Joe Bob 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.

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Sanjida Pervin · Accepted Answer

Final Answer : C, Explanation :  Option C is the only one that reflects the idea that 4 units of good 1 can be perfectly substituted for 2 units of good 2. The function takes the minimum of the two goods, which means that the marginal utility of each good is equal. Therefore, Ike is willing to substitute good 1 units for good 2 units at a constant rate of 2:1. The other options do not reflect this perfect substitutability.

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