Joe Bob from Problem 12 Has a Cousin Sam Who

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.

Correct Answer:

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