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Microeconomic Theory

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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Question 4:
Consider an economy with two goods (apples and oranges) and two agents, Elisa and Bob. Elisa
is initially endowed with w= (5; 30) of apples and oranges respectively and Bob endowment
w (20; 20). Elisa and Ben have the same utility given by
U(x2, x2)=2lnx₁ + 2lnx2
Plot an Edgeworth box and mark the initial endowments.

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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) c) Assume that Kim has preferences Uk (Xk, Yk) = 3Xk + 3Yk and Jung has preferences Uj (Xj, Yj) = Xj + 3Yj. Will Kim and Jung trade? Calculate the general equilibrium allocation for Kim and Jung. Compute the utility at the endowment point and at the general equilibrium allocation. Is the new allocation on the contract curve?
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?
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?
Suppose that David and his friend Wilson derive utility from consuming two types of snacks: onion rings (9₁) and chips (9₂). The utility function for each individual is U (9₁, 92) = 9192. Their indifference curves for these two goods are assumed to have the usual (convex) shape. Suppose David has an initial endowment of 35 onion rings and 10 chips, and Wilson's initial endowment consists of 5 onion rings and 20 chips. (1) Draw an Edgeworth box and show the initial allocation of goods, to be labelled e. Indicate the initial quantities of each person's goods on the four axes.
N=7
2
A and B consume only two goods, cider (C) and dumplings (D). A has an initial endowment of 10 bottles of C and 30 of D. Bob has an initial endowment of 50 bottles of cider and 50 dumplings. Alice’s utility function is uA(CA,DA) = 9ln(CA) + 10ln(DA), where CA and DA represent consumption of C and D, respectively. B’s utility function is uB(CB,DB) = CBXDB, where CB and DB denote B's consumption of C and D. a) Find the competitive equilibrium, i.e. the price ratio, of this exchange economy and the resulting equilibrium allocation. b) Find the expression of the contract curve for this economy and use your answer to check that the equilibrium allocation you found in (b) is indeed Pareto optimal.
For the next three questions, assume that there are two consumers in an economy that have utility functions UA(2,3)=2¹/42/4 U" (x,y)=1¹/2¹/2 The two consumers begin with equal endowments of the two goods === e = 50 29. If the price of z and y were both set to 1, there would be (a) An excess demand for r so the equilibrium price ratio must be less than 1 (b) An excess supply of r so the equilibrium price ratio must be less than 1 (c) An excess demand for y so the equilibrium price ratio must be greater than 1 (d) An excess supply of y so the equilibrium price ratio must be greater than 1 (e) No excess supply or demand for either good, so the equilibrium price ratio is 1 30. What is the equilibrium price ratio? (a) 2/3 (b) 5/2 (c) 3/5 (d) 1 (e) None of these 31. Consumer A increases his endowment of both goods to 100 (e = e = 100). This will cause (a) No change in the equilibrium price ratio (b) The equilibrium price ratio to increase, causing consumer B to decrease their consumption of…
John and Belle consume only two goods, x and y. They have strictly convex preferences and no kinks in their indifference curves. At the initial endowment point, the ratio of John's marginal utility of x to his marginal utility of y is J and the ratio of Belle's marginal utility of x to her marginal utility of y is B, where J B. b. C < J. c. C = J. d. C = B. e. J
5
E1
Jack Sparrow and his wife consume wine (W) and books (B). Jack Sparrow's utility function is Ujack(W, B) = W. His wife's utility function is Uwife(W, B) = B. Jack's endowment is 17 bottles of wine and 5 books and Jack's wife's endowment is 20 bottles of wine and 14 books. In the Edgeworth box, Jack's consumption is measured from the lower left corner, and his wife's from the upper right corner of the box; the wine is on the horizontal axis and books are on the vertical axis. Therefore, in an Edgeworth box for Jack and his wife, there is only one Pareto Optimal allocation that is located in the top left corner of the box. True or False? Please submit 1 if True and O if False.

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