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.

$$x_1=20$$

$$x_2=40$$