Joe Bob has a cousin Pete who consumes goods 1 and 2.Pete thinks that 3 units of good 1 is always a perfect substitute for 4 units of good 2.Which of the following utility functions is the only one that would not represent Pete's preferences?

A) U(x₁, x₂)  40x₁  30x₂  10,000.
B) U(x₁, x₂)  4x₁  3x₂  1000.
C) U(x₁, x₂)  min4x₁, 3x₂.
D) U(x₁, x₂)  16x²₁  24x₁x₂  9x²₂.
E) More than one of the above does not represent Pete's preferences.

Question

Rylee Williams · Accepted Answer

Final Answer : C, Explanation :  Pete's preferences are such that he always thinks that 3 units of good 1 is a perfect substitute for 4 units of good 2. This means that his indifference curves must be straight lines with a slope of -3/4. Out of the given utility functions, only option C has a form that yields this property. In option C, the utility function takes the minimum value of either 4 units of good 1 or 3/4 units of good 2, which means that for any combination of goods, he would choose the combination that gives the same level of utility at the least cost. Thus, option C represents Pete's preferences.

Definitions

Learning Objectives

Learning Objectives

Related questions