Given the utility function U = X0.5+Y0.5 and budget constraint I=Px X+ Py Y, (a) Is this utility function is homothetic? (b) Derive the consumer’s demand functions for goods X and Y. (c) Obtain the numerical values of the own-price elasticity, cross-price elasticity, and the income elasticity of demand for X and Y.
Given the utility function U = X0.5+Y0.5 and budget constraint I=Px X+ Py Y, (a) Is this utility function is homothetic? (b) Derive the consumer’s demand functions for goods X and Y. (c) Obtain the numerical values of the own-price elasticity, cross-price elasticity, and the income elasticity of demand for X and Y.
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.12P
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Question
Given the utility function U = X0.5+Y0.5 and budget constraint I=Px X+ Py Y,
(a) Is this utility function is homothetic?
(b) Derive the consumer’s demand functions for goods X and Y.
(c) Obtain the numerical values of the own-price elasticity, cross-price elasticity, and the income elasticity of demand for X and Y.
(d) Derive the indirect utility function and the expenditure function for this consumer.
e) Obtain the compensated demand functions for goods X and Y. (f) Prove that the Slutsky equation holds in this case.
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