The following quasiconcave function describes the preferences of a consumer for two goods 1 and 2, with the non-negative quantities x, and x,, in a traditional model of consumer choice. U = k x; x; 1-a where 0
The following quasiconcave function describes the preferences of a consumer for two goods 1 and 2, with the non-negative quantities x, and x,, in a traditional model of consumer choice. U = k x; x; 1-a where 0
MATLAB: An Introduction with Applications
6th Edition
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Question
![The following quasiconcave function describes the preferences of a consumer for two
goods 1 and 2, with the non-negative quantities x, and x,, in a traditional model of
consumer choice.
U = k x; x
,1-a
where 0<a <1, and the constant k e R . . Prices ( p,, p, ) and money income (M)
are not determined by the consumer and positive.
(a) What are the endogenous variables and what are the exogenous variables of the
model?
(b) Use the utility function to prove that the axiom non-satiation of the preference relation
E is fulfilled. Briefly mention why the preference relation must also be convex.
(c) Solve the model and derive the Marshallian demand functions x and x. Given
1
what you know about the utility function, why will the solution be a global maximum?
(d) Prove that there are no corner solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbf4fbfb-40a4-4a88-8b2c-1e716f690a23%2F761a4da9-5600-4a3c-bb73-8102d4c4c5ac%2Fgms37yf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The following quasiconcave function describes the preferences of a consumer for two
goods 1 and 2, with the non-negative quantities x, and x,, in a traditional model of
consumer choice.
U = k x; x
,1-a
where 0<a <1, and the constant k e R . . Prices ( p,, p, ) and money income (M)
are not determined by the consumer and positive.
(a) What are the endogenous variables and what are the exogenous variables of the
model?
(b) Use the utility function to prove that the axiom non-satiation of the preference relation
E is fulfilled. Briefly mention why the preference relation must also be convex.
(c) Solve the model and derive the Marshallian demand functions x and x. Given
1
what you know about the utility function, why will the solution be a global maximum?
(d) Prove that there are no corner solutions.
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