Question

In decomposing the total effect of a price change into income and substitution, we can solve it using consumer optimization. Utility U=XY+20X and total income is $200. Original price of X, Px=$4 and price of good Y, Py=$1. The original optimal bundle is (X=27.5, Y=90). Then the price of X decreases to $2. And the new optimal consumption is (X=55, Y=200). Write out the Lagrange for the expenditure minimization problem solving for the optimal bundle at the new prices and old utility level.

Answer Choices:

	L=2X+Y+λ(3025-XY-20X)
	L= XY+20X+λ(200-2X-Y)
	L= XY+20X+λ(200-4X-Y)
	L=4X+Y+ λ (12100-XY-20X)

Answer 1

Langrage function for minimization

F(X,Y,) = f(x,y) - (x,y)

f(x,y) = utility function = XY+20X

(x,y) = income function

I = Px X + Py Y

200 = 4X+Y

200-4X-Y = Income function

(x,y) = 200-4X-Y

Langrage function for minimization

F(X,Y,) = f(x,y) - (x,y)

F(X,Y,) = XY+20X -  (200-4X-Y)

Answer: Option C