Eva\'s monthly income is 300 Euros. Her utility function is given by U(x,y) =x +

Question

Eva's monthly income is 300 Euros. Her utility function is given by U(x,y) =x + 72y-3y, where x and y denote the quantity consumed of good x and good y, respectively. The market prices of both goods in Euros are p 2 and py 24 a) What is the marginal rate of transformation (MRT) between goods x and y? b) What is Eva's marginal rate of substitution (MRS) between goods x and y? c) Determine Eva's optimal consumption bundle at the given prices Suppose now that the price of good x has become 4 Euros whereas the price of the other good and Eva's income remained unchanged. d) What are now the MRT and the MRS between goods x and y? How will the optimal choice of Eva change after the price increase? What is the total effect of the price change? g What is the substitution effect of the price change? h) What is the income effect of the price change?

Explanation / Answer

Minimize M=4x+10y subject to u (x,y)=min ( x,5y)

To solve this problem let us form lagrange expression z= 4x+10y+£ (u-min (x,5y)) where £ is the Lagrange multiplier.The F.o.c requires

4- £x=0

10- £5y=0

X= f (4,10)and

Y=f (4,10)

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