Task 2:A utility function is given by the equation U = 20xe-01x, where x is the number of glasses ofwine consumed.(a) Show that this utility function has a maximum value and calculate the maximum utility.(b) Describe how marginal utility changes for glasses of wine consumed after the maximumutility is reached. Do you consider this reasonable? Give an explanation. Task 3:(a) Show that the function Q= a/P, where a and e are constants, has a constant elasticity ofdemand: eg =-c.(b) (i) Determine the elasticity of demand for train journeys on a given route when the demandfunction is Q= 1200/P2, where Q is the number of fares in thousands.(ii) If the fare increases by 5%, use elasticity to calculate the percentage change indemand.(iii) If the fare decreases by 5%, use elasticity to calculate the percentage change in demand.

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A utility function is given by the equ= wine consumed. (a) Show that this utility function ha (b) Describe how marginal utility ch. utility is reached Do vou conside

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.1: Quadratic Functions And Models

Problem 56E: When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream...

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Question

Task 2:
A utility function is given by the equation U = 20xe-01x, where x is the number of glasses of
wine consumed.
(a) Show that this utility function has a maximum value and calculate the maximum utility.
(b) Describe how marginal utility changes for glasses of wine consumed after the maximum
utility is reached. Do you consider this reasonable? Give an explanation.

Task 3:
(a) Show that the function Q= a/P, where a and e are constants, has a constant elasticity of
demand: eg =-c.
(b) (i) Determine the elasticity of demand for train journeys on a given route when the demand
function is Q= 1200/P2, where Q is the number of fares in thousands.
(ii) If the fare increases by 5%, use elasticity to calculate the percentage change in
demand.
(iii) If the fare decreases by 5%, use elasticity to calculate the percentage change in demand.

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