Demand and supply curves

A classic application of $2\times 2$ systems is modelling the market of a good through its demand and supply curves.

Definition — Demand and supply

Given a good, we denote by $p$ the unit price and by $Q$ the quantity (in units or tonnes). The demand and supply curves are two empirical relationships $Q=Q(p)$, deduced from market observations:

• demand $Q_d(p)$: the quantity consumers are willing to buy at price $p$. It is decreasing in $p$ (if it costs more, you buy less of it).
• supply $Q_s(p)$: the quantity producers are willing to sell at price $p$. It is increasing in $p$ (if you sell for more, you produce more of it).

In the linear model (valid over small intervals): $Q_d(p) = a - b\,p, \qquad Q_s(p) = -c + d\,p, \qquad a,b,c,d > 0.$

Links

Topics: Linear systems
Concepts: Supply and demand · Linear model
Methods: Supply demand
Skills: Model