Question

A firm producing baseball bats has a production function given by Q = 2K1/2L 1/2. In the short-run, the firm’s amount of capital equipment is fixed at K = 100. The rental rate for capital is r=$1, and wage rate for labor is w = $4.

a. Calculate the firm’s short-run total cost curve.

b. Calculate the firm’s short run average variable cost curve.

c. The firms short-run marginal cost curve is given by MC= Q/50. What is total cost, marginal cost, and average total cost for the firm if it produces 25 hockey sticks?

d. At what level of output does the short run average total cost curve reach its minimum value?

e. Graph the average total cost and marginal cost functions

Answer 1

Total cost in short run we have =wL+rK=1*100+4L

SRC=100+4L

Answer for B)

Average Short run variable cost=4L/Q=4L/2(100)^(1/2)*(L)^(1/2)=0.2*(L)^(1/2)

Answer for c)

MC=1/2=0.5 and if MC=Q/50 Then TC=Q^2/100=6.25

ATC=6.25/25=0.25

Ans for d)

SRATC=(100+4L)/Q=(100+4L)/20L^(0.5)=5L^(-0.5)+(0.2)L^(0.5)

We need to minimise SRATC with respect to L

-0.25*L^-1.5+0.01*L^-0.5=0

0.25L^(-1.5)=0.01L^(-0.5)

25=L optimum for minimum SRATC

Q=2*10*(25^1/2)=100 At which SRATC will be minimum