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utility function

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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3. Consider an economy with two individuals, A and B, with quasi-linear preferences over a private good x; with i = A, B, and over a public good, G, represented by the utility function U (x₁, G) = x₁ + InG. Each of them has income mi with i = A, B that can be spent on the private good x₁ or contributed to the public good, G. Each individual's contribution is g₁. One unit of individual contribution is used to produce one unit of the public good, G. The social planner has a Rawlsian social welfare function given by: W(UA, UB) = min{5UA, 5UB}. a) Write the budget constraint for each individual, A and B. b) Derive the Lagrangean corresponding to the optimization problem of individual B. c) Calculate the first order conditions. d) Derive the best response function for individual B, 9B. e) Calculate the demand functions for x, (the private good) and G (the public good).
Transcribed Image Text:3. Consider an economy with two individuals, A and B, with quasi-linear preferences over a private good x; with i = A, B, and over a public good, G, represented by the utility function U (x₁, G) = x₁ + InG. Each of them has income mi with i = A, B that can be spent on the private good x₁ or contributed to the public good, G. Each individual's contribution is g₁. One unit of individual contribution is used to produce one unit of the public good, G. The social planner has a Rawlsian social welfare function given by: W(UA, UB) = min{5UA, 5UB}. a) Write the budget constraint for each individual, A and B. b) Derive the Lagrangean corresponding to the optimization problem of individual B. c) Calculate the first order conditions. d) Derive the best response function for individual B, 9B. e) Calculate the demand functions for x, (the private good) and G (the public good).
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