3. A society consists of 3 identical individuals who derive utility from a publicgood. The public good can be provided at a constant marginal cost of 2. Letx, denote the level of public good provision by i, where i=1,2,3. Let X-x1 + x2 + x3 be the total provision. The net benefit enjoyed by individual i fromproviding x, units of the public good is given by4 In X-2x,U(x,x)where i=1,2. Is the total provision X under individual optimisation higheror lower than the socially optimal level of provision Xº? Explain the intuitionfor your result.4. If the price of a factor of production rises, a profit maximising firm might usemore of that factor. Is this true or false? Explain your answer by drawing com-parison for consumer choice for a Giffen good.

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3. A society consists of 3 identical individuals who derive utility from a public good. The public good can be provided at a constant marginal cost of 2. Let x, denote the level of public good provision by i, where i 1,2,3. Let X- x1 + x2 + x3 be the total provision. The net benefit enjoyed by individual i from providing x, units of the public good is given by U(x,, X) -4 ln X-2x, where i=1,2. Is the total provision X under individual optimisation higher or lower than the socially optimal level of provision Xº? Explain the intuition for your result.

3. A society consists of 3 identical individuals who derive utility from a public good. The public good can be provided at a constant marginal cost of 2. Let x, denote the level of public good provision by i, where i 1,2,3. Let X- x1 + x2 + x3 be the total provision. The net benefit enjoyed by individual i from providing x, units of the public good is given by U(x,, X) -4 ln X-2x, where i=1,2. Is the total provision X under individual optimisation higher or lower than the socially optimal level of provision Xº? Explain the intuition for your result.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Consider two consumers who each choose how to split their income, m, between a private good, x, and a public good. The amount of public good consumer į buys is denoted by g, and the total amount of public good is G. The price of each good is 1 and the consumer's utility functions are as below: u, = 2 log(x,)+log(G) uz = log(x,)+ log(G) a) By referring to the utility functions, explain why goodG satisfies the definition of a public good. b) Find each individual's best-response function. c) Find the Nash Equilibrium amount of public goods purchased. d) Use the Samuelson rule to show that the level of public goods purchased in the Nash Equilibrium is inefficient. Explain your answer.
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