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Q2 Consider the Cobb-Douglas utility function, u,(X, Y) = Xª Y' -ª for a rational consumer i. Derive the Marshallian demand functions for X and Y. ii. Use the Marshallian demand functions for X and Y above to compute the indirect utility function and the expenditure function. uith Shephard's lemma

Q2 Consider the Cobb-Douglas utility function, u,(X, Y) = Xª Y' -ª for a rational consumer i. Derive the Marshallian demand functions for X and Y. ii. Use the Marshallian demand functions for X and Y above to compute the indirect utility function and the expenditure function. uith Shephard's lemma

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Please Show Each and Every Working VERY CLEARLY. Please Answer ONLY (ii)
Q2 Consider the Cobb-Douglas utility function, u;(X, Y) = Xª Y' -ª for a rational consumer i. Derive the Marshallian demand functions for X and Y. ii. Use the Marshallian demand functions for X and Y above to compute the indirect utility function and the expenditure function. iii. Using the expenditure function obtained in part (ii) together with Shephard's lemma, derive the Hicksian compensated demand function for X and Y. iv. Suppose a = 0.5, Px = Py = $2, M (money income per week) = $100, find the consumer's optimal bundle. Illustrate your results graphically as well. v. If the government gives $10 financial support weekly for each family during the COVID-19 lockdown period, how would the results be changed in iv? While presenting the calculations clearly, illustrate the outcome graphically.
Transcribed Image Text:Q2 Consider the Cobb-Douglas utility function, u;(X, Y) = Xª Y' -ª for a rational consumer i. Derive the Marshallian demand functions for X and Y. ii. Use the Marshallian demand functions for X and Y above to compute the indirect utility function and the expenditure function. iii. Using the expenditure function obtained in part (ii) together with Shephard's lemma, derive the Hicksian compensated demand function for X and Y. iv. Suppose a = 0.5, Px = Py = $2, M (money income per week) = $100, find the consumer's optimal bundle. Illustrate your results graphically as well. v. If the government gives $10 financial support weekly for each family during the COVID-19 lockdown period, how would the results be changed in iv? While presenting the calculations clearly, illustrate the outcome graphically.
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