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)
Chapter1: Making Economics Decisions
Section: Chapter Questions
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![7.
Suppose consumers have preferences over consumption of wine and beer
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 på, and that individuals have wealth I which they split
between purchases of each good, in other words, their budget constrain is
Pw 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 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)
d)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe19cf19f-797a-4b87-9ad7-0f58a4d4a7be%2Fb082ef96-8a45-4f58-934a-12c1cf0d44f4%2F3u6p65m_processed.png&w=3840&q=75)
Transcribed Image Text:7.
Suppose consumers have preferences over consumption of wine and beer
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 på, and that individuals have wealth I which they split
between purchases of each good, in other words, their budget constrain is
Pw 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 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)
d)
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