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

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

Problem 3
The preferences of a typical Californian can be represented by the following
utility function:
U (x1, 82) = a In(x1)+(1 – a) In(x2)
Here, xi and x2 are the quantities of electricity and gasoline, respectively. The
consumer faces prices given by pi 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, т —
100, and p1 = P2 = 1, find the optimal consump-
tion bundle of gasoline and electricity. Is the electricity rationing
constraint binding (meaning does x¡ = 50)?
(b)
Suppose that a =
What is the optimal consumption bundle? Is the rationing con-
straint on electricity consumption binding?
0.75, but the other parameters are the same.

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