Please no written by hand 7.Suppose consumers have preferences over consumption of wine and beersummarized by the utility function u = u(w, b). Suppose furthermore that the price of wineis pw per unit, the price of beer is på, and that individuals have wealth I which they splitbetween purchases of each good, in other words, their budget constrain isPw w+ Pb b = I.Let u(w, b) = a Inw + ß ln b.a)Suppose the consumer's goal is to maximize utility. Formally state theconsumer's constrained maximization problem:Rewrite this problem as an unconstrained univariate maximization problem.Write the first order condition and solve the first order condition to obtain theoptimal wine and beer consumption.Verify that the SOC holds for maximization.b)c)d)

Optimal consumption bundle: The optimal consumption bundle is such that at that bundle the…

Suppose consumers have pre ences over consumption of wine an summarized by the utility function u = u(w, b). Suppose furthermore that the price of wine is pw per unit, the price of beer is pb, and that individuals have wealth I which they split between purchases of each good, in other words, their budget constrain is Let u(w, b) = a Inw + ß ln b. a) Suppose the consumer's goal is to maximize utility. Formally state the consumer's constrained maximization problem: Rewrite this problem as an unconstrained univariate maximization problem. Write the first order condition and solve the first order condition to obtain the optimal wine and beer consumption. Verify that the SOC holds for maximization. b) c) . Pw w+ Pb b = I. d)

Suppose consumers have pre ences over consumption of wine an summarized by the utility function u = u(w, b). Suppose furthermore that the price of wine is pw per unit, the price of beer is pb, and that individuals have wealth I which they split between purchases of each good, in other words, their budget constrain is Let u(w, b) = a Inw + ß ln b. a) Suppose the consumer's goal is to maximize utility. Formally state the consumer's constrained maximization problem: Rewrite this problem as an unconstrained univariate maximization problem. Write the first order condition and solve the first order condition to obtain the optimal wine and beer consumption. Verify that the SOC holds for maximization. b) c) . Pw w+ Pb b = I. d)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

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