Joe Bob from Problem 12 has a cousin Sam who consumes goods 1 and 2. Sam thinks that 2 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 Sam's preferences? A) U(x₁, x₂) = 16x²₁ + 16x₁x₂ + 4x²₂. B) U(x₁, x₂) = min{ 4x₁, 2x₂}. C) U(x₁, x₂) = 40x₁ + 20x₂ - 10,000. D) U(x₁, x₂) = 4x₁ + 2x₂ + 1000. E) More than one of the above does not represent Sam's preferences.

Question

Quizplus · Accepted Answer

Sam's preferences suggest that 2 units of good 1 is always a perfect substitute for 4 units of good 2. In other words, the marginal rate of substitution between the two goods is always 2:4, or 1:2. This means that Sam is always willing to give up twice as much of good 1 for an additional unit of good 2. The only utility function that reflects this is choice B, where the minimum of 4x₁ and 2x₂ represents the amount of utility that Sam can get from consuming the goods at the given quantities. In all the other choices, the marginal rate of substitution varies across different levels of consumption of the goods, which does not match with Sam's stated preferences.

Joe Bob from Problem 12 Has a Cousin Sam Who