Poindexter's utility function is U(x, y) = min{x + 2y, 3x + y}, where x is butter and y is guns. If the price of butter is $4 and the price of guns is $5, what would it cost Poindexter to buy the cheapest bundle that he likes as well as 4 units of butter and 3 units of guns?
A) $31
B) $32
C) $29
D) $28
E) None of the above.

Question

Quizplus · Accepted Answer

First, we need to find the cheapest bundle that Poindexter likes with his utility function. We can do this by setting the two parts of the function equal to each other:

x + 2y = 3x + y
y = 2x

Now, we can plug in the prices and Poindexter's desired consumption levels:

C = (4*4) + (5*3) + min{(4)+(2*3), (3*4)+(3)} 
C = 16 + 15 + min{10, 15}
C = 31

So, it would cost Poindexter $31 to buy the bundle of goods he wants along with 4 units of butter and 3 units of guns. Therefore, the answer is D.

Poindexter's Utility Function Is U(x, Y) = Min{x + 2y