Class 13: Competitive Firms in Competitive Markets
Textbook reading: Kreps, Chapter 14, sections 14.1 through 14.4 and 14.6, plus the two stories in 14.5 (high-fructose corn syrup and shale oil, pages 326 to 329). Skip the toy model with sunk costs on pages 324 to 326 (it needs present values) and the subsection “Is Long-Run Supply Flat?” Where Kreps finds minimum average cost by setting a derivative to zero or equating two formulas, read it off the cost table instead, as in Class 12.
Key Ideas
The price taker
- Competitive firm: one of many sellers of an identical good, prices widely known, too small to move the price
- It sells as much as it wants at p and nothing above it, so MR = p
Economic profit
- Accounting profit: revenue minus the costs the firm pays out
- Economic profit: revenue minus every cost, including what the owners’ capital and time would earn in their best alternative use (Class 12)
- The difference is the owners’ outside option, so economic profit is the payoff from being in the industry relative to staying out
- Entry and exit are a game, and the industry is at a Nash equilibrium when no firm inside would do better by leaving and no firm outside would do better by entering (Class 2). With free entry and equal access to technology, that requires zero economic profit: positive profit invites entry, negative profit forces exit
- Zero economic profit is not failure: the owners earn a normal return on everything they put in
Demand and profit
- A firm with market power keeps its gains from stronger demand: price, quantity and profit all rise (Class 6)
- A competitive industry with free entry keeps none of them for long: the price rises until entrants arrive, then returns to minimum average cost, and economic profit returns to zero. Stronger demand changes how many firms supply the market, not how much each earns
When profits survive
- A firm with a superior input earns a rent to that input (better land, a patent)
Problems of the Day
Q37: One Firm, Then Fifty
A competitive firm can sell as much as it likes at the going price. Its fixed cost of $100 is avoided entirely by producing nothing. The marginal cost row gives the extra cost per unit of the last 50 units, as in Class 12.
| Output x | 50 | 100 | 150 | 200 | 250 | 300 |
|---|---|---|---|---|---|---|
| Total cost | $225 | $400 | $625 | $900 | $1,225 | $1,600 |
| Average cost | $4.50 | $4.00 | $4.17 | $4.50 | $4.90 | $5.33 |
| Marginal cost (last 50) | $2.50 | $3.50 | $4.50 | $5.50 | $6.50 | $7.50 |
The going price is $5. The owner asks two questions: how much should we make, and what should we charge? Answer both, and find the profit.
The price falls to $3. The marginal cost row points to 50 units. Should the firm make 50 units, or nothing? What is the lowest price at which it produces anything?
There are 50 identical firms and no entry. Fill in industry supply and find the equilibrium price and each firm’s output.
| Price | $4 | $5 | $6 |
|---|---|---|---|
| Industry supply | ___ | ___ | ___ |
| Demand | 8,000 | 7,500 | 7,000 |
Q38: A Resting Place
Every firm that is in or could enter this industry has the cost table below. The $100 fixed cost is avoidable by leaving the industry, and there is an unlimited queue of potential entrants who will enter if profits are above 0. Buyers want 600 units at $7.
| Output x | 25 | 50 | 75 | 100 | 125 |
|---|---|---|---|---|---|
| Total cost | $200 | $350 | $550 | $800 | $1,100 |
| Average cost | $8.00 | $7.00 | $7.33 | $8.00 | $8.80 |
| Marginal cost (last 25) | $4 | $6 | $8 | $10 | $12 |
The price is $7. Why can it not stay at $8? Why can it not stay at $6? How many firms are there at $7, and what does each earn?
Demand rises: buyers now want 1,100 units at $7. For a while the price sits at $9, with the same firms each making 75 units and earning $125. Why does the price not stay there, where does it end up, and how many firms are there then?
Starting again from (a), demand falls: buyers now want only 100 units at $7. For a while the price sits at $5, with each firm cut back to 25 units and losing $75. Why does the price not stay there, where does it end up, and how many firms are there then?
Q39: Who Earns the Profit
The industry of Q38 has come to rest at $7. Four of its firms hold a patented process that no one else may use, with the cost table below. Ordinary firms can still enter freely.
| Output x | 25 | 50 | 75 | 100 |
|---|---|---|---|---|
| Total cost | $150 | $250 | $400 | $600 |
| Average cost | $6.00 | $5.00 | $5.33 | $6.00 |
| Marginal cost (last 25) | $2 | $4 | $6 | $8 |
At $7, how much does a patent-holding firm make, and what does it earn? Why does entry not drive this profit to zero, as it did in Q38?
The patent belongs to an inventor who charges each of the four firms a fee per period for using it. What is the most a firm would pay? After paying it, what is the firm’s economic profit? Who ends up with the money, and what are they being paid for?
Answers
Q37. (a) Make 150 units: the last 50 cost $4.50 each and sell for $5, while the next 50 would cost $5.50 each; every block up to 150 adds more than it costs, every block beyond it the reverse. Charge $5: at $5.01 the firm sells nothing, and at $4.99 it gives money away, so the price question has no content. Profit is 750 − 625 = $125. (b) Nothing. At 50 units average cost is $4.50, so every unit loses $1.50 and the firm would lose $75, when staying out loses $0. The firm produces only when the price covers the lowest average cost it can reach, $4 at 100 units; below that, the marginal cost rule still finds the best output, but the best output is not worth running. (c) Industry supply is fifty times one firm’s: 5,000 at $4, 7,500 at $5, 10,000 at $6. It meets demand at $5, where each firm makes 150. The industry curve is nothing new, only the firm’s marginal cost row with every entry multiplied by fifty.
Q38. (a) At $8 every firm earns a profit (the price is above the $7 minimum of average cost), so someone in the queue enters, supply rises, and the price falls. At $6 every firm loses money whatever it makes, since no entry in the average cost row is below $7, so someone leaves and the price rises. Only $7 gives no one a reason to come or go: 600 / 50 = 12 firms, each earning zero economic profit, a normal return on the owners’ capital and nothing more. (b) At $9 the twelve firms earn $125 each, which is the invitation: entrants arrive, supply grows, and the price falls until the profit is gone, at $7. Buyers want 1,100 at $7, so 1,100 / 50 = 22 firms, ten of them new. (c) At $5 every firm is losing $75, so firms leave, supply shrinks, and the price rises until the survivors stop losing money, at $7. Buyers want 100 at $7, so two firms remain. Either shock moves the price for a while, but what it changes for good is the number of firms: the price comes back to $7 from above and from below, because $7 is the only price at which nobody wants to enter and nobody wants to leave.
Q39. (a) The patent firm makes 75 units, since the last 25 cost $6 each and the next 25 would cost $8, and earns 525 − 400 = $125. Entry cannot remove it: entrants can only copy the ordinary technology, and ordinary entry holds the price at $7 as in Q38 but no lower, since at any lower price ordinary firms leave. The $7 is set by the firm that is easiest to replace; the patent firm is cheaper than that and keeps the difference. (b) Up to $125 a period, since at any fee below that it still earns more than the zero it would earn as an ordinary firm. After paying, its economic profit is zero, like everyone else’s. The $125 ends up with the inventor, and it is a payment for the one thing in the industry that cannot be duplicated. A lasting profit in a competitive industry is never a reward for being there; it is the rent on whatever scarce input makes one firm cheaper than the firm at the margin, and it belongs to whoever owns that input.