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

The marginal rate of substitution (MRS) is given by the negative of the ratio of the marginal utility of X to the marginal utility of Y. Given Clara's utility function U(X, Y) = (X + 2)(Y + 1), the marginal utility of X (MUx) is the partial derivative of U with respect to X, which is Y + 1, and the marginal utility of Y (MUy) is the partial derivative of U with respect to Y, which is X + 2. Therefore, MRS = -(MUx/MUy) = -(Y + 1)/(X + 2). We are given that MRS = -5 and X = 15. Substituting these values in gives us -5 = -(Y + 1)/(15 + 2), simplifying to -5 = -(Y + 1)/17. Solving for Y gives Y = 84.

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