Question

Utility function u=x^0.5 y^0.5where px= 12birr,px=4birr and the income of the consumer is M=240birr

Answer 1

complete question:Given utility function U= X0.5Y0.5 where Px= 12 Birr, Bir, Py=4 Birr and the income of

the consumer is, M= 240 Birr.

A. Find the utility maximizing combinations of X and Y.

B. Calculate marginal rate of substitution of X for Y (MRSX.Y) at equilibrium and inierpiet

your result.

solution

A)

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

B)

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