All firms in a competitive industry have the following long-run total

All firms in a competitive industry have the following long-run total cost curve:

C(q) = q3 €“ 10q2 + 36q
where q is the output of the firm.
a. Compute the long run equilibrium price. What does the long-run supply curve look like if this is a constant cost industry? Explain.
b. Suppose the market demand is given by Q = 111 €“ p. Determine the long-run equilibrium number of firms in the industry.

ANSWER

a. Long run equilibrium is determined by (1 ) the minimum of the AC curves, and (2 ) the demand equation.
The AC is at a minimum where AC = MC:
Q = 5, AC = MC = 11
Therefore, the long run price will be $11 and each firm will produce 5 units.

b. The market quantity (from demand) is 100 and so 20 firms will exist in this market. The long run supply curve is flat at $11 because the price will always equal this due to free entry and exit of firms.