Suppose a consumer has M = $200 to spend on two goods,X and Y.If the per-unit prices of X and Y are respectively given by P_X = $2 and P_Y = $4,then utility maximization subject to a budget constraint can be found from which of the following Lagrangians? A) ℒ = U(X,Y) +  (200 − 2X − 4Y) B) ℒ = U(X,Y) +  (200 − 2P_X − 4P_Y) C) ℒ = (200 − 2X − 4Y) +  U(X,Y) D) ℒ = U(X,Y) +  (2X − 4Y + 200)

Question

Quizplus · Accepted Answer

The correct Lagrangian is A) ℒ = U(X,Y) + λ(200 − 2X − 4Y) because it correctly represents the utility function U(X,Y) subject to the budget constraint (200 - 2X - 4Y = 0) by incorporating the budget constraint into the utility maximization problem with the help of a Lagrange multiplier (λ).

Suppose a Consumer Has M = $200 to Spend on Two