Question

a) If you have Cobb Douglas utility function ……………………………….. ( 7 marks)
U: U (x. y) = x0.5 y0.5
Assume that the consumer is able to spend $40 on goods b, and c. where Px = 1, and Py= 2. Find the maximum quantities of b, and c the consumer can afford to buy and give him the highest utility.

Answer 1

Solution:

$$MU_x=\frac{0.5y^{0.5}}{x^{0.5}}$$

$$MU_y=\frac{0.5x^{0.5}}{y^{0.5}}$$

$$p_xq_x+p_yq_y=40$$

$$x+2y=40$$

$$\frac{MU_x}{p_x} = \frac {MU_y}{p_y}$$

$$\frac{0.5y^{0,5}}{x^{0.5}} = \frac{0,5x^{0,5}}{2y^{0,5}}$$

$$2y=x$$

$$2y+2y=40$$

$$y=10$$

$$x=20$$