Ambrose has the utility function . If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 39 units of nuts?
A) 8
B) 12
C) 25
D) 6
E) 3

Question

Ambrose has the utility function  . If Ambrose is initially consuming 25 units of nuts and 17 units of berries, then what is the largest number of berries that he would be willing to give up in return for an additional 39 units of nuts?
A) 8 
B) 12 
C) 25 
D) 6 
E) 3

Quizplus · Accepted Answer

To solve the problem, we need to find the marginal rate of substitution (MRS) of berries for nuts. This is given by the partial derivative of the utility function with respect to berries (holding nuts constant) divided by the partial derivative of the utility function with respect to nuts (holding berries constant).

MRS = (6/11) x (nuts/berries)

At the initial consumption of 25 nuts and 17 berries, the MRS is (6/11) x (25/17) = 1.69. This means that Ambrose is willing to give up 1.69 berries in exchange for one more nut.

We want to know how many berries Ambrose would be willing to give up in exchange for 39 more nuts, so we set up the following equation:

MRS = 1.69 = (6/11) x (64/berries)

Solving for berries, we get berries = 12.

Therefore, the largest number of berries Ambrose would be willing to give up in exchange for 39 more nuts is 12. The answer is B.

Ambrose Has the Utility Function