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.
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.12P
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Transcribed Image Text: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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