SUPPOSE THE PRODUCTION FOR GOOD X IS CHARACTERIZED BY THE FO

SUPPOSE THE PRODUCTION FOR GOOD X IS CHARACTERIZED BY THE FOLLOWING PRODUCTION FUNCTION, Q=K 0.5 L 0.5, WHERE K IS THE FIXED INPUT IN THE SHORT RUN. IFTHE PER UNIT RENTAL RATE OF CAPITAL, R, IS $86.80 AND THE PER UNIT WAGE, W IS $20, THEN THE AVERAGE TOTAL COST OF USING 25 UNITS OF CAPITAL AND 49 UNITS OF LABOR IS:

A. $90

B. $5

C. THERE IS INSUFFICIENT INFORMATION TO DETERMINE THE AVERAGE TOTAL COST

D. $75

Solution

Lets calculate the output at given level of capital and Labor

Q = (25)^0.5 * (49)^0.5 = 35

Hence the total output at K=25 and L = 49 is 35

Now the costs

C = Wl+Rk

=20*49+86.8*25

=3150

ATC = TC/Q = 3150/35 =90