Assume a consumer with the utility function U= U (X, Y) = (X + 2) (Y + 1) And th

Question

Assume a consumer with the utility function U= U (X, Y) = (X + 2) (Y + 1) And the budget constraint (M = 95, Px =10 and Px =5) 95 = 10x + 5Y a. Set up the constrained maximization problem, and derive the first-order conditions. b. Find the amounts of goods X and Y the consumer will purchase in equilibrium.

Explanation / Answer

Hi, If you like my answer rate me first...that way only I can earn points. Thanks The Constrained maximization equation is L = (X+2)*(Y+1) - a(10X+5Y-95) EQUATING Derivative wrt a to 0 gives => 10X+5 Y =95 EQUATING Derivative wrt x to 0 gives => y+1 - 10a=0 EQUATING Derivative wrt a to 0 gives => x+2 - 5a=0 or 10*(5a -2 ) + 5*(10a - 1) =95 or a = 1.2 y = 11 x = 4 Quantity of X = 4 units Quantity of Y = 11 units

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