(a) Briefly describe the differences between the ordinary demand function and the compensated demand function. Provide an expression that relates the two. (b) A consumer enjoys two goods, x1 and x2, according to the following utility: u(x) = x1x2+ X2. The prices of the goods are p = (P1, P2), and the consumer's income is w. Find the consumer's ordinary demand functions and the compensated demand functions for x1 and x2- (c) Suppose that the consumer's income is w = 125, and that the price vector de- creases from p = (25, 10) to p' = (20, 10). Find the minimum amount of money that would compensate the consumer for the price change and make him/her just as well of as s/he was before the price decrease.
(a) Briefly describe the differences between the ordinary demand function and the compensated demand function. Provide an expression that relates the two. (b) A consumer enjoys two goods, x1 and x2, according to the following utility: u(x) = x1x2+ X2. The prices of the goods are p = (P1, P2), and the consumer's income is w. Find the consumer's ordinary demand functions and the compensated demand functions for x1 and x2- (c) Suppose that the consumer's income is w = 125, and that the price vector de- creases from p = (25, 10) to p' = (20, 10). Find the minimum amount of money that would compensate the consumer for the price change and make him/her just as well of as s/he was before the price decrease.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![(a) Briefly describe the differences between the ordinary demand function and the compensated demand function. Provide an expression that relates the two.
(b) A consumer enjoys two goods, \( x_1 \) and \( x_2 \), according to the following utility:
\[ u(x) = x_1x_2 + x_2. \]
The prices of the goods are \( p = (p_1, p_2) \), and the consumer’s income is \( w \). Find the consumer’s ordinary demand functions and the compensated demand functions for \( x_1 \) and \( x_2 \).
(c) Suppose that the consumer’s income is \( w = 125 \), and that the price vector decreases from \( p = (25, 10) \) to \( p' = (20, 10) \). Find the minimum amount of money that would compensate the consumer for the price change and make him/her just as well off as s/he was before the price decrease.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7f4e788-ef76-42cd-ba71-0d980b205d9f%2F54e3eb60-2b03-4347-9be2-e023a8d2a5e8%2Fzneseu_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Briefly describe the differences between the ordinary demand function and the compensated demand function. Provide an expression that relates the two.
(b) A consumer enjoys two goods, \( x_1 \) and \( x_2 \), according to the following utility:
\[ u(x) = x_1x_2 + x_2. \]
The prices of the goods are \( p = (p_1, p_2) \), and the consumer’s income is \( w \). Find the consumer’s ordinary demand functions and the compensated demand functions for \( x_1 \) and \( x_2 \).
(c) Suppose that the consumer’s income is \( w = 125 \), and that the price vector decreases from \( p = (25, 10) \) to \( p' = (20, 10) \). Find the minimum amount of money that would compensate the consumer for the price change and make him/her just as well off as s/he was before the price decrease.
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