Answer to Question #238448 in Macroeconomics for Simagn Ojulu

Question

Given utility function u=x⁰.⁵, y⁰.⁵ where px=12 birr py=4birr and the income pf the consumer is M=240 birr
A. Find the utility maximizing combination of x and y
B. Calculate marginal rate of substitution of x for y (MRSX,Y) at equilibrium and interpret for your result
Find the minimum value of AVC and MC

Answer 1

$A. \; MU_x= 0.5 \frac{x0.5}{y0.5} \\ MU_y = 0.5 \frac{x^{0.5}}{y^{0.5}} \\ \frac{MU_x}{p_x} = \frac{MU_y}{p_y} \\ x \times p_x + y \times p_y = M \\ y = 3x \\ 12x + 4y= 240 \\ x=10 \\ y=30 \\ B. \; \frac{∂U}{∂x∂y} = \frac{0.25}{(xy)^{0.5}} \\ MRS_{x,y} = \frac{∂U}{∂x∂y} = \frac{0.25}{(10 \times 30)^{0.5}} = 0.015$

C. Average Variable Cost (AVC) is the variable cost per unit of output and is obtained by dividing the variable cost by the volume of output: AVC = VC/Q.

There are no enough data for calculation of AVC and MC.