Question

# Suppose a representative firm producing in a perfectly competitive industry has the following cost function: C(q)...

Suppose a representative firm producing in a perfectly competitive industry has the
following cost function:
C(q) = q2 + 8q + 36
a. Solve for the firm’s average cost function.
b. At what level of q is average cost minimized (i.e. what is the minimum efficient scale for the
firm)? What is the value of average cost at this level of q?
c. Suppose all firms in this industry are identical and the demand function for this industry is as
follows:
Qd = 400 – 2P
Solve for the long run equilibrium price and quantity in this industry.

A) Average cost = C(q)/q = (q²/q)+(8q/q)+(36/q) = q+8+(36/q)

b) at min. AC,

d(AC)/dq = 0

Or, d[ q+8+(36/q)] /dq = 0

Or, 1+0+ (-36/q²) = 0

Or, -36/q² = -1

Or, q² = 36

Or, q= 6

Therefore, at q=6, AC is minimized.

When, q=6,

AC = 6 + 8 + (36/6) = 20

C) At long run equilibrium, in a Perfectly competitive industry, each firm produces at the point where Price= minimum point of ATC. Hence, each firm earns 0 economic profit.

At minimum Point of ATC, ATC=price= 20 (calculated in the previous part)

And at price=20, Qd= 400 - 2(20) = 360

Therefore, long run equilibrium price is p=20, and quantity in this industry is 360 units.