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 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? Let W1 price ratio 2. Now, assume that agents have endowments of the two goods which determines their income. (2, 1) and w₂ = (1,3) be the respective endowments. Calculate the market clearing 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.

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 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? Let W1 price ratio 2. Now, assume that agents have endowments of the two goods which determines their income. (2, 1) and w₂ = (1,3) be the respective endowments. Calculate the market clearing 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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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, vi(Pa, Py, m) = (pi+p₂) r 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.
1. a) Consider an economy with 3 agents, Mohammed (M), David (D) and Susan (S). There are two goods available, good x, and good y. The marginal rates of substitution (where good x is on the horizontal axis and good y is on the vertical axis) are given by for Mohammed, for David and for Mohammed and David are both consuming twice as much of the good x than good y, while Susan is consuming equal amounts of x and y. What are the conditions for Pareto efficiency in an exchange economy? Are these consumption levels economically efficient? Can these consumption allocations be observed in a perfectly competitive equilibrium in an exchange economy without production? Explain. b. There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A’s marginal rate of technical substitution of labour for capital is 4 while B’s marginal rate of technical…
Suppose that an individual with income I cares about two goods, X and Y. The prices of the two goods are px and py. The individual has the utility function U(X,Y)= 5 ln X + 3 ln Y. (a) Derive the Marshallian demands for the two goods. (b) Find the indirect utility function.
please sir solve question 7
1. A consumer in a two-good economy (x1 and x2) with prices pi and p2 and utility equal to u faces the Cobb-Douglas expenditure function: (1-a) e (p, и) — ир*р. where a E (0, 1). 1.1 Derive the indirect utility function v(p, y) for this consumer. 1.2 Derive the Hicksian demand functions for the consumer x" (p, u). 1.3 Suppose you know that expenditure share for the ith good, w;, is defined as: P;r# (p, u) е (p, и) Wi = Using the Hicksian demand functions derived in part 1.2 above, along with the expenditure function provided at the beginning of the question, find an expression for w1 + w2 and interpret this expression within the context of the Cobb-Douglas framework.
True/False? Briefly explain. Assume good x is a normal good. In terms of consumer behavior, a cash grant and a small (relative to the initial consumption of x) limited non-matching grant on good x (with the limit that is equal to the cash grant) are essentially equivalent.
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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3. Answer the problem and provide solutions.
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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.
Question 3 3.1 Slutsky's equation relates the Marshallian demand function to the Hicksian demand func- tion, and therefore provides a way in which to decompose the total effect of a price change on quantity demanded into the substitution and income effects. Provide an expression for the general Slutsky equation of a good (x;) with respect to changes in the price of x;, and clearly label the total effect, substitution effect and income effect. 3.2 Now consider the case of a consumer with Cobb-Douglas indirect utility function v(р, у) (1-a) and Hicksian demand function for good 1 * (p, u) P2 ( Pi = au Pi P2 Demonstrate that the Slutsky equation holds for the own-price effect for good r1-