the sense that the smaller is B, the higher is the weight the consumer assigns to preserrt consumption relative to future consumption. Assume that B = U11. The representative household has initial net foreign wealth of {1 + rlt I] = 1, with r = [1.1, and is endowed with Ell = 5 units of goods in period 1 and 02 = ID units in period 2. The world interest rate paid on assets held from period lto period 2, r * , equals 16% {i.e., r * = [1.1] and there is free international capital mobility. 1. Calculate the equilibrium levels of consumption in period 1, C1, consumption in period 2, C2, the trade balance in period 1, T El, and the current accourrt balance in period 1, CA1. 2. Suppose now that the government imposes capital corrtrols that require that the country's net foreign asset position atthe end of period 1 be nonnegative {3* 1 a D}. Compute the equilibrium value of the domestic interest rate, r1, consumption in periods 1 and 2, and the trade and currerrt account balances in period 1. 3. Evaluate the effect of capital corrtrols on welfare. Specically, nd the level of utility under capital controls and compare it to the level of utility obtained under free capital mobility. 4. Forthis question and the next, suppose that the country experiences a temporary increase in the endowment of period 1 to El = '3, with period 2 endowment unchanged. Calculate the effect of this output shod: on C1, C2, T Bl, CA1, and r1 in the case that capital is freely mobile across courrtries
