Question 2. An economy has two goods denoted by X and Y, and two agents, Agent 1 and Agent 2. For both agents, their indirect utility functions identical: For i = 1,2, (pi+p2) m where pa, py denote prices the two goods, m the income and r is a fixed parameter. 1. What is the Marshallian Demand for Good Y of each agent? 2. Now, assume that agents have endowments of the two goods which determines their income. Let w₁=(2, 1) and w2=(1,3) be the respective endowments. Calculate the market clearing price ratio px/py. vi(Px, py, m) =

Question 2. An economy has two goods denoted by X and Y, and two agents, Agent 1 and Agent 2. For both agents, their indirect utility functions identical: For i = 1,2, (pi+p2) m where pa, py denote prices the two goods, m the income and r is a fixed parameter. 1. What is the Marshallian Demand for Good Y of each agent? 2. Now, assume that agents have endowments of the two goods which determines their income. Let w₁=(2, 1) and w2=(1,3) be the respective endowments. Calculate the market clearing price ratio px/py. vi(Px, py, m) =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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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Question 2. An economy has two goods denoted by X and Y, and two agents, Agent 1 and Agent 2. For both agents, their indirect utility functions identical: For i = 1, 2, 1 rm Vi (Px, Py, m) = (p₁ + p² )¯¯ \m where pa, py denote prices the two goods, m the income and r is a fixed parameter. 1. What is the Marshallian Demand for Good Y of each agent? 2. Now, assume that agents have endowments of the two goods which determines their income. Let w₁ = (2, 1) and w₂ = (1,3) be the respective endowments. Calculate the market clearing price ratio px/py. 3. In an economy such as this, explain why the area under the Marshallian Demand curve is a good measure of the change in welfare resulting from the change in the price of just one good.
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B4
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. (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 equilibrium price is Px = 2.
Consider an exchange economy with two consumers J and K and two goods F and C. Suppose the consumers have preferences with the following MRS of F in terms of C MUP MU 5CJ MRS FC FJ and MU MRSC = CK MUŽ FK where J, K are labels for the consumer, not powers. Suppose the economy has 24 units of good F and 20 units of good C. If consumer J is endowed with 12 units of good F and the consumers are given a Pareto efficient allocation, how many units of good C will consumer ** K** be provided?
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Consider an Edgeworth box economy, where preferences and endowments are given by. ( attached below ) In the following, use the normalization p2 = 1.(a) Find all the Pareto optimal allocations (use x1 to parameterize thePO allocations). (b) Suppose the government wants individual 1 to have the bundle x1 = (5, 9). Show whether the government can induce this outcome an equilib- rium with transfers. Find the supporting prices and transfers if possible. (c) State the Second Fundamental Theorem of Welfare and explain how the result in part (b) relates to that theorem. (d) Suppose the government does not care what bundle individual 1 gets and only wants to ensure that the individual 1 receives utility level equal to 45. Show whether this can be achieved as an equilibrium with transfers. Find the supporting prices and transfers if possible.
3. Answer the problem and provide solutions.
9. Consider an Edgeworth box economy with two consumers, whose utility func- tions and endowments are u'(x},x}) = (x}Xx})} (5,5) In the following, use the normalization p2 = 1. (a) Find the competitive equilibrium price. (b) State the first fundamental theorem of welfare and verify that it holds in this economy. (e) Consider the allocation ĩ = (x',) = (2,3), (8, 7). Show whether this allo- cation can supported as an equilibrium with transfers. (d) State the second fundamental theorem of welfare, and briefly discuss whether the result in part (c) conform with or violate this theorem. 3.