Consider an general equilibrium endowment economy with two goods and two individuals. The two individuals A and B have the following endowments {(w^, w), (wP ,w?)} = {(4,3), (2, 1)} The utility functions for A and B are: UA (2f, 교) %3D0.5log(2수) + log(»솔) UP(P,교물) = log(2P) + 0.5 log(2) ** Part a State the market clearing conditions. ** Part b Draw the Edgeworth box, including: • the x-y coordinates of the 4 corners. • the x-y coordinates of endowment point. • a sketch of some indifference curves for both individuals. ** Part c (10 Given the relative price p > 0, find the demand of good 1 for both individuals.

Consider an general equilibrium endowment economy with two goods and two individuals. The two individuals A and B have the following endowments {(w^, w), (wP ,w?)} = {(4,3), (2, 1)} The utility functions for A and B are: UA (2f, 교) %3D0.5log(2수) + log(»솔) UP(P,교물) = log(2P) + 0.5 log(2) Part a State the market clearing conditions. Part b Draw the Edgeworth box, including: • the x-y coordinates of the 4 corners. • the x-y coordinates of endowment point. • a sketch of some indifference curves for both individuals. ** Part c (10 Given the relative price p > 0, find the demand of good 1 for both individuals.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter13: General Equilibrium And Welfare

Section: Chapter Questions

Problem 13.5P

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Other bookmarks E Reading list Consider a two-person general equilibrium with two economic agents A and B. Agent A's utility function is: U^(r*, «$) = log(x4)+ log(x") Agent B's utility function is: U*(xf, r}) = 2 log xf + = The endowments are: {(w, w), (wf,w)} = {(1,2), (1,2)} Denote the relative price by p > 0. ** Part a Find the demands of Good 1 of Person A and B given an arbitrary relative price p. ** Part b Using the market clearing condition for Good 1, find the competitive equilibrium price p. ** Part c Solve for the contract curve in terms of (x, x).
Competitive general equilibrium Amy(A) and Brian (B) have the following utility function U^A= 2XaYa, U^B= √XbYb Were there endowment of consumption good X and Y are as follows: Xa= 60 Ya = 80 Xd=30 Yb=180 At the endowment point what is the marginal rate of substitution of X for Y for Amy? For Brian? Find the competitive equilibrium price of the goods at which the consumers trade with each other In the competitive equilibrium for each unit of good Y how many units of good X can be exchanged. Find both brian and amy preferred consumption bundles in the equilibrium Is the allocation of resources achieved in part d pareto-optimal? Explain. Draw the edgeworth box that shows all possible allocations and plot the endowment points. Plot the indifferent curves of the two consumers and the contract curve in the edgeworth box as well.
For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) d) Assume that a social planner could redistribute initial wealth (the amounts of ? and ? that Kim and Jung have). Can they reallocate resources so that Kim and Jung reach the allocation (Xk, Yk) = (20,20) and (Xj, Yj) = (20,20) as a general equilibrium (i.e. post-trade) allocation? Can the social planner redistribute resources to make the allocation where Jung owns all the resources in the economy a general equilibrium allocation?
For the rest of this question consider a two goods economy where Kim and Jung can trade Ferraris (good x) and VR headsets (good y) with each other. Kim and Jung both enjoy driving Ferraris and having more VR headsets (so more friends can play the same game). They start at the same (high) level of income. Kim has an initial endowment of (x0k, y0k) = (10,30) and Jung has an initial endowment of (x0j, y0j) = (30,10) a) Illustrate the initial endowment in an Edgeworth box. Clearly label the axes and explain the dimensions of the box. Show the indifference curve each of them is on at the endowment point. b) Consider an allocation where Kim gets (xk, yk) = (40,40) and Jung gets the remaining Ferraris and VR headsets. Show where this point is in the Edgeworth box. Is this allocation Pareto efficient? Is it equitable? How likely is this to arise in practice?
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Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 2 units of good X and 6 units of good Y. Consumer B is given an initial endowment of 6 units of good X and 2 units of good Y. Consumer A's utility function is given by: UAXY) = X"Y, and consumer B's utility function is given by: Ug(X,Y) - MIN (2X, Y). If the prices are Px-1 and Py- 2, if each consumer sells her initial endowment and buys back her and in the optimal bundle, then in the Market for Good X there is Select) Market for Good Y there is [Select)
= 5. Consider an economy with a single (representative) agent with utility function u(x, lc) = x¹/514/5 and an endowment of 0 units of x and 10 units of time, which the agent can use as leisure (c) or labor (L) (i.e., L + lc = 10). The agent owns a firm that produces good x using L as an input, with technology of production given by x(L) = 3√L. Let the price of x be p = 1 and let w denote the price of time (i.e., the price of leisure and the wage). Find the competitive price of time w and the competitive allocation.
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