Consider a 2-good, 2-agent pure exchange economy with complete markets (no externalities) and let the initial endowment be eд= (10, 10), eg = (20, 10). Which 2 of the following 8 options are false: At prices p = (1, 1) both agents' budget sets are subsets of the Edgeworth box. O 21 If preferences are represented by UA, UB: RR where uA (XA) = XA1 XA2 and us (X) = x₁x2 then the initial endowment is Pareto efficient. If Andy has strongly monotonic preferences then the bottom left corner of the Edgeworth box, OA, is Pareto efficient. The Edgeworth box is 30 units wide and 20 units high. If in Walrasian Equilibrium players trade to XA = (14, 8), XB = (16, 12) then Walrasian Equilibrium prices must be p = (1, 2). If Andy has strongly monotonic preferences then the top right hand corner of the Edgeworth box, Og, is Pareto efficient. If Andy has strongly monotonic preferences then it is impossible to have a Walrasian Equilibrium where one of the prices equals 0. If preferences are represented by UA, UB: RR where uA (XA) = XA1 XA2 and uB (XB) = XB1XB2 then in Walrasian Equilibrium the price of good 2 must be higher than the price of good 1

Consider a 2-good, 2-agent pure exchange economy with complete markets (no externalities) and let the initial endowment be eд= (10, 10), eg = (20, 10). Which 2 of the following 8 options are false: At prices p = (1, 1) both agents' budget sets are subsets of the Edgeworth box. O 21 If preferences are represented by UA, UB: RR where uA (XA) = XA1 XA2 and us (X) = x₁x2 then the initial endowment is Pareto efficient. If Andy has strongly monotonic preferences then the bottom left corner of the Edgeworth box, OA, is Pareto efficient. The Edgeworth box is 30 units wide and 20 units high. If in Walrasian Equilibrium players trade to XA = (14, 8), XB = (16, 12) then Walrasian Equilibrium prices must be p = (1, 2). If Andy has strongly monotonic preferences then the top right hand corner of the Edgeworth box, Og, is Pareto efficient. If Andy has strongly monotonic preferences then it is impossible to have a Walrasian Equilibrium where one of the prices equals 0. If preferences are represented by UA, UB: RR where uA (XA) = XA1 XA2 and uB (XB) = XB1XB2 then in Walrasian Equilibrium the price of good 2 must be higher than the price of good 1

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider an economy which is in general equilibrium. Ann and Bob are (the only) two consumers in an economy. They both consume both good and good X . This implies that O d. Both statements are false. y. mu X mu y (i) The equality is important with regards to efficiency because it implies that there are no Pareto Improving trades of x and y between Ann and Bob. (ii) The equality is important with regards to efficiency because it implies that (for x and y) the prices that producers see reflect the (relative) values that consumers place on the goods. O a. Only statement (ii) is true. O b. Only statement (i) is true. O c. Both statements are true. mu mu B X B y Consider the truth of the following two statements:
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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…
2. General Equilibrium Consider a market with two goods, x and z, and two consumers, A and B. The utility functions for consumers A and B are as follows UA ÜB 2 1 == XBZB and the initial endowments for each consumer are @ eA = (4,2) еB = (2,6) where consumer B is endowed with 2 unit of good x and 6 units of good z, respectively. a) Draw the Edgeworth Box (Don't worry about the shape of the utility curves. Just pick a general shape that we have used before). b) Derive the contract curve.
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6. In an Edgeworth box for two consumers, A and B, with endowments of commodities Xa and d 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).
1.) In an endowment economy with market exchange, let two consumers have preferences given by the utility function U^{h}=(x_{1}^{h})^{a}*(x_{2}^{h})^{1-a}for consumer h (1,2) with endowments given by\omega _{1}^{1}=6, \omega _{2}^{1}=4, \omega_{1}^{2}=4, and \omega_{2}^{2}=6. a.) Calculate the consumers' demand functions. b. Selecting good 2 as the measure of value (i.e. p2=1) and with alpha=1/4, find the equilibrium price of good 1 which implies equilibrium levels of consumption of both goods for both consumers. c. Demonstrate whether both consumers' indifference curves are tangential at the equilibrium. Demonstrate whether both consumers' indifference curves are tangential at the initial endowment.
please only do: if you can teach explain each why convex: The budget set consists of all convex combinations of the points How to know these: can you show each the points can be derive (0, 0), (0, w/p2), (2,(w p1)/p2), and (1 + w/p1, 0). The upper-right boundary of this region consists of two line segments meeting at a kink, with the segment to the left of the kink being flatter than the one to the right. b) how to solve it?