The preferences of a typical Californian can be represented by the following utility function: U (x₁, x2) = a ln(x₁) + (1 − a) ln(x₂) Here, ₁ and 2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p₁ and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x₁ ≤ 50). Call this restriction a rationing constraint. (a) If a = 0.25, m = 100, and p₁ = P2 = 1, find the optimal consump- tion bundle of gasoling and oloctriciter Is the ologtrigitu rationing

The preferences of a typical Californian can be represented by the following utility function: U (x₁, x2) = a ln(x₁) + (1 − a) ln(x₂) Here, ₁ and 2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p₁ and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x₁ ≤ 50). Call this restriction a rationing constraint. (a) If a = 0.25, m = 100, and p₁ = P2 = 1, find the optimal consump- tion bundle of gasoling and oloctriciter Is the ologtrigitu rationing

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.9P

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No written by hand solution Assume Fred has the following preference relation on [0, 1]: x ≿ y if and only if x ≤ y for all x ̸= 1 and y ̸= 1; and 1 ≻ z for all z ∈ (0, 1), 1 ∼ 1 and 0 ≻ 1. Does there exists a utility representation for this preference relation? If yes, provide a utility function. If no, explain. Show your work.
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