(2) Consider the utility function u(z,y) := ry for all nonnegative z and y. Given the budget constraint p.z + Pyl = m, show that the Slutsky equation which is given by Op. Op. 3p (3) Recall the proof in question (2). Given that all prevailing conditions remain constant except the price of good y, Py. show further that the total effect of a price change in y results in the equality "de "de u (z,y) := r*y (4) Consider the Cobb-Douglas utility function of a consumer is given as where a > b and the sum(a, b) and the product(a, b) are 1 and 2/9 respectively, find a. the budget needed, m, to be able to afford the desired utility mumber u if price of good z and y are p, and p, respectively. b. Given that p, = 2.00, P, = 3.00 and m = 150, what is the optimal bundle available to the consumer? e. Given that the price of commodity y increases by 20%, what becomes the new optimal bundle available to the consumer (5) The salary of a consumer increased from ¢90, 000 to ¢110, 000, which represents his salary for 2021 and 2022 respectively. If he spends all his salary on baskets of apples which costed ¢100 in 2021

(2) Consider the utility function u(z,y) := ry for all nonnegative z and y. Given the budget constraint p.z + Pyl = m, show that the Slutsky equation which is given by Op. Op. 3p (3) Recall the proof in question (2). Given that all prevailing conditions remain constant except the price of good y, Py. show further that the total effect of a price change in y results in the equality "de "de u (z,y) := r*y (4) Consider the Cobb-Douglas utility function of a consumer is given as where a > b and the sum(a, b) and the product(a, b) are 1 and 2/9 respectively, find a. the budget needed, m, to be able to afford the desired utility mumber u if price of good z and y are p, and p, respectively. b. Given that p, = 2.00, P, = 3.00 and m = 150, what is the optimal bundle available to the consumer? e. Given that the price of commodity y increases by 20%, what becomes the new optimal bundle available to the consumer (5) The salary of a consumer increased from ¢90, 000 to ¢110, 000, which represents his salary for 2021 and 2022 respectively. If he spends all his salary on baskets of apples which costed ¢100 in 2021

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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