Price Elasticity of Supply (Midpoint Form)

The same arithmetic, the other side of the market, and the sign flips. Sellers offer more as the price rises, so $E_s$ is positive — and this page uses the same midpoint form as the demand page, for the same reason: it gives one number whichever direction you walk the price change.

What supply elasticity measures is how easily output can be expanded, and that is overwhelmingly a question about TIME and about spare capacity. Three cases are worth having in mind, because almost everything sits between them.

Perfectly inelastic, $E_s = 0$. The quantity is fixed and no price moves it. A fixed stock of land, the seats in a stadium tonight, a harvest already in the barn, an original painting by a dead artist. Everything interesting about taxation, rent and windfall gains hangs on this case, because when supply cannot move, a tax changes who gets the money and changes nothing else — which is the entire argument behind a land value tax, and it holds exactly as far as the inelasticity does.

Perfectly elastic, $E_s \to \infty$. Any quantity at all is available at one price and none at a penny less. A small buyer in a world commodity market faces this. In practice it describes an industry with easily replicable capacity and no scarce input.

In between, which is nearly everything. A factory with idle machines and a labour market to hire from has an elastic supply. The same factory at full capacity has an inelastic one — until it can build another factory, at which point it becomes elastic again. This is why supply elasticity is really a statement about a time horizon, and why the same industry can be quoted at 0.2 and at 3.0 without either figure being wrong.

The practical consequence is about who bears a tax, and it is the one result from this page that people use. The side of the market that can move away from the tax pays less of it. A tax on a good with inelastic supply and elastic demand falls almost entirely on the producers, because the buyers can go elsewhere and the sellers cannot stop producing. Reverse the elasticities and the buyers pay almost all of it. Nothing about who physically writes the cheque to the government affects this, which is why "the employer pays half the payroll tax" is a statement about paperwork rather than about incidence.

Two cautions on the arithmetic. First, a supply elasticity computed from two observations assumes the supply curve stayed put between them, and a cost shock, a strike or a bad season moves the whole curve — in which case the ratio you compute is measuring the shock and not the response to price. Second, a negative result is worth taking seriously rather than treating as a typo: backward-bending supply is real in labour markets, where a high enough wage buys leisure instead of hours. But it is much more often a sign that the two observations do not belong to one curve.