QueRobert's utility function isU(x, y) = 2/T + y.In every graph for this question, set y in the vertical axis and z in the horizontal axis.(a) Obtain the marginal rate of substitution MRS. Obtain the equation of the indifferencecurves for Ū = 2 and Ū = 4 (solving for y as a function of 1). Draw these indifferencecurves, identifying the intersections with each of the axes.(b) Suppose p, = 2 and Robert's income is M = 6. In a new graph, show the total, incomeand substitution effects (on the demand of r) of a drop in the price of z from p, = 4 toPz = 2.(c) Now, the store where Robert goes for shopping has changed the prices to p, = 2 and py = 6,however, it also has a new special offer: for any amount of Y that Robert buys, he gets thesame amount of X for free. Robert's income is M = 6. Draw Robert's budget line. Writedown the equation of this line. Find Robert's utility-maximising bundle.(d)(d.1) Arthur's income is M = 6 and he goes to the same store as Robert. His utility functionis U(x, y) = min{r, y}. What is his optimal bundle under the prices of part (c),including the special offer. Provide a graphical argument justifying your answer.(d.2) Simon's income is M = 6 and he goes to the same store as well. His utility function isU(r, y) = 2x + 2y. What is his optimal bundle under the prices of part (c), includingthe special offer. Provide a graphical argument justifying your answer.

Qu Robert's utility function is U(1, y) = 2/T + y. n every graph for this question, set y in the vertical axis and z in the horizontal axis. (a) Obtain the marginal rate of substitution MRS. Obtain the equation of the indifference curves for Ū = 2 and Ū = 4 (solving for y as a function of 2). Draw these indifference curves, identifying the intersections with each of the axes. (b) Suppose py = 2 and Robert's income is M = 6. In a new graph, show the total, income and substitution effects (on the demand of r) of a drop in the price of r from p, = 4 to Pz = 2.

Qu Robert's utility function is U(1, y) = 2/T + y. n every graph for this question, set y in the vertical axis and z in the horizontal axis. (a) Obtain the marginal rate of substitution MRS. Obtain the equation of the indifference curves for Ū = 2 and Ū = 4 (solving for y as a function of 2). Draw these indifference curves, identifying the intersections with each of the axes. (b) Suppose py = 2 and Robert's income is M = 6. In a new graph, show the total, income and substitution effects (on the demand of r) of a drop in the price of r from p, = 4 to Pz = 2.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.13P

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