Question

Brucely Brothers' short-run cost curve is: C = (2q^2/K)+10K, where q is the number of outputs produced and K is the number of robot hours they hire. Currently, they hire 40 robot hours per period. The short-run marginal cost curve is: MC = 4q/K (i) If Brucely Brothers receive $8 for every unit of output they produce, what is their profit maximizing output level? (ii) Calculate their profits. Should they shut down in the short-run? Explain why.

Answer 1

(i) Profit maximizing output level is that where price (P) = MC
So, 8 = 4q/K
So, q = 8*(K/4) = 8*(40/4) = 80 (as K = 40)

Profit maximizing output level is 80.

(ii) Profit = Total revenue - C = P*q - C
P*q = 8*(80) = 640
C = (2q^2/K)+10K = (2*80^2/40)+10*(40) = 320 + 400 = 720
Profit = 640 - 720 = -$80

Firm will shut down if price is less than minimum of Average Variable Cost (AVC) in short run.

C = (2q^2/K)+10K
So, Total Variable Cost (TVC) = (2q^2/K)
So, AVC = TVC/q = (2q^2/K)/q = 2q/K = 2q/40 = q/20 = 0.05q
AVC at q = 80 is 0.05*(80) = 4

And, MC = 4q/K = 4q/40 = q/10 = 0.1q

So, MC > AVC which means that AVC is rising. Thus, they should not shut down in the short run as P > minimum of AVC.