Anna and Bess are assigned to write a joint paper within a 24-hour period about the Pareto optimal provision of public goods. Let A denote the number of hours that Anna contributes to the project and B the number of hours that Bess contributes. The numeric grade that Anna and Bess earn is a function, 23 In(A + B), of the total number of hours that they contribute to the project. If Anna contributes tA, then she has (24 - A) hours in the day for leisure. Anna's utility function is UA = 23 In(A + B) + In(24 - A); and Bess' utility function is UB = 23 In(A + B) + In(24 - B). If they choose the hours to contribute simultaneously and independently, what is the Nash equilibrium number of hours that each will provide? What is the number of hours each should contribute to the project that maximizes the sum of their utilities?

Anna and Bess are assigned to write a joint paper within a 24-hour period about the Pareto optimal provision of public goods. Let A denote the number of hours that Anna contributes to the project and B the number of hours that Bess contributes. The numeric grade that Anna and Bess earn is a function, 23 In(A + B), of the total number of hours that they contribute to the project. If Anna contributes tA, then she has (24 - A) hours in the day for leisure. Anna's utility function is UA = 23 In(A + B) + In(24 - A); and Bess' utility function is UB = 23 In(A + B) + In(24 - B). If they choose the hours to contribute simultaneously and independently, what is the Nash equilibrium number of hours that each will provide? What is the number of hours each should contribute to the project that maximizes the sum of their utilities?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Welfare Analysis

Welfare analysis of the society is related to welfare economics. From the economic point of view former welfare economics refers to that subject which uses the techniques of microeconomics to analyse and evaluate the welfare at the economic or aggregate level.

Question

Anna and Bess are assigned to write a joint paper within a 24-hour period about
the Pareto optimal provision of public goods. Let A denote the number of hours that Anna
contributes to the project and B the number of hours that Bess contributes. The numeric
grade that Anna and Bess earn is a function, 23 In(A + B), of the total number of hours that
they contribute to the project. If Anna contributes tA, then she has (24 - A) hours in the day
for leisure. Anna's utility function is UA = 23 In(A + B) + In(24 - A); and Bess' utility function is
UB = 23 In(A + B) + In(24 - B). If they choose the hours to contribute simultaneously and
independently, what is the Nash equilibrium number of hours that each will provide? What is
the number of hours each should contribute to the project that maximizes the sum of their
utilities?

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