2 Contract Curve Suppose there are two consumers, A and B. There are two goods, X and Y. There is a total of 5 units of X and a total of 18 units of Y. The consumers' utility functions are given by: U₁(X,Y)= XY³ UB(X,Y)=3X + Y Using an Edgeworth Box, illustrate the contract curve. Your graph must be carefully labeled and you should clearly indicate what allocations in the Edgeworth Box are on the contract curve.

2 Contract Curve Suppose there are two consumers, A and B. There are two goods, X and Y. There is a total of 5 units of X and a total of 18 units of Y. The consumers' utility functions are given by: U₁(X,Y)= XY³ UB(X,Y)=3X + Y Using an Edgeworth Box, illustrate the contract curve. Your graph must be carefully labeled and you should clearly indicate what allocations in the Edgeworth Box are on the contract curve.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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For the case of two goods, give an example of a utility function U(x1, x2) that represents the preferences of a consumer who regards the two goods as perfect complements. Next, take the transformation f(U) = U³ of the your example utility function and explain if this newly gener ated function represents the original preferences. Further, provide clear arguments supporting or rejecting the claim that "f(U(x1, x2)) must be strongly increasing in (x1, x2)."
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Problem 1 Consider an economy with two goods only. For each part below draw a carefully labeled diagram showing the income and substitution effects for both goods. (a) The price of good 1 increases and both goods are normal. (b) The price of good 2 decreases and good 1 is normal while good 2 is inferior. (You may be tempted to use a clever trick and flip the axis so that you cann copy from a case we did in class, and in general this is perfectly fine, but for the sake of this exercise please leave good 1 on the x-axis and good 2 on the y-axis).
Kevin has a $100 monthly exercise budget, which he spends at Tarheel Gym on yoga classes (Y) and spin classes (S). The price of yoga class is $10, and the price of a spin class is $5. Draw his budget constraint for each of the following scenarios. Use a separate graph for each part and label all axes, intercepts, and the coordinates of any kink points. Treat each case separately and graph yoga classes on the x-axis and spin classes on the y-axis. a. The price of a yoga class drops to $8 after 5 classes, and again to $5 after 10 classes. b. After every 4 yoga classes you buy, you get the next one for half off. c. After purchasing 5 yoga classes, you become a “Tarheel Yogi. " Becoming a Tarheel Yogi costs $20, but it also reduces the price of each subsequent yoga class to $5. d. For every 5 yoga classes you buy, you get $5 in gym credit that can be used on any class at Tarheel Gym.
Person A has a utility function of and person B has a utility function Agent A and agent B have identical endowments of (1/2,1/2). (a) Illustrate this situation in an Edgeworth box diagram. (b) What is the equilibrium relationship between p1and p2? (c) What is the equilibrium allocation?
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Graph make graph
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7. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and Ya are A's endowments, Xb and Yb are B's, and Xo = Xa + Xb, Yo = Ya + Yb), the competitive equilibrium allocation of the two commodities represents a mutual tangency of both consumers' indifference curves with each other and with a common budget line. (a) The conditions require that A and B consume at a point on their budget lines where their indifference curves have the same marginal rate of substitution, and equilibrium for the market as a whole requires that the sum of the individuals' demands for each commodity must equal the totals (Xo and Yo) available. Mathematically express the point of equilibrium, that is, express the above statement with equations in relating each endowments, equilibrium points (Xa, Xb, Ya, Yb), and totals ((Xo, Yo). (b) Suppose MRSa = Ya/Xa, MRSB = Yb/Xb, Xa = 10, Ya, = 100, Xb = 50, Yb = 20, and let good Y be the numeraire (Py =1). Verify that the competitive…
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2(b)There are three people and two goods in an economy. The utility functions and the initial bundles are given below: U1 = X11X 12 U = 2x 21+ X 22 U3 = X 31 X 3z+X 32 W; = (0,8) W;= (2,2) Wy= (8,0) Suppose it is suggested that the three traders move to the allocation x given by x;= (1,2), x2= (8,4), X3= (1,4) b. Show that x makes no one worse off than the original allocation.