Consider the following utility functions: U(X.) X2+2rFor the above utility function, derive the demand functions for X and Y as funetions of prices anda-)income. Explain whether these goods are nomal goods Explain whether two goods are complements orsubstitutesSppose now that Price of good Y isS48 and income equals 1440, Using three distinct values of priceof X (P 6.P -12.P-24) draw Price consumption curve and then using Price Consumption curve draw theb-)demand curve for X.Suppose Price of good Y is $48 and price of X is equal to 6. Using three distinet income values (I 1440,7 = 2880.1 = 4320). draw Income Consumption curve and then using Income Consumption curve drawthe Engel curve for good X.d-)Consider initially that Income (I) $1440, Pr 6 and Py 48. What is the initial optimalconsumption levels of X and Y? Suppose that P, rises from S6 to $12. Find the substitution effect, income effectand total effect on good X. Explain the steps carefully and support your result wvith an explanation and a graph.

We have Utility function = U(x,y)=x12+2y, where x= quantity of good x and y= quantity of good y…

Consider the following utility functions: U(Xx.n-x2+2r For the above utility function, derive the demand functions for X and Y as functions of prices and income. Explain whether these goods are nomal goods. Explain whether two goods are complements or substitutes.

Consider the following utility functions: U(Xx.n-x2+2r For the above utility function, derive the demand functions for X and Y as functions of prices and income. Explain whether these goods are nomal goods. Explain whether two goods are complements or substitutes.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.7P

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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

Consider the following utility functions: U(X.) X2+2r
For the above utility function, derive the demand functions for X and Y as funetions of prices and
a-)
income. Explain whether these goods are nomal goods Explain whether two goods are complements or
substitutes
Sppose now that Price of good Y isS48 and income equals 1440, Using three distinct values of price
of X (P 6.P -12.P-24) draw Price consumption curve and then using Price Consumption curve draw the
b-)
demand curve for X.
Suppose Price of good Y is $48 and price of X is equal to 6. Using three distinet income values (
I 1440,7 = 2880.1 = 4320). draw Income Consumption curve and then using Income Consumption curve draw
the Engel curve for good X.
d-)
Consider initially that Income (I) $1440, Pr 6 and Py 48. What is the initial optimal
consumption levels of X and Y? Suppose that P, rises from S6 to $12. Find the substitution effect, income effect
and total effect on good X. Explain the steps carefully and support your result wvith an explanation and a graph.

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