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. The utility maximizing combination of x and y is:

$MUx/MUy = Px/Py$ and $Px×x + Py×y = M.$

$MUx = u'(x) = 0.5(y/x)^{0.5}$ ,

$MUy = u'(y) = 0.5(x/y)^{0.5}.$

y/x = 12/4 = 3,

y = 3x,

12x + 4×(3x) = 240,

24x = 240,

x = 10 units, y = 30 units.

B. Marginal rate of substitution of x for y (MRSX,Y) at equilibrium is:

MRSx,y = Px/Py = 12/4 = 3.

So, you need to give up 3 units of y to buy one more unit of x.

C. The minimum value of AVC is at AVC = MC.