Consider a simple quasi-linear utility function of the formU(x, y) = x + In y.a. Calculate the income effect for each good. Also calculatethe income elasticity of demand for each good.b. Calculate the substitution effect for each good. Alsocalculate the compensated own-price elasticity ofdemand for each good.c. Show that the Slutsky equation applies to this function.d. Show that the elasticity form of the Slutsky equation alsoapplies to this function. Describe any special features youobserve.e. A modest generalization of this quasi-linear utilityfunction is given by U(x, y) = x + f(y), where f' > 0,f" < 0. How, if at all, would the results from parts a-ddiffer if this general function were used instead of In y inthe utility function?

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Consider a simple quasi-linear utility function of the form U(x, y) = x + In y. a. Calculate the income effect for each good. Also calculate the income elasticity of demand for each good. b. Calculate the substitution effect for each good. Also calculate the compensated own-price elasticity of demand for each good. c. Show that the Slutsky equation applies to this function.

Consider a simple quasi-linear utility function of the form U(x, y) = x + In y. a. Calculate the income effect for each good. Also calculate the income elasticity of demand for each good. b. Calculate the substitution effect for each good. Also calculate the compensated own-price elasticity of demand for each good. c. Show that the Slutsky equation applies to this function.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider a simple quasi-linear utility function of the form
U(x, y) = x + In y.
a. Calculate the income effect for each good. Also calculate
the income elasticity of demand for each good.
b. Calculate the substitution effect for each good. Also
calculate the compensated own-price elasticity of
demand for each good.
c. Show that the Slutsky equation applies to this function.
d. Show that the elasticity form of the Slutsky equation also
applies to this function. Describe any special features you
observe.
e. A modest generalization of this quasi-linear utility
function is given by U(x, y) = x + f(y), where f' > 0,
f" < 0. How, if at all, would the results from parts a-d
differ if this general function were used instead of In y in
the utility function?

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