Adrienne consumes three goods, x,y, and z. Her consumption preference is given by the utility function: u(x, y, 2) = x†y} z#, %3D = (Px-Py, Pz) where x, y, and z are the quantities she consumes (respectively). Let p = be the prices of the goods. Answer the following questions, and justify your answers carefully and mathematically. (a) Last year p = (1, 10, 10) and Adrienne's income was 35. Find her optimal con- sumption bundle last year. (b) This year, the prices of x and z have both risen 3.5% while the price of y has risen 7%, and Adrienne got an income raise of 3%. Find the (approximate) percentage changes of her consumption in the three goods due to these changes in prices and income. Does her raise adequately compensate her for the changed prices? What additional percentage change of her income would be needed if we were to restore Adrienne to last year's exact utility level?
Adrienne consumes three goods, x,y, and z. Her consumption preference is given by the utility function: u(x, y, 2) = x†y} z#, %3D = (Px-Py, Pz) where x, y, and z are the quantities she consumes (respectively). Let p = be the prices of the goods. Answer the following questions, and justify your answers carefully and mathematically. (a) Last year p = (1, 10, 10) and Adrienne's income was 35. Find her optimal con- sumption bundle last year. (b) This year, the prices of x and z have both risen 3.5% while the price of y has risen 7%, and Adrienne got an income raise of 3%. Find the (approximate) percentage changes of her consumption in the three goods due to these changes in prices and income. Does her raise adequately compensate her for the changed prices? What additional percentage change of her income would be needed if we were to restore Adrienne to last year's exact utility level?
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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Transcribed Image Text:Adrienne consumes three goods, x, y, and z. Her consumption preference is given by
the utility function:
u(x, y, z) = x*y} z#,
(Pz-Py, Pz)
where x, y, and z are the quantities she consumes (respectively). Let p =
be the prices of the goods. Answer the following questions, and justify your answers
carefully and mathematically.
(a) Last year p =
sumption bundle last year.
(1, 10, 10) and Adrienne's income was 35. Find her optimal con-
(b) This year, the prices of x and z have both risen 3.5% while the price of y has risen
7%, and Adrienne got an income raise of 3%. Find the (approximate) percentage
changes of her consumption in the three goods due to these changes in prices and
income. Does her raise adequately compensate her for the changed prices? What
additional percentage change of her income would be needed if we were to restore
Adrienne to last year's exact utility level?
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