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6.16 Let x = (x¹,...,x) be an allocation of goods to agents, and let the economy's feasible set of allocations be T. Suppose x* maximises the utilitarian social welfare function, W = ₁ u¹(x¹), subject to x € T. N (a) Let ¹ for i = 1, ..., N be an arbitrary set of increasing functions of one variable. Does x* maximise (vi)) over y c 72 Why or why not?

6.16 Let x = (x¹,...,x) be an allocation of goods to agents, and let the economy's feasible set of allocations be T. Suppose x* maximises the utilitarian social welfare function, W = ₁ u¹(x¹), subject to x € T. N (a) Let ¹ for i = 1, ..., N be an arbitrary set of increasing functions of one variable. Does x* maximise (vi)) over y c 72 Why or why not?

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
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From The Book Advanced Microeconomic Theory, Jehle And Reny, Chapter 6. 6.16

N 6.16 Let x = (x¹, xª) be an allocation of goods to agents, and let the economy's feasible set of allocations be T. Suppose x* maximises the utilitarian social welfare function, W = Σ¼₁ u²(x¹), subject to x € T. i=1 (a) Let ⁄i for i=1, N be an arbitrary set of increasing functions of one variable. Does x* maximise Σ₁¹(u²(x¹)) over x ≥ 7? Why or why not? (b) If in part (a), ¹ = y for all i, what would your answer be? (c) If y¹ = a¹ + b¹u¹(x¹) for arbitrary a¹ and b¹ > 0, what would your answer be? (d) If y¹ = a + bu¹ (x¹) for arbitrary a¹ and b > 0, what would your answer be? (e) How do you account for any similarities and differences in your answers to parts (a) through (d)?
Transcribed Image Text:N 6.16 Let x = (x¹, xª) be an allocation of goods to agents, and let the economy's feasible set of allocations be T. Suppose x* maximises the utilitarian social welfare function, W = Σ¼₁ u²(x¹), subject to x € T. i=1 (a) Let ⁄i for i=1, N be an arbitrary set of increasing functions of one variable. Does x* maximise Σ₁¹(u²(x¹)) over x ≥ 7? Why or why not? (b) If in part (a), ¹ = y for all i, what would your answer be? (c) If y¹ = a¹ + b¹u¹(x¹) for arbitrary a¹ and b¹ > 0, what would your answer be? (d) If y¹ = a + bu¹ (x¹) for arbitrary a¹ and b > 0, what would your answer be? (e) How do you account for any similarities and differences in your answers to parts (a) through (d)?
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