Question

The Q & H company produces toothpaste and its cost function is C(Q)=4+Q^(1/2). Calculate the value of S (S=AC/MC, the measure of economies of scale). Does the production exhibit economies of scale (increasing returns to scale)?

Answer 1

Answer : Given,

C(Q) = 4 + Q(1/2)

AC (Average Cost) = C(Q) / Q

=> AC = [4 + Q(1/2)] / Q

=> AC = (4/Q) + 1/2

MC = C(Q) / Q

=> MC = 1/2

Now,

S = AC / MC

=> S = [(4/Q) + 1/2] / (1/2)

=> S = [(4/Q) / (1/2)] + [(1/2) / (1/2)]

=> S = [4/Q * 2/1] + 1

=> S = (8/Q) + 1

The value of S is, S = (8/Q) + 1.

Now let Q = 1. So,

S = (8/1) + 1

=> S = 9

Like Q =1 at every quantity level the value of S will be greater than 1. This means that here at every quantity level S > 1. The economies of scale situation occur when S > 1. Here as at every quantity level the value of S is greater than 1, hence here "the production exhibits the economics of scale".