Joe Bob has a cousin Don who consumes goods 1 and 2.Don thinks that 3 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 Don's preferences?

A) U(x₁, x₂)  min2x₁, 3x₂.
B) U(x₁, x₂)  20x₁  30x₂  10,000.
C) U(x₁, x₂)  2x₁  3x₂  1000.
D) U(x₁, x₂)  4x²₁  12x₁x₂  9x²₂.
E) More than one of the above does not represent Don's preferences.

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Jaliyah Reese · Accepted Answer

Final Answer : A, Explanation :  In order for an utility function to represent Don's preferences, it must satisfy the condition that 3 units of good 1 is always a perfect substitute for 2 units of good 2. The only utility function that does not satisfy this condition is option A, where the marginal utility of good 1 is twice the marginal utility of good 2. This implies that Don would not be willing to substitute 3 units of good 1 for 2 units of good 2 at all levels of consumption, which contradicts his stated preference.

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