Question

Mustapha’s utility function is as follows: U = 10x0.8 y0.6

Budget constraint: 100 = 6x + 4y

a. Solve for the utility-maximizing bundle

b. Find the equation of the indifference curve that contains the utility-maximizing bundle.

c. Sketch the solution, labeling all relevant items, x on the horizontal axis and y on the vertical axis.

d. At the utility-maximizing bundle, what is the increase in Mustapha’s utility from the last dollar spent on good X? What about for good Y?

e. Mustapha is moving to Maryland, where the price of X is 12 and the price of Y is 3. Find the minimum income Mustapha needs to maintain his current utility level (given by the bundle found in part a).

Answer 1

A)U=10*x^0.8*y^0.6

Optimal bundle condition,

Mux/px=muy/py

8*y^0.6/6*x^0.2=6*x^0.8/4*y^0.4

32y=36x

Y=9x/8

100=6x+4(9x/8)=6x+4.5x=10.5x

X=100/10.5=200/21=9.5

Y=9/8)*(200/21=150/14=10.7

B)U=10*9.5^0.8*10.7^0.6

Indifference equation,

10*9.5^0.8*10.7^0.6=10*x^0.8*y^0.6

(9.5/x)^0.8=(y/10.7)^0.6

C)

e budgetina 9.5 x 16.66

D)MUx/px=8*y^0.6/6*x^0.2=8*10.7^0.6/6*9.5^0.2=4*10.7^0.6/3*9.5^0.2{ utility from last dollar from x}

MUy/py=6*x^0.8/4*y^0.4=3*9.5^0.8/2*10.7^0.4{ utility from last dollar from y}