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?

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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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

M⁵

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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