Two individuals, A and B, have the following utility functions UA min {x¹, y^} UB min {x¹, y³} = and the endowments are of the same unit and quantity: x = y = 100. (a) Sketch the Edgeworth box and draw the contract curve. (b) If A has a different utility function UA = x² + y^ would the contract curve be different? Explain. (c) If we add the production of goods x and y in the economy, and the technology is con- stant return to scale for both goods, can the competitive equilibrium still be achieved? Explained.

Two individuals, A and B, have the following utility functions UA min {x¹, y^} UB min {x¹, y³} = and the endowments are of the same unit and quantity: x = y = 100. (a) Sketch the Edgeworth box and draw the contract curve. (b) If A has a different utility function UA = x² + y^ would the contract curve be different? Explain. (c) If we add the production of goods x and y in the economy, and the technology is con- stant return to scale for both goods, can the competitive equilibrium still be achieved? Explained.

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 a two-person endowment economy characterized by the Edgeworth Box below: a. b. C. X2. OA A E B OB X1 Are the allocations depicted at points A and B Pareto efficient? Explain your reasoning. Add bowed indifference curves that reflect the utility that the two consumers get from the endowment depicted at point E (assume that they value both goods). What is meant by the term "Pareto improvement." In your diagram highlight the set of Pareto improving allocations given the endowment.
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Consider a 2-good, 2-agent pure exchange economy where there are 10 units of each good and preferences are represented by UA, UB: RR where uA (XA) = 2XA1 + XA2 and uB (XB) = XB1 + 2XB2- Which 2 of the following 8 options are true: There are initial endowments from which we can have a Walrasian Equilibrium with prices p = (1, 0). O The only Pareto efficient allocation is XA = (10, 0), XB = (0, 10). Every Pareto efficient allocation can be supported as a Walrasian Equilibrium after some reallocation of resources. We cannot apply the First Welfare Theorem because preferences violate local non-satiation. The allocation XA = (5, 10), XB = (5, 0) is Pareto efficient. For all price vectors PER3 we have p1z₁ + P2z2 = 0 where z; is the excess demand of good i € {1, 2}. O Preferences of both players satisfy strict convexity. At initial endowment eA= (5, 5), eg = (5, 5), there is a Walrasian Equilibrium with prices p = (1, 2).
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