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.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.13P
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Transcribed Image Text:Que
Robert's utility function is
U(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 indifference
curves for Ū = 2 and Ū = 4 (solving for y as a function of 1). Draw these indifference
curves, 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, income
and substitution effects (on the demand of r) of a drop in the price of z from p, = 4 to
Pz = 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 the
same amount of X for free. Robert's income is M = 6. Draw Robert's budget line. Write
down 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 function
is 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 is
U(r, y) = 2x + 2y. What is his optimal bundle under the prices of part (c), including
the special offer. Provide a graphical argument justifying your answer.
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