Question

Use the following long run total cost (LTC) function to answer the question that follows, : LTC=Q^3-100Q^2+2550Q

a. What levels of output will this firm experience economies of scale?

   i. Q<

b. What levels of output will this firm experience diseconomies of scale?

ii.  Q>

Answer 1

To find the economies of scale and diseconomies of scale, we neet to find the long run average cost (LATC) from the long run total cost (LTC) as:

Now we will find the quantity at which the LATC is minimum. So, as long as the Output is less than the output at which the AC is minimum the firm will said to experience increasing returns to scale. On the other hand, as long as the Output is more than the output at which the AC is minimum the firm will said to experience increasing returns to scale.

Minimisation of LATC:

We have,

1st order condition:

2nd order condition:

Since, the LATC''(Q)>0, the problem is minimised.

And thus, when Q=50, the LATC is minimised.

Answer to the question no. a:

Thus, as long as the Q<50, the LAC is falling, and this is the situation of increasing returns to scale. The firm experiences increasing returns to scale simulteniously with the economies of scale.

Answer to the question no. b:

Thus, as long as the Q>50, the LAC is rising, and this is the situation of decreasing returns to scale. The firm experiences decreasing returns to scale simulteniously with the diseconomies of scale.