Suppose the following Lagrangian is formed to maximize a consumer's utility subject to her budget constraint: ℒ = U(X,Y)+  (1,000 − 50X − 5Y).The first-order conditions for this problem imply: A) MRS = 10. B) P_X / P_Y = 10. C) (  U/  X) / (  U/  Y) = 10. D) All of the statements associated with this question are correct.

Question

Quizplus · Accepted Answer

The first-order conditions for utility maximization subject to a budget constraint involve setting the marginal rate of substitution (MRS) equal to the ratio of the prices of the two goods, which is given by the coefficients of X and Y in the budget constraint (50 and 5, respectively). Thus, MRS = 10. All options essentially express this relationship in different notations, making them all correct interpretations of the first-order condition.

Suppose the Following Lagrangian Is Formed to Maximize a Consumer's