Answer to Question #132834 in Microeconomics for Elias Machechali

Question

For the utility functions:

A: U(x1, x2)  x11/2 x2
B: U(x1, x2)  min{ ½ x1, x2 }
C: U(x1, x2)  ½ x1 + x2
1. Derive the consumers optimal consumption at the budget B(p1,p2,m) = (1,1,100).
2. Derive the consumer’s optimal consumption at the budget B(p1,p2,m) = (1,2,100).
(10 marks)

Answer 1

$u(x_1,x_2)=x_1^{0.5}x_2$

$MU_{x_1}=\frac{x_2}{2x_1^{0.5}}$

$MU_{x_2}=x_1^{0.5}$

$p_1x_1+p_2x_2=m$

1.

$x_1+x_2=100$

$x_1=33.3$

$x_2=66.7$

2.

$x_1=20$

$x_2=40$