Question

Let the total cost function be C (q) = 50 + 2q + 0:5q2. For what values of q we have economies of scale?

Answer 1

Before solving the question, let us know about the term Economies of Scale.

When a firm increases its production, initially the Average Cost falls. Here, the firm experiences Economies of Scale up to that level of output for which its Average Cost falls and reaches its minimum value. Hence, we need to find out the minimum point of the Average Cost curve. The firm will experience Economies of Scale up to that level of production. After that level of production, the firm will experience Diseconomies of Scale as the Average Cost will rise again with increase in production.

Hence, from the Cost function, we get

The Average Cost is,

AC(q) = C(q)/q =

Now, we will find out the minimum point of the AC(q) curve and for that we need to differentiate AC(q) with respect to q and then put it equal to zero.

Hence,

dAC(q)/dq = 0

or,

or,

or,

or, q = 10

The minimum point of the AC curve is at q=10. Hence the firm will exibit Economies of Scale up to q=10. Hence, the range of values of q would be, .

Hence, the values of q for which we have economies of scale are, .

Hope the solution is clear to you my friend.