Firms, Costs & Profit
Quantity comes from MR = MC; for a competitive firm MR = P, so P = MC. Then compare P to ATC at that quantity — profit is a rectangle, never a triangle.
Why the competitive firm is a price taker
Each firm is too small for its own output to move the price, so the demand curve facing one firm is horizontal at the market price and MR is flat and equal to P. A North Dakota oil rig takes the world oil price as given.
Costs, carefully
- Fixed cost Cf
- Does not vary with output — drilling the well, the facility, the equipment.
- Variable cost Cv(q)
- Varies with output — labor and materials used up.
- Marginal cost
- MC = C′(q) = Cv′(q). Fixed costs drop out.
- Average total cost
- ATC = C(q)/q = Cf/q + Cv(q)/q. Starts high, falls, then rises.
- MC cuts ATC at its minimum
- MC below ATC drags the average down; above, it pulls it up. Calculus: ∂(C(q)/q)/∂q = 0 gives C′(q) = C(q)/q.
Entry, exit and the long run
Positive profits attract entry, supply shifts out, the price falls. Negative profits cause exit, supply shifts in, the price rises. Zero profit is the resting point — Adam Smith's invisible hand, and why economists dislike barriers to entry.
| Firms are… | Long-run supply | Who earns what |
|---|---|---|
| Identical | Perfectly elastic — horizontal at minimum ATC | P = MC = ATC; zero profit for everyone |
| Different productivity better and worse oil wells | Slopes up | All set P = MC; the marginal (least productive) firm earns zero; better firms earn returns to their better wells |
Rules that earn points
- Find quantity from MR = MC. For a competitive firm, P = MC.
- Compare P to ATC at that quantity to sign the profit.
- Draw profit as a rectangle: height (P − ATC), width q.
- In the long run, ask whether entry is free. Free entry ⇒ zero profit for the marginal firm.
- Confusing producer surplus with profit. Producer surplus ignores fixed costs; profit subtracts them.
- Letting fixed costs into marginal cost. They are not there.
- Shutting down over negative short-run profit. If price covers variable cost, keep producing.
- Reading zero profit as failure. It means all opportunity costs, including the owner's, are covered.
Market demand for wheat slopes down, yet the demand curve facing one wheat farm is horizontal. Why?
- ABecause wheat has no substitutes
- BBecause the farm is small relative to the market, so its output does not move the price
- CBecause the farm's marginal cost is constant
- DBecause consumers buy wheat in fixed quantities regardless of price
Answer
B — the firm is small relative to the market.
It can sell as much as it wants at the going price and nothing at all above it. The consequence is that MR is flat and equal to P, so MR = MC collapses to P = MC.
C is the trap: it confuses a property of cost with a property of revenue. The firm's MC still rises — that is what makes its supply curve slope up.
The marginal cost curve crosses the average total cost curve:
- AAt the minimum of MC
- BAt the minimum of ATC
- CWhere ATC is still falling
- DWherever fixed costs equal variable costs
Answer
B — at the minimum of ATC.
Arithmetic of averages: when MC < ATC the next unit drags the average down, when MC > ATC it pulls the average up. The average stops falling and starts rising exactly where MC passes through it.
A is the trap: MC has its own minimum, well to the left, and it is not where the two curves meet.
A competitive firm faces P = $12. At its profit-maximizing output of 100 units, ATC = $10 and average variable cost = $7. Economic profit is:
- A$200
- B$500
- C$1,200
- DZero, because competitive firms make zero profit
Answer
A — $200.
Profit = (P − ATC) × q = ($12 − $10) × 100 = $200. The rectangle's height is the gap between price and average total cost.
B is the trap: ($12 − $7) × 100 uses variable cost, which gives producer surplus, not profit. Producer surplus ignores fixed costs; profit subtracts them.
In long-run competitive equilibrium with identical firms, economic profit is zero. This means:
- AFirms are losing money and will soon exit
- BEvery input, including the owner's time and capital, earns exactly its next-best return
- CAccounting profit is also zero
- DPrice has fallen below average variable cost
Answer
B — every input earns its opportunity cost.
Total cost is the opportunity cost of all inputs. At P = MC = ATC there is simply no force pushing entry or exit.
C is the trap: accounting profit is typically positive here, because accountants do not charge the firm for the owner's time or the return its capital could earn elsewhere.
Draw a competitive firm making positive economic profit in the short run. Then show what happens to the market and to the firm in the long run, assuming firms are identical.
Model answer
Short run: flat MR at P₁ above the ATC curve. Quantity q₁ where MC = MR. Profit is the rectangle (P₁ − ATC₁) × q₁.
Long run: those profits attract entry. Market supply shifts out, the market price falls, and the firm's flat MR line slides down. Entry stops only when P equals minimum ATC, where P = MC = ATC and economic profit is zero.
With identical firms the long-run industry supply curve is a horizontal line at that minimum ATC.
- MR drawn flat, and quantity taken from MC = MR, not from the ATC minimum.
- Profit drawn as a rectangle with height (P₁ − ATC₁) and width q₁.
- Entry shown shifting market supply, with the firm's MR sliding down as a consequence.
- The end point named precisely: P = MC = ATC at minimum ATC.
- Long-run industry supply identified as perfectly elastic.
Once a farmer already owns a chicken farm, what determines the marginal cost of an egg, and is it high or low? What does that imply about the shape and position of the supply curve?
Model answer
Marginal cost is the cost of keeping one more laying hen — feed, water, henhouse space, some fencing or a guard dog. A hen lays about one egg a day. These costs are low, so the marginal cost of an egg is low.
The supply curve therefore slopes upward but sits low: marginal cost still rises with production, as for most physical goods, but from a low base. The farm itself is a fixed cost and does not enter marginal cost at all.
- Listing actual marginal inputs (feed, water, space), not "the cost of the farm".
- Explicitly excluding the farm as a fixed cost.
- Both features of the curve: upward-sloping and low.
- Connecting MC to supply — the firm's supply curve is its MC curve.