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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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.
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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