A representative firm with long-run total cost given by TC = 2,000 + 20 q + 5 q 2 operates in a competitive industry where the market demand is given by QD = 10,000 – 40 P. The long-run equilibrium output of the industry will be:

Output = 22.88

Explanation:

Below is the given functions:

TC = 2,000 + 20 q + 5 q^2

QD = 10,000 – 40 P

P = (QD - 10000) / 40

Find the MC from TC.

Take tha first derivative of TC.

MC = 20 + 10q

Now TR = PQ

TR = ( (10000 - Q) / 40) Q       QD = Q

TR = 10000Q/40 - Q^2 / 40

MR =250 - Q/20

Now equate = MR =MC

250 - Q/20 = 20 + 10Q

-0.05Q - 10Q = 20 - 250

-10.05Q = - 230

Q = 22.88

Output = 22.88

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