Question

3. Consider a perfectly competitive market. Every firm has the same short-run cost function: STC=2,000+2q3-20q2+150q.
   1. (8) Derive and draw the short-run supply curve of the individual firm.
   2. (7) Find the range of price for which the individual firm makes a positive profit in the short-run.

Answer 1

Given,

In a perfectly competitive market the marginal cost curve represents the supply curve. Differentiate the STC curve wrt q we get

The MC curve from minimum point is the short run supply curve. Determining the Point where MC is minimum.

Differentiate MC and equate it to zero

Now, equating it zero

12q - 40= 0

=> 12q = 40

=> q = 40/12 = 10/3

MC is minimum at q= 10/3

In addition to above the firm will produce above the minimum AVC.

Determining the point where AVC is minimum. Differentiate AVC wrt q we get

Now, equate it to zero

4q - 20 = 0

=> 4q = 20

=> q = 5

Thus the firms supply curve must start from q = 5.

B. The firm will make positive profit in the short run when the price is above ATC. First determine the ATC.

Differentiate ATC wrt q we get

Now, equate it to zero

When q = 10,

Then the above equation satisfies the condition. Thus ATC is minimum at q = 10.

Minimum ATC will be at q = 10

Thus the firms would earn a positive profit above a price of $ 350.