Demand curve

The relationship between the price and the quantity of a good is one of the most classic functional models: how many products are customers willing to buy as the price varies?

Definition — Demand curve

The demand curve $D(p)$ expresses the quantity of a good that consumers are willing to buy as a function of the price $p$. It is a decreasing function of $p$: the higher the price, the fewer purchases. Simplified linear model: $D(p) = a - b\,p, \qquad a,b>0.$ $a$ is the quantity demanded at zero price; $a/b$ is the reservation price (beyond which nobody buys: $D(p)=0$).

Example — Gelmini & Cremonini's anti-anxiety drug

A pharmaceutical company produces a drug at a cost of $5$ € per box. At zero price customers would buy $10\,000$ boxes a month; the maximum price at which anyone is willing to buy it is $28$ € (beyond that price nobody buys).

Requiring the demand to pass through the two points $(0;\,10\,000)$ and $(28;\,0)$, the line is $D(p) = -\frac{10\,000}{28}\,p + 10\,000 = 10\,000\Bigl(1 - \frac{p}{28}\Bigr).$ For $p=14$ €: $D(14) = 5\,000$ boxes/month.

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Topics: Functions and properties
Concepts: Demand curve · Reservation price
Functions: Line
Methods: Linear demand curve
Skills: Modelling