Charlie's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. When Charlie is consuming 20 apples and 80 bananas, if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is
A) -8.
B) -1/4.
C) -20.
D) -4.
E) -1/8.

Question

Quizplus · Accepted Answer

The slope of an indifference curve is given by the marginal rate of substitution (MRS), which measures the rate at which one good can be substituted for another while keeping the utility constant.

The MRS between apples and bananas for Charlie is given by the ratio of the marginal utility of apples to the marginal utility of bananas:

MRS = MU(A) / MU(B) = B / A

At his current consumption of 20 apples and 80 bananas, the MRS is:

MRS = 80 / 20 = 4

This means that Charlie is willing to give up 4 bananas to get one more apple and still remain equally happy.

The slope of the indifference curve can also be expressed as the change in bananas (vertical axis) over the change in apples (horizontal axis). Using the MRS formula, we can derive this as:

slope = - (MU(B) / MU(A)) = - (B / A)

At his current consumption, the slope is:

slope = - (80 / 20) = -4

Therefore, the correct answer is D, -4.

Charlie's Utility Function Is U(A, B) = AB, Where a and B