Question

A firm producing hockey sticks has a production function given by . In the short run, the firm's amount of capital equipment is fixed at K = 100. The rental rate for K is $1 and the wage rate for L is $4.

2LK

a. What is the firm's fixed rate cost?
b. What is the firm's total cost function, TC(Q)?

Answer 1

Answer

(a)

Fixed Cost is the cost incurred to hire fixed Input.

Here In the short run, the firm's amount of capital equipment(K) is fixed.

Hence Fixed cost is the total cost incurred to hire this K and here K = 100

total cost incurred to hire this K = Rental rate*K = 1*100 = 100

Hence, the firm's fixed rate cost = $100.

(b)

Q = 2(LK)^0.5 and K = 100 (fixed and constant)

=> Q = 2(100L)^0.5

=> L = Q²/400

TC = Total Cost = wage rate*L + Rental Rate*K

=> TC = 4(Q²/400) + 1*100

=> TC = TC(Q) = 100 + Q²/100 ----------------Total Cost function is the short run.