Question

Utility function u=x^0.5y^0.5 where px=4 and the income of the consumer is 240
Find
A= utility maximization combination of x and y
B=MRSXY at equilibrium And interpret the resualt

Answer 1

Solution:

A)

$$MU_x=0.5 \frac {y^{0.5}}{x^{0.5}}$$ $$MU_y=0.5 \frac {x^{0.5}}{y^{0.5}}$$ $${\frac{MU_x}{p_x}}=\frac {MU_y}{p_y}$$ $$x \times p_x+ y \times p_y=M$$ $$y=3x$$ $$12 \times x+4 \times y=240$$ $$x=10, y=30.$$

D)

$$\frac {\partial U}{\partial x \partial y} =\frac {0.25} {(xy)^{0.5}}$$ $$MRS x.y = \frac {\partial U} {\partial x \partial y} = \frac {0.25}{(10 \times 30)^{0.5}}=0.015$$