Question

4.) Given the following information: utility function is U(x,y)=〖4x〗^0.5 y^0.5 , price of good X is N$5, the price of good Y is N$10 and the consumer income N$400.
What is the level of quantity demanded of good Y when the price of good X decreases to N$2.5 while the price of good Y remains at N$10? Let us assume good X is on the x-axis.

Answer 1

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

$$MU_x=\frac {\delta M}{\delta x}=(\frac {y}{x})^{0.5}$$

$$MU_y=\frac {\delta M}{\delta y}=(\frac {x}{y})^{0.5}$$

$$10 (\frac{y}{x})^{0.5}=5(\frac{x}{y})^{0.5}$$

$$2y=x$$

$$x p_x+yp_y=400$$

$$5x+10y=400$$

$$20y=400$$

$$y=20, x=40$$

If $p_x=2.5$ then 4y=x

$$20y+10y=400$$

$$y=13.7, x=53.3$$