1. Consider the following utility functions: (a) u(x1, x2)=x1x2, I (b) u(x1, x2)=xx, (c) u(x1, x2) = ln x1 + ln x2, and (d) u(x1, x2)=√√x1x2, where x is the amount of good 1 and x2 is the amount of good 2. (1) (2) (3) (4) For each of the utility functions, find the marginal utility (MU₁) with respect to good 1. (5 points) For each of the utility functions, find the marginal utility (MU2) with respect to good 2. (5 points) For each of the utility functions, consider the following indifference curve: k = u(x1, x2) for some constant k. Find the marginal rate of substitution (MRS) of good 1 for good 2 at a point (x1, x2) on the indifference curve. (5 points) Show that each of the utility functions has a diminishing MRS. (5 points)
1. Consider the following utility functions: (a) u(x1, x2)=x1x2, I (b) u(x1, x2)=xx, (c) u(x1, x2) = ln x1 + ln x2, and (d) u(x1, x2)=√√x1x2, where x is the amount of good 1 and x2 is the amount of good 2. (1) (2) (3) (4) For each of the utility functions, find the marginal utility (MU₁) with respect to good 1. (5 points) For each of the utility functions, find the marginal utility (MU2) with respect to good 2. (5 points) For each of the utility functions, consider the following indifference curve: k = u(x1, x2) for some constant k. Find the marginal rate of substitution (MRS) of good 1 for good 2 at a point (x1, x2) on the indifference curve. (5 points) Show that each of the utility functions has a diminishing MRS. (5 points)
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics
Section: Chapter Questions
Problem 5QP
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Transcribed Image Text:1.
Consider the following utility functions:
(a)
u(x1, x2)=x1x2,
I
(b)
u(x1, x2)=xx,
(c)
u(x1, x2) = ln x1 + ln x2, and
(d)
u(x1, x2)=√√x1x2,
where x is the amount of good 1 and x2 is the amount of good 2.
(1)
(2)
(3)
(4)
For each of the utility functions, find the marginal utility (MU₁) with respect to
good 1. (5 points)
For each of the utility functions, find the marginal utility (MU2) with respect to
good 2. (5 points)
For each of the utility functions, consider the following indifference curve:
k = u(x1, x2) for some constant k. Find the marginal rate of substitution (MRS)
of good 1 for good 2 at a point (x1, x2) on the indifference curve. (5 points)
Show that each of the utility functions has a diminishing MRS. (5 points)
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