3. Consider an economy with two individuals, A and B, with quasi-linearpreferences over a private good x; with i = A, B, and over a public good, G,represented by the utility functionU (x₁, G) = x₁ + InG.Each of them has income mi with i = A, B that can be spent on the private goodx₁ or contributed to the public good, G. Each individual's contribution is g₁. Oneunit 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 ofindividual 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 publicgood).

The price constraint range constraint represents the boundaries or constraints that individuals face…

Answered: utility function

Business

Economics

utility function

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

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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Step 1: Define Budget Constraint

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Step 2: Explain the budget constraint for each individual, A and B.

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Step 3: Explain the Lagrangian corresponding to the optimization problem of individual B.

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Step 4: Explain the first order conditions

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Step 5: Explain the best response function for individual B, GB

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