Source: Microeconomic Theory, Ch. 8 (Texas A&M University)
Tags: long-run equilibrium, zero economic profit, free entry and exit, long-run average cost, LRAC, long-run marginal cost, LRMC, minimum efficient scale, number of firms, long-run supply curve, constant-cost industry, increasing-cost industry, decreasing-cost industry
In the long run, free entry and exit drives economic profit to zero in competitive markets. Price settles at the minimum of long-run average cost, and each firm produces at its efficient scale. The number of firms adjusts until total market supply meets demand at that price. The slope of the long-run market supply curve depends on what happens to input prices as the industry expands.
Long-run equilibrium
The state in which no firm wants to enter or exit the market. Each existing firm earns zero economic profit, price equals both marginal cost and the minimum of average cost, and the market clears.
Zero economic profit
In long-run competitive equilibrium, firms earn enough revenue to cover all costs, including the opportunity cost of the owner's time and capital. "Zero economic profit" does not mean the firm is struggling; it means it is earning a normal return, exactly what its resources could earn in their next-best use.
Free entry and exit
The ability of firms to enter a market when profits are positive and leave when profits are negative, without facing legal, financial, or structural barriers. This mechanism is what drives long-run profits to zero.
Long-run average cost (LRAC)
Total cost per unit when all inputs (including plant size) are variable. The minimum point of LRAC determines the long-run equilibrium price.
Long-run marginal cost (LRMC)
The cost of producing one additional unit when all inputs can be adjusted. In long-run equilibrium, LRMC = LRAC = p at the efficient scale of output.
Minimum efficient scale
The smallest quantity at which LRAC reaches its minimum. This is the output level each firm produces in long-run equilibrium.
Constant-cost industry
An industry in which input prices do not change as the industry expands or contracts. The long-run market supply curve is horizontal (perfectly elastic) at the minimum LRAC.
Increasing-cost industry
An industry in which input prices rise as the industry expands (e.g., specialised labour becomes scarcer). The long-run supply curve slopes upward.
Decreasing-cost industry
An industry in which input prices fall as the industry expands (e.g., through economies of scale in input supply). The long-run supply curve slopes downward.
The driving mechanism is free entry and exit.
If firms are earning positive economic profit, new firms enter, increasing market supply, which pushes the market price down until profit is zero.
If firms are earning negative economic profit (losses), some exit, reducing supply, which pushes price back up until profit is zero.
This is specifically about economic profit, not accounting profit. Firms in long-run equilibrium are still covering all their costs and earning a normal return on investment.
The other characteristics of perfect competition (identical products, information, many firms) support the process, but free entry and exit is the direct cause.
Three conditions hold simultaneously for each firm:
Economic profit = 0
p = AC (price equals average cost, so profit per unit is zero)
p = MC (the profit-maximisation condition still applies)
Because p = AC and p = MC at the same output, it follows that AC = MC, which only occurs at the minimum of the AC curve. So each firm produces at minimum average cost in the long run.
The general method:
Find the minimum of LRAC by setting LRAC = LRMC and solving for q. This gives the efficient scale per firm.
Plug that q back into LRAC to find the long-run equilibrium price.
Substitute the price into the market demand equation to find total market quantity.
Divide market quantity by the per-firm quantity to get the number of firms: n = Q / q.
Worked example (potatoes):
Minimum LRAC = $0.50/lb at q = 200 lbs per firm.
Long-run price = $0.50.
Market demand: Q = 5,000 / p = 5,000 / 0.50 = 10,000 lbs.
Number of firms: n = 10,000 / 200 = 50 firms.
Worked example (LRAC = 20 - 2q + 2q², LRMC = 20 - 3q + 4q²):
Set LRAC = LRMC to find efficient scale:
20 - 2q + 2q² = 20 - 3q + 4q²
Simplify: q - 2q² = 0, so q(1 - 2q) = 0.
q = 0 (trivial) or q = 0.5.
Alternatively, minimise LRAC by taking the derivative and setting it to zero:
d(LRAC)/dq = -2 + 4q = 0, giving q = 0.5.
Long-run price: LRAC at q = 0.5 = 20 - 2(0.5) + 2(0.25) = 20 - 1 + 0.5 = 19.50.
Market demand at p = 19.50: Q = 300 - 5(19.50) = 300 - 97.5 = 202.5.
Number of firms: n = 202.5 / 0.5 = 405 firms.
The shape of the long-run supply curve depends on how input prices respond to industry expansion:
Constant-cost industry: input prices unaffected by industry size. Long-run supply is horizontal at minimum LRAC. Most textbook examples assume this case.
Increasing-cost industry: input prices rise as the industry grows (more firms bidding for the same specialised inputs). Long-run supply slopes upward. This is the most common real-world case.
Decreasing-cost industry: input prices fall as the industry grows (e.g., suppliers achieve their own economies of scale). Long-run supply slopes downward. This is the least common case.
A downward-sloping long-run supply curve requires that input prices fall as the industry expands. It does not come from firms being identical or from the number of firms being restricted.
Long-run equilibrium conditions: p = MC = min(LRAC), economic profit = 0
Finding efficient scale: set LRMC = LRAC and solve for q (or minimise LRAC by taking its derivative)
Long-run equilibrium price: LRAC evaluated at the efficient scale q
Number of firms: n = Q_demand(p*) / q*
Market demand gives Q at the equilibrium price
⚠️ The reason profits are zero in the long run is free entry and exit, not identical products, not information, not constant returns to scale. This is a favourite distractor on multiple-choice exams.
⚠️ "All of the above" is correct when asked what holds in long-run equilibrium: economic profit = 0, p = AC, and p = MC all hold simultaneously.
⚠️ A downward-sloping long-run supply curve comes from falling input prices, not from restricting the number of firms. Do not confuse the direction of slope with barriers to entry.
⚠️ When computing the number of firms, always find the efficient scale first (set LRMC = LRAC), then find the price, then use demand to get Q, and finally divide. Skipping steps leads to errors.
⚠️ Zero economic profit does not mean zero accounting profit. The firm is still covering all costs including the owner's opportunity cost. Students often confuse this on short-answer questions.
Q: Why do long-run economic profits equal zero in a competitive market?
A: Because of free entry and exit. Positive profits attract new firms, which increases supply and drives price down. Losses cause firms to exit, reducing supply and pushing price back up. The process continues until economic profit is zero.
Q: In long-run competitive equilibrium, which of the following are true: economic profit = 0, p = AC, p = MC?
A: All three. They hold simultaneously. Since p = AC and p = MC, it follows that AC = MC, which occurs only at the minimum of AC.
Q: Under what condition is the long-run market supply curve downward-sloping?
A: When input prices fall as the industry expands. This is called a decreasing-cost industry.
Q: Minimum LRAC for potato firms is $0.50 at q = 200. Market demand is Q = 5,000/p. How many firms in the long run?
A: Price = $0.50. Q = 5,000/0.50 = 10,000. Number of firms = 10,000/200 = 50.
Q: If LRAC = 20 - 2q + 2q² and LRMC = 20 - 3q + 4q², what is the efficient scale per firm?
A: Set LRAC = LRMC: 20 - 2q + 2q² = 20 - 3q + 4q². Simplify to q = 2q², giving q = 0.5.
Q: In a constant-cost industry, what shape is the long-run supply curve?
A: Horizontal (perfectly elastic). The long-run price stays at the minimum of LRAC regardless of how much the industry expands, because input prices do not change.
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