The preferences of a typical Californian can be represented by the following utility function: U (x1, #2) = a ln(x1)+(1 – a) In(x2) Here, r1 and r2 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 (11 < 50). Call this restriction a rationing constraint. If a = 0.25, m = 100, and p1 = P2 = 1, find the optimal consump- tion bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does a¡ = 50)? (a) Suppose that a = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing con- straint on electricity consumption binding? (Ь)
The preferences of a typical Californian can be represented by the following utility function: U (x1, #2) = a ln(x1)+(1 – a) In(x2) Here, r1 and r2 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 (11 < 50). Call this restriction a rationing constraint. If a = 0.25, m = 100, and p1 = P2 = 1, find the optimal consump- tion bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does a¡ = 50)? (a) Suppose that a = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing con- straint on electricity consumption binding? (Ь)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Answer part a, b and c
![](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45737196-1fee-42d2-a61c-38f0d39d70d9%2Fc1324f6b-fc86-4dfb-81be-3002fe5a8e21%2Fq3os9i8.png&w=3840&q=75)
![The preferences of a typical Californian can be represented by the following
utility function:
U (x1, #2) = a ln(x1)+(1 – a) In(x2)
Here, r1 and r2 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 (11 < 50). Call
this restriction a rationing constraint.
If a = 0.25, m = 100, and p1 = P2 = 1, find the optimal consump-
tion bundle of gasoline and electricity. Is the electricity rationing
constraint binding (meaning does a¡ = 50)?
(a)
Suppose that a = 0.75, but the other parameters are the same.
What is the optimal consumption bundle? Is the rationing con-
straint on electricity consumption binding?
(Ь)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45737196-1fee-42d2-a61c-38f0d39d70d9%2Fc1324f6b-fc86-4dfb-81be-3002fe5a8e21%2Ffzzt5vz.png&w=3840&q=75)
Transcribed Image Text:The preferences of a typical Californian can be represented by the following
utility function:
U (x1, #2) = a ln(x1)+(1 – a) In(x2)
Here, r1 and r2 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 (11 < 50). Call
this restriction a rationing constraint.
If a = 0.25, m = 100, and p1 = P2 = 1, find the optimal consump-
tion bundle of gasoline and electricity. Is the electricity rationing
constraint binding (meaning does a¡ = 50)?
(a)
Suppose that a = 0.75, but the other parameters are the same.
What is the optimal consumption bundle? Is the rationing con-
straint on electricity consumption binding?
(Ь)
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