Consider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) Set up the plannerís problem.(b) Calculate the first-best outcome 2. Consider an economy with 2 goods and 2 identical agents, each of whom has thefollowing utility function, 11(31, 3:2) = In 3:; + 2111332. The aggregate endowments ofthe 2 goods are given by (1, 2). Suppose there is a. social planner who cares aboutagents equally. (a) Set up the planner’s problem.(b) Calculate the ﬁrst-best outcome (11.6., the social planner’s solution).

Consider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) Set up the plannerís problem.(b) Calculate the first-best outcome 2. Consider an economy with 2 goods and 2 identical agents, each of whom has thefollowing utility function, 11(31, 3:2) = In 3:; + 2111332. The aggregate endowments ofthe 2 goods are given by (1, 2). Suppose there is a. social planner who cares aboutagents equally. (a) Set up the planner’s problem.(b) Calculate the ﬁrst-best outcome (11.6., the social planner’s solution).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.12P

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Consider an economy with 2 goods and 2 identical agents, each of whom has the following utility function, u (x1; x2) = ln x1 + 2 ln x2. The aggregate endowments of the 2 goods are given by (1; 2). Suppose there is a social planner who cares about agents equally.(a) Set up the plannerís problem. Calculate the first-best outcome
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A husband and wife would produce incomes Yh and Yw in their fallback situations. The utility each derives in any circumstance is just equal to his or her consumption expenditure in that circumstance. In their fallback situations, their consumption expenditure levels are just equal to their incomes. Thus their fallback levels of utility are Yh and Yw. If they cooperate, they produce Z>Yh + Yw. They engage in Nash cooperative bargaining to determine how to allocate Z across the consumption of the husband, Ch, and consumption of the wife, Cw, subject to the budget constraint that Ch + Cw = Z. Under any bargained allocation, the two would derive utilities of Ch and Cw. a) The surplus associated with cooperation is S = Z − Yh − Yw. Show that each spouse consumes his or her fallback income plus half the surplus in the Nash cooperative bargaining solution. Please do fast ASAP fast please.
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