In Problem 2, Clara's utility function is U(X, Y) = (X + 2)(Y + 1). If Clara's marginal rate of substitution is -5 and she is consuming 15 units of good X, how many units of good Y is she consuming?
A) 5
B) 85
C) 20
D) 84
E) 11

Question

Quizplus · Accepted Answer

To find how many units of good Y Clara is consuming, we need to use the marginal rate of substitution (MRS) formula:

MRS = MU_X / MU_Y

where MU_X is the marginal utility of good X and MU_Y is the marginal utility of good Y.

From the utility function given, we can find the marginal utility of good X and good Y as:

MU_X = Y + 1
MU_Y = X + 2

Since Clara is consuming 15 units of good X, we know that MU_X = 1 (the change in consumption of X is 1 unit). Since we are given that her MRS is -5, we can set up the equation:

-5 = 1 / MU_Y
MU_Y = -1/5

Now we can solve for Y:

-1/5 = (15 + 2) + Y
Y = 84

Therefore, Clara is consuming 84 units of good Y. The answer is D.

In Problem 2, Clara's Utility Function Is U(X, Y) =