Consider the long run equilibrium in the market with the number of firms you found in (b) above each producing the amount you found in (c). Now demand increases to [math: Q2(P)], where [math: Q2(P)Q1(P)] for all [math: P].In the short run, will each incumbent firm produce more than, less than, or the same amount as what you found in (c)?

Question

Consider the long run equilibrium in the market with the number of firms you found in (b) above each producing the amount you found in (c). Now demand increases to [math: Q2(P)], where [math: Q2(P)>Q1(P)] for all [math: P].In the short run, will each incumbent firm produce more than, less than, or the same amount as what you found in (c)?

BlackTom AI · Accepted Answer

Price-taking firms in the short run produce where P = MC, so a higher market price induces each firm to increase output until its marginal cost equals the new price.

1) Relevant concepts:
- Long-run competitive equilibrium: P1 = min ATC and each firm produces q1 where MC(q1) = P1 (zero economic profit).
- Short-run for a fixed number of firms: market demand shifts change the market price; firms are price-takers and choose output q to satisfy P = MC(q).
- If MC is upward-sloping in the relevant range, higher P implies higher q.

2) Step-by-step reasoning:
- Initially, at the long-run equilibrium corresponding to Q1(P), the market price P1 equals the minimum average total cost and each firm’s output q1 satisfies MC(q1) = P1.
- Demand increases to Q2(P) > Q1(P) for all P. With the number of firms fixed in the short run, the market-clearing price rises to some P2 > P1.
- Each incumbent firm faces this new price P2 and, as a price-taker, sets output such that P2 = MC(q2).

3) Intermediate/equational step:
- Let MC(·) be strictly increasing around q1. From the initial condition MC(q1) = P1 and P2 > P1, invert MC to get q2 = MC^{-1}(P2). Because MC^{-1} is increasing, q2 > q1.

4) Why the correct answer is correct:
- Because firms equate price and marginal cost and marginal cost increases with output, a higher short-run market price leads each firm to expand production above the long-run quantity q1. Thus each incumbent produces more than in (c).

5) Why the other choices are incorrect:
- B (less than): contradicts P = MC logic — a higher price does not reduce a profit-maximizing price-taker’s output.
- C (the same): would hold only if MC were flat at that range or price did not change; here demand raises the equilibrium price in the short run, so output changes.
- D (not enough information): unnecessary — given standard assumptions (upward-sloping MC and price-taking firms), the direction of change is determined.

Conclusion: Each incumbent firm produces more in the short run than the amount in (c). This matches answer A.

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