Long-run competitive equilibrium: why profit does not last
Learning goals
After this page, you can:
- Explain the chain profit → entry → more supply → lower price → profit gone (and the reverse for losses and exit), ending at P = min ATC.
- Compute the long-run price, output per firm and number of firms from a cost table and a market demand.
- Tell zero economic profit from zero accounting profit, name what slows entry, and describe consumer and producer surplus in words.
The idea
A town gets its first two craft-beer taprooms. Both are full every night. Three years later there are nine. The weekday tables are half empty. Each owner now earns about what she could earn running someone else’s bar. Nobody agreed to cut the profit. Entry did it.
Profit is a signal. In a competitive market anyone can start a firm. When the firms in a market earn more than they could elsewhere, outsiders notice. Some of them come in. This is entry. When firms lose money year after year, some leave when their leases end. This is exit.
The entry chain. Follow one step at a time.
- Firms earn a profit.
- New firms enter.
- Each new firm adds its output, so market supply shifts right.
- With more for sale, the market price falls.
- The lower price shrinks each firm’s profit.
The chain keeps running as long as there is profit left. It stops only when profit is zero. The exit chain runs the other way: losses → firms leave → supply shifts left → the price rises → losses shrink. It also stops at zero.
Where it stops: P = min ATC. Profit is zero when the price equals average total cost. And each firm still produces where P = MC. Both are true at one point only: the bottom of the ATC curve. So in the long-run competitive equilibrium:
- the price equals the lowest ATC;
- each firm produces the output where ATC is lowest;
- economic profit is zero.
Notice a nice side effect. In the long run, competition pushes every firm to produce at its lowest possible cost per unit. Buyers pay that lowest cost and no more.
How many firms? In the long run the price is min ATC. At that price, market demand tells you the total quantity buyers want. Each firm makes the output at min ATC. So: number of firms = market quantity demanded at min ATC ÷ output per firm. If demand grows, the long-run price does not change. New firms enter until the price is back at min ATC. The market simply ends up with more firms, each the same size as before.
“Zero profit” is not as bad as it sounds. Economists mean economic profit: accounting profit minus the owners’ opportunity costs — what their time and their money could earn in the next-best use. An owner with zero economic profit still covers all her bills. She also earns as much as she would in her best other option. That is called a normal return. So her books can show a healthy profit, while her economic profit is zero. She has no reason to leave. Newcomers have no reason to come in.
What slows entry. Profit lasts only where something blocks newcomers. These are barriers to entry:
- licenses or permits that cap the number of sellers (taxi medallions, liquor licenses);
- a large scale needed to be efficient (a new steel mill is expensive);
- strong brands and customer habits;
- patents and secret know-how.
When you see a market that stays very profitable for years, ask what barrier is protecting it. Week 5 picks up this thread.
Who gains from trade? One last idea, in words only. Say a miller would pay up to $9.00 for a bushel, and pays the market price of $7.50. She keeps $1.50 of value. That is consumer surplus: what a buyer would pay minus what she pays. The farm grew that bushel for an extra $6.00 and sells it for $7.50. It keeps $1.50. That is producer surplus: the price minus the seller’s extra cost. The single trade creates $3.00 of value that did not exist before. A competitive market makes every trade where the buyer’s value is above the seller’s cost.
Long run: P = min ATC · each firm produces at min ATC · economic profit = 0
Number of firms = market quantity demanded at min ATC ÷ output per firm
Economic profit = accounting profit − owners’ opportunity costs (time and capital)
Consumer surplus = what the buyer would pay − price · Producer surplus = price − the seller’s extra cost
Try it
Left: the wheat market, with demand Q = 1,400 − 80P (thousand bushels). Right: one Cedar Ridge farm. Every farm has the same costs (min ATC $7.50 at 8 thousand bushels).
- Press 80 farms (profitable), then Next year a few times. Watch supply shift and the green rectangle shrink.
- Press 130 farms (losing), then Run to the long run. Where does the price end up?
- Set demand to +10% and run again. How many farms are there at the end? What is the price?
Worked example
Problem. Every wheat farm has Cedar Ridge’s costs: min ATC $7.50 at 8 thousand bushels. Market demand is Q = 1,400 − 80P (Q in thousand bushels). Today there are 80 farms. Find today’s outcome and the long run.
Step 1. Today. At $8.50 each farm grows 9 thousand bushels (its MC rule). Market supply = 80 × 9 = 720 thousand. Demand at $8.50 = 1,400 − 80 × 8.50 = 720. The market clears. Each farm earns +$8,000 of economic profit.
Step 2. Entry. Profit attracts new farms. With 95 farms the price is $8.00. Each farm grows 8 thousand: 95 × 8 = 760 = 1,400 − 640. Profit falls to +$4,000.
Step 3. The long run. Entry stops when profit is zero, at P = min ATC = $7.50. Demand at $7.50 = 1,400 − 600 = 800 thousand bushels. Each farm grows 8 thousand. Number of farms = 800 ÷ 8 = 100 farms. Economic profit = zero.
Step 4. Zero economic profit ≠ zero accounting profit. An owner’s books show $60,000 of profit. She could earn $45,000 managing another farm, and $15,000 by renting her land to a neighbor. Economic profit = 60,000 − 45,000 − 15,000 = $0. She covers every opportunity cost, so she is not tempted to leave.
Step 5. Surplus in words. The miller would pay $9.00 and pays $7.50: consumer surplus $1.50. The farm’s extra cost was $6.00: producer surplus $1.50. Together the trade creates $3.00 of value.
Check yourself
Every wheat farm has the same costs: lowest average total cost $7.50 a bushel at 8,000 bushels. At $7.50 the market buys 800,000 bushels. How many farms will there be in the long run?
Number of firms = market quantity at min ATC ÷ output per firm.
In long-run equilibrium, a farm owner’s books show a $60,000 profit. She could earn $45,000 managing another farm and $15,000 by renting her land to a neighbor. What is her economic profit?
Economic profit = accounting profit − the owners’ opportunity costs.
Wheat sells for $8.50 and every farm earns $8,000 of economic profit a year. Anyone can rent land and start a farm. What happens over the next few years?
Profit → entry → more supply → lower price → profit gone.
Which change would let high profits in a market last the longest?
Profits last only where something stops entry.
A miller would pay up to $9.00 for a bushel of wheat and buys it at the market price of $7.50. The farm’s extra cost of growing that bushel was $6.00. How much value does this one trade create for the two of them together?
Gains from trade = consumer surplus + producer surplus = value to the buyer − cost to the seller.
Video
Video coming soon.