Question

2. An individual consumer consumes two commodities X1 & X2. The utility function is U = X 0.4 X26 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 X & X2 and derive the demand curves for the two commodities.​

Answer 1

Answer:

At the utility maximizing level of X1 & X2:

MU1/P1 = MU2/P2MU1/P1=MU2/P2 or MU1/MU2 = P1/P2,

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

0.6,

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

(X1)=0.6(X1/X2)

0.4

So, we get:\frac{2X2} {3X1} = \frac{ 3} {4} ,

3X1

2X2

=

4

3

,

X1 = 8/9 X2,

According to the budget equation:

3X1 + 4X2 = 108, we get:

3×8/9×X2 + 4X2 = 108,3×8/9×X2+4X2=108,

20/3×X2 = 108,20/3×X2=108,

X2 = 16.2 units,

X1 = 8/9×16.2 = 14.4X1=8/9×16.2=14.4 units.