(1) A consumer's utility function is given by u (z_y) := z/2y/2 for any nonnegative z and y, representing the consumption quantities of goods z and y, respectively. Suppose that the price of good y is constantly ¢1, and that the consumer is given income m cedis (and nothing else). Denote p, for the price of good z. Based on the quantity demandi (p., m) for good z. a. Given that p, > 1/(4m), calculate i (P.. m) and i (p.- Py. m), then use the Slutsky equation to deduce what the substitution effect r (P.-y) is equal to. b. Given that p, < 1/(4m), calculate (Pa. m) and i(P.-Py.m), then use the Slutsky equation to deduce what the substitution effect +r (P.-y) is equal to. c. What is your interpretation of the your result in a and b above? (2) Consider the utility function u(z, y) := z/aya/3 for all nonnegative z and y. Given the budget constraint p.r+ Pvy = m, show that the Slutsky equation which is given by dp, Op, 3p

(1) A consumer's utility function is given by u (z_y) := z/2y/2 for any nonnegative z and y, representing the consumption quantities of goods z and y, respectively. Suppose that the price of good y is constantly ¢1, and that the consumer is given income m cedis (and nothing else). Denote p, for the price of good z. Based on the quantity demandi (p., m) for good z. a. Given that p, > 1/(4m), calculate i (P.. m) and i (p.- Py. m), then use the Slutsky equation to deduce what the substitution effect r (P.-y) is equal to. b. Given that p, < 1/(4m), calculate (Pa. m) and i(P.-Py.m), then use the Slutsky equation to deduce what the substitution effect +r (P.-y) is equal to. c. What is your interpretation of the your result in a and b above? (2) Consider the utility function u(z, y) := z/aya/3 for all nonnegative z and y. Given the budget constraint p.r+ Pvy = m, show that the Slutsky equation which is given by dp, Op, 3p

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.11P

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