Joe Bob from Problem 12 has a cousin Ike who consumes goods 1 and 2. Ike thinks that 4 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Ike's preferences? A) U(x₁, x₂) = 2x₁ + 4x₂ + 1000. B) U(x₁, x₂) = 4x²₁ + 16x₁x₂ + 16x²₂. C) U(x₁, x₂) = min{ 2x₁, 4x₂}. D) U(x₁, x₂) = 20x₁ + 40x₂ - 10,000. E) More than one of the above does not represent Ike's preferences.

Question

Quizplus · Accepted Answer

Ike considers 4 units of good 1 as a perfect substitute for 2 units of good 2. Thus, he will always choose the combination of goods that gives him the highest level of satisfaction for a given budget. Option A) and D) are linear utility functions, meaning that the marginal utility of each good is constant. Ike's satisfaction, however, is dependent on the relative prices of the two goods, and hence, these utility functions would not represent his preferences. Option B) has a term 4x²₁, which indicates that the marginal rate of substitution is not constant and increases with the consumption of good 2. Thus, this utility function would not represent Ike's preferences. Option C) has a utility function that represents perfect substitution between the two goods, and thus, it represents Ike's preferences.

Joe Bob from Problem 12 Has a Cousin Ike Who