Supply and Demand

Definition

Demand is the relation that associates, with each possible price, the quantity buyers wish to acquire. Supply is the relation that associates, with each price, the quantity sellers wish to part with.

These are relations, not numbers. From this comes the most frequent confusion in the field:

Saying "demand rises because the price falls" is therefore incorrect: it is the quantity demanded that rises, moving along an unchanged demand.

The law of demand

All other things being equal, the quantity demanded of a good decreases when its price rises.

This regularity is massively confirmed, but it is not a theorem: consumer theory guarantees without exception only the substitution effect. Two distinct mechanisms are at work:

• the substitution effect: the good that has become relatively more expensive is abandoned in favour of others rendering a similar service. It is never of the contrary sense — theory guarantees that it cannot act upwards; at most it is nil;
• the income effect: with money income unchanged, a price rise cuts purchasing power. For a normal good — one bought in greater amounts as one grows richer — the quantity acquired falls. For an inferior good, it rises: the income effect then works against the substitution effect.

The clause "all other things being equal" is not an ornament: it isolates the effect of price from that of the other determinants — incomes, prices of other goods, preferences, number of buyers. A price and a quantity rising together are therefore not a counter-example to the law: the clause is broken, a curve has shifted.

Supply

For a seller who takes the market price without being able to bend it, the quantity supplied rises with the price: a higher price makes profitable units whose cost of production was previously prohibitive.

That cost is itself an opportunity cost: devoting resources to producing a unit means giving up their best other use. A seller produces as long as the price covers that abandoned value.

This positive slope rests on a firmer foundation than the law of demand: it follows from profit maximisation, with no income effect to work against it. Its limit lies elsewhere — the horizon. In the very short run, a quantity already produced can no longer be adjusted: above the price at which sellers agree to part with it, the curve becomes vertical.

The arrival of new sellers, by contrast, does not describe this slope: it shifts the entire supply curve.

The cases urged against the law of demand

A Giffen good is a good whose quantity demanded rises with its price. This presupposes an inferior good that absorbs a large share of the budget and has no close substitute: its price rise cuts purchasing power; the good being inferior, this impoverishment pushes towards buying more of it, and this income effect outweighs the substitution effect. These three conditions are necessary, not sufficient: a good may meet them all without the income effect prevailing, and then see its quantity demanded fall when its price rises.

Consumer theory does not exclude it: the possibility is a fact of theory. Its empirical demonstration, on the other hand, is rare and disputed — the cases put forward are the object of methodological debate, and none amounts to uncontested proof. Observed existence remains an open question.

A Veblen good is sought after because its high price signals status. The effect is observed in studies of consumer behaviour, without being universal. Above all, it does not invalidate the law: the price there alters the perceived nature of the good, which breaks the clause "all other things being equal" instead of contradicting the relation itself.

Equilibrium

In a market where neither buyers nor sellers set the price, the equilibrium price is the one at which the quantity supplied equals the quantity demanded. At that price, and at that price alone, no buyer or seller willing to trade goes away disappointed.

This is what explains why a price held by authority below equilibrium goes together with a shortage: at the imposed price, the quantity demanded exceeds the quantity supplied, and the price, being blocked, cannot take the value at which the two quantities would coincide.

Convergence towards equilibrium

That equilibrium exists is proved under assumptions of continuity and of behaviour at the bounds — in particular, the gap between the two quantities must change sign. That is a fact of theory. That it should be reached is of an altogether different nature.

This second claim presupposes an adjustment process — sellers lower their price in the face of unsold stock, raise it in the face of shortage — whose convergence is not guaranteed in general. Reaction lags may sustain oscillations around equilibrium instead of damping them. Equilibrium is a solid reference point for analysis; the movement leading to it is a model, and taking it for granted goes beyond what theory establishes.

Summary

An equilibrium price is not a property of the thing: it is the only value at which what buyers wish to acquire and what sellers wish to part with coincide.