Pg. 1 of 4 1) What happens in a competitive industry in the long run when firms

Question

Pg. 1 of 4 1) What happens in a competitive industry in the long run when firms enter because profits are being made in the short run? Consider a competitive industry with firms that have these cost functions: TC = q3-8q2 +24q MC = 3q2-16q + 24 Ill. In the short run, if P = 20, A.What q will the firm produce? (Feel free to round off.) B. Whatwill the firm make? (Feel free to round off.) IV. In the long run, for the same TC, AC, and MC as #2: Show what quantity each firm will produce on a graph of the company's AC What will the firms charge? What quantity will the industry produce if D is: 1 P = 1008-2Q How many firms will there be? V. Evaluate the efficiency of this competitive firm in short run and long run equilibrium

Explanation / Answer

(I)

In the short run, competitive firms may make excess profit if their price is above their average total cost. Attracted by this excess profit, new firms enter the market (since entry is free), which erodes the excess profit. Eventually, long run equilibrium is established where no excess profit exists anymore.

Number of firms increases, output per firm decreases and there is no long run excess profit.

(II) Only data to be used for next question is provided.

(III) A competitive firm establishes equilibrium by equating its price with MC.

MC = 3q2 - 16q + 24

So:

20 = 3q2 - 16q + 24

3q2 - 16q + 4 = 0

This is a quadratic equation of the form: ax2 + bx + c = 0

q = - b ±(b2 – 4ac) / 2a

= [16 ±(256 – 48)] / 6 = (16 ± 14.42) / 6

= (30.42/6) or ((1.58/6)

= 10 or 0.26

(ii) When q = 10,

Profit = revenue - cost

= P x q - (q3 - 8q2 + 24q)

= (20 x 10) - (1000 - 800 + 240) = 200 - 440

= - 240 (Loss)

When q = 0.26,

Profit = (20 x 0.26) - (0.0176 - 0.54 + 6.24)

= 5.2 - 5.72

= - 0.50 (Loss)

(IV)

For this question onward: I suggest you cross-check your data. There is no unique quantity that firm will produce - it can produce either 0.26 units or 10 units, both of which are producing losses only. But this question suggests there exists only a single level of output, which is inconsistent with the answer.

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