A fixed amount of a good has to be allocated between two individuals, h = 1; 2 with utility functions Where xh is the amount of the good allocated to consumer h. a. How should be allocated to maximize a utilitarian SWF? Illustrate the answer graphically. How do the optimal values of x1 and x2 change among the cases a1 2, a1 = a2, and a1 > a2? b. What is the allocation maximizing the Bernoulli-Nash SWF ? Illustrate graphically. How do the optimal values of x1 and x2 change with the preference parameters a1 and a2? c. What is the allocation maximizing the maxim in-Rawlins SWF? Illustrate graphically. How does the allocation change with preference parameters a1 and a2?

Objective: Maximize the sum of individual utilities Constraint: Total amount of the good (fixed)…

Answered: utility functions

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A fixed amount

of a good has to be allocated between two individuals, h = 1; 2 with utility functions

Where x^h is the amount of the good allocated to consumer h.

a. How should be allocated to maximize a utilitarian SWF? Illustrate the answer graphically. How do the optimal values of x¹ and x² change among the cases a¹ ², a¹ = a², and a¹ > a²?

b. What is the allocation maximizing the Bernoulli-Nash SWF ? Illustrate graphically. How do the optimal values of x¹ and x² change with the preference parameters a¹ and a²?

c. What is the allocation maximizing the maxim in-Rawlins SWF? Illustrate graphically. How does the allocation change with preference parameters a¹ and a²?

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