In Problem 2, Clara's utility function is U(X, Y) = (X + 2)(Y + 1). If Clara's marginal rate of substitution is -6 and she is consuming 8 units of good X, how many units of good Y is she consuming?
A) 14
B) 60
C) 59
D) 6
E) 13

Question

Quizplus · Accepted Answer

The marginal rate of substitution (MRS) is defined as the rate at which one good can be substituted for another while maintaining the same level of utility. In other words, MRS = ΔY/ΔX = MUx/MUy. 
Here, Clara's MRS is given as -6. Therefore, MUx/MUy = -6.
Also, Clara's utility function is U(X, Y) = (X + 2)(Y + 1).
Differentiating the utility function with respect to X and Y, we get:
MUx = Y + 1 and MUy = X + 2
Substituting the MRS equation in the MUx/MUy equation, we get:
(Y + 1)/(X + 2) = -6
Solving for Y, we get:
Y = -6X - 13
Now, we know that Clara is consuming 8 units of good X. Substituting this in the equation for Y, we get:
Y = -6(8) - 13 = -61
Therefore, Clara is consuming 61 units of good Y. 
Hence, the answer is C.

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