Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = ln(x) + 3y a) Initially, p=1, Py=6 and I=102. Then, the price of x increases to 2 (p=2). Calculate the changes in the demand for r. Please also calculate the substitution and income effects of the change in p, on r. (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 p on y. c) Instead of doubling to 2, suppose pz is only increased by a small amount. Use the Slutsk equation to find the substitution and income effects of the change in the price of r on I Compare your result to (a). Explain why there's no income effect of the change in p, on a Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change Pa on y. Compare your result to (b).

Suppose the preferences of an individual are represented by a quasilinear utility function: U(x, y) = ln(x) + 3y a) Initially, p=1, Py=6 and I=102. Then, the price of x increases to 2 (p=2). Calculate the changes in the demand for r. Please also calculate the substitution and income effects of the change in p, on r. (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 p on y. c) Instead of doubling to 2, suppose pz is only increased by a small amount. Use the Slutsk equation to find the substitution and income effects of the change in the price of r on I Compare your result to (a). Explain why there's no income effect of the change in p, on a Show your result on an indifference curve. d) Use the Slutsky equation to find the substitution and income effect of the change Pa on y. Compare your result to (b).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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