Suppose the preferences of an individual are represented by a quasilinear utility function:U(x, y) = In(x) + 3ya) Initially, Px=1, Py=6 and 1=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 Pr 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 Pa 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). 4Suppose the preferences of an individual are represented by a quasilinear utility function:U(x, y) = ln(x) + 3ya) Initially, px=1, py=6 and I=102. Then, the price of x increases to 2 (px=2). Calculatethe changes in the demand for x. Please also calculate the substitution and income effectsof the change in px on x. (Hint: since the change in price is not small, you cannot use theSlutsky 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 Slutskyequation 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 inPx on y. Compare your result to (b).

**a) Changes in demand for \(x\) and substitution & income effects:** 1. **Initial Demand…

Answered: 4 Suppose the preferences of an…

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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Suppose the preferences of an individual are represented by a quasilinear utility function:

U(x, y) = In(x) + 3y

a) Initially, Px=1, Py=6 and 1=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 Pr 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 Pa 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).