A demand schedule says how much buyers want at each price; a supply schedule says how much sellers offer. Only one price makes the two equal, and at any other price the market is visibly out of balance — a queue or a pile of unsold stock — which is what pushes the price back.
Write them as straight lines, which is how examination questions almost always give them:
\[ Q_d = 900 - 3 P \qquad\qquad Q_s = 100 + 5 P \]Given: the two schedules above. Asked: the price and quantity at which the market clears.
Set \( Q_d = Q_s \), because equilibrium means the two are equal:
\[ 900 - 3 P = 100 + 5 P \]Collect the price terms on one side and the numbers on the other:
\[ 900 - 100 = 3 P + 5 P \qquad\Longrightarrow\qquad 800 = 8 P \] \[ P^{*} = \frac{800}{8} = 100 \]Substitute back into either schedule — use both, as a check:
\[ Q_d = 900 - 3(100) = 600 \qquad Q_s = 100 + 5(100) = 600 \]Both give 600, so the arithmetic is right. The market clears at a price of 100 with 600 units traded.
What it means: at any price above 100, supply exceeds demand and sellers cut prices to shift stock; below it, buyers compete and bid the price up. Only at 100 does nobody have a reason to move.
For a linear demand curve \( Q_d = a - bP \), the slope \( dQ/dP \) is just \( -b \), so the elasticity at a point is \( b \cdot P/Q \). Note that it changes as you move along the curve even though the slope does not — a fact examiners like.
| Value | Name | Meaning |
|---|---|---|
| \( E_p = 0 \) | Perfectly inelastic | Quantity does not respond at all |
| \( 0 < E_p < 1 \) | Inelastic | Quantity responds less than proportionately |
| \( E_p = 1 \) | Unitary | Revenue unchanged by a price change |
| \( E_p > 1 \) | Elastic | Quantity responds more than proportionately |
| \( E_p = \infty \) | Perfectly elastic | Any rise loses every buyer |
At \( P = 100,\; Q = 600 \), with \( b = 3 \):
\[ E_p = 3 \times \frac{100}{600} = \frac{300}{600} = 1/2 \]That is inelastic: a 1% rise in price costs only half a per cent of quantity. So revenue rises when price rises — which is the link examiners test. Total revenue moves with price when demand is inelastic, against price when it is elastic, and does not move at all when elasticity is exactly one.
Other elasticities, same shape. Income elasticity replaces \( P \) with income; a negative value marks an inferior good. Cross elasticity replaces the price of the good with the price of another; positive means substitutes, negative means complements. The site’s undergraduate Demand Analysis unit works those in detail, including Engel curves and the Leontief and Pigou methods of estimation, and is worth reading beside this section rather than after it.
Put a tax of 20 per unit on sellers. They will supply the same quantity only if they receive the old price, so the supply schedule shifts: the price in it becomes \( P - 20 \).
\[ Q_s = 100 + 5(P - 20) = 100 + 5 P - 100 = 5 P \]Set demand equal to the new supply:
\[ 900 - 3 P = 5 P \qquad\Longrightarrow\qquad 900 = 8 P \qquad\Longrightarrow\qquad P = 112.5 \]So the price paid by buyers rises from 100 to 112.5 — a rise of 12.5, not of 20. Sellers receive \( 112.5 - 20 = 92.5 \), which is 7.5 less than before.
The tax is shared, and the split is not arbitrary. Buyers bear 12.5 and sellers 7.5, in the ratio \( 12.5 : 7.5 = 5 : 3 \) — which is exactly \( b_s : b_d \), the ratio of the two slopes. The side that responds less to price bears more of the tax. Here supply responds more (slope 5 against 3), so sellers escape the larger share and buyers carry it.
That single sentence is the answer to most tax-incidence questions: incidence falls on the inelastic side.
How many sellers? Is the product identical across them? Can a new firm enter? Does any one firm have power over price? The four standard structures are the four useful combinations of those answers.
| Perfect competition | Monopoly | Monopolistic competition | Oligopoly | |
|---|---|---|---|---|
| Sellers | Very many | One | Many | Few |
| Product | Identical | No close substitute | Differentiated | Identical or differentiated |
| Entry | Free | Blocked | Free | Restricted |
| Power over price | None — a price taker | Considerable | Some, within its niche | Considerable, but interdependent |
| Demand curve facing the firm | Horizontal | The market curve, downward | Downward, quite elastic | Kinked |
| Long-run profit | Normal only | Can be supernormal | Normal only | Can be supernormal |
The kinked demand curve is the oligopoly answer worth remembering: rivals match a price cut but not a price rise, so demand is elastic above the going price and inelastic below it. The kink makes the marginal revenue curve discontinuous, and that gap is why oligopoly prices are sticky even when costs move.
A firm maximises profit where
\[ MR = MC \qquad\text{and}\qquad MC \text{ is rising} \]The first part is necessary: while an extra unit adds more to revenue than to cost, making it raises profit. The second part rules out the minimum, which also satisfies \( MR = MC \) — a point examiners test by asking why one condition is not enough.
Under perfect competition the firm is a price taker, so \( AR = MR = P \) and the condition becomes \( P = MC \). Under monopoly the demand curve slopes down, so \( MR < AR \), and price is read off the demand curve above the profit-maximising quantity — not off the \( MR = MC \) intersection itself. Taking price from the wrong curve is the classic error in this topic.
The liquidity trap is the case examiners ask about: at a very low rate, everyone expects rates to rise and bond prices to fall, so the demand for money becomes perfectly elastic and further increases in the money supply are absorbed without the rate moving. Monetary policy loses its grip; that is the argument for fiscal policy in a slump.
Rent, wages and interest are contracted in advance. Profit is what is left afterwards, and it can be negative — which is why the theories of profit are theories of why a residual should exist at all:
Normal profit is a cost, supernormal profit is not. Normal profit is the minimum that keeps the entrepreneur in this business rather than the next one, so it is included in cost; anything above it is the surplus that attracts entry.