Consider a consumer whose preference is represented by the utility function u(x₁, x₂) = ln(x₁+1) + x₂ where good 2 represents all other goods. Suppose the consumer's income is m > 1, let p2 = 1. a) Derive x₁(p₁, m), the consumer's demand function for good 1. b) Letting m = 10, graph the consumer's demand curve, with x₁ on the horizontal axis and p₁ on the vertical axis. c) Suppose that at first the price of good 1 is p₁ = 1, but then the price rises to p₁ = 1. What is the loss of consumer surplus associated with this price increase?

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 6QP
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Consider a consumer whose preference is represented by the utility function
u(x1, x2) = In(xx1 +1) + x2
where good 2 represents all other goods. Suppose the consumer's income is m > 1, let p2 = 1.
a) Derive x1(p, m), the consumer's demand function for good 1.
b) Letting m =
10, graph the consumer's demand curve, with xị on the horizontal axis and pı
on the vertical axis.
c) Suppose that at first the price of good 1 is p1 =, but then the price rises to pi = 1. What
is the loss of consumer surplus associated with this price increase?
Transcribed Image Text:Consider a consumer whose preference is represented by the utility function u(x1, x2) = In(xx1 +1) + x2 where good 2 represents all other goods. Suppose the consumer's income is m > 1, let p2 = 1. a) Derive x1(p, m), the consumer's demand function for good 1. b) Letting m = 10, graph the consumer's demand curve, with xị on the horizontal axis and pı on the vertical axis. c) Suppose that at first the price of good 1 is p1 =, but then the price rises to pi = 1. What is the loss of consumer surplus associated with this price increase?
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