Answer to Question #142643 in Microeconomics for Jyotiramay Rout

Question

An individual consumer consumes two commodities X1 & X2. The utility function is U = X1^0.4 X2^0.6. The price of commodity one is P1 = Rs. 3.00, the price of commodity two is P2 = Rs. 4.00, the individual's income per period is Rs. 108. Determine the utility maximizing level of X1 & X2 and derive the fans curve for the two commodities.

Answer 1

At the utility maximizing level of X1 & X2:

$MU1/P1 = MU2/P2$ or MU1/MU2 = P1/P2,

$MU1 = U'(X1) = 0.4(X2/X1)^{0.6} ,$

$MU1 = U'(X1) = 0.6(X1/X2)^{0.4},$

So, we get:

$\frac{2X2} {3X1} = \frac{ 3} {4} ,$

X1 = 8/9 X2,

According to the budget equation:

3X1 + 4X2 = 108, we get:

$3×8/9×X2 + 4X2 = 108,$

$20/3×X2 = 108,$

X2 = 16.2 units,

$X1 = 8/9×16.2 = 14.4$ units.