4 Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = ln(x) + 3y a) Initially, px=1, py=6 and I=102. Then, the price of x increases to 2 (px=2). Calculate the changes in the demand for x. Please also calculate the substitution and income effects of the change in px on x. (Hint: since the change in price is not small, you cannot use the Slutsky equation. You need to have numbers instead of functions as the answer.) b) Please also calculate the substitution and income effects of the change in pa on y. c) Instead of doubling to 2, suppose px is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of x on x. Compare your result to (a). Explain why there's no income effect of the change in px on x. Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change in Px on y. Compare your result to (b).
4 Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = ln(x) + 3y a) Initially, px=1, py=6 and I=102. Then, the price of x increases to 2 (px=2). Calculate the changes in the demand for x. Please also calculate the substitution and income effects of the change in px on x. (Hint: since the change in price is not small, you cannot use the Slutsky equation. You need to have numbers instead of functions as the answer.) b) Please also calculate the substitution and income effects of the change in pa on y. c) Instead of doubling to 2, suppose px is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of x on x. Compare your result to (a). Explain why there's no income effect of the change in px on x. Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change in Px on y. Compare your result to (b).
Principles of Microeconomics (MindTap Course List)
8th Edition
ISBN:9781305971493
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter21: The Theory Of Consumer Choice
Section: Chapter Questions
Problem 5CQQ
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