Demand and supply functions

A demand equation or demand function expresses demand $q$ (the number of items demanded—for example the number sold) as a function of the unit price $p$ (the price per item).

A supply equation or supply function expresses supply $q$ (the number of items a supplier is willing to bring to the market—for example the number manufactured) as a function of the unit price $p$ (the price per item).

It is usually the case that demand decreases and supply increases as the unit price increases.

Demand and supply are said to be in equilibrium when demand equals supply. The corresponding values of $p$ and $q$ are called the equilibrium price and equilibrium demand. To find the equilibrium price, determine the unit price $p$ where the demand and supply curves cross (sometimes we can determine this value analytically by setting demand equal to supply and solving for $p$). To find the equilibrium demand, evaluate the demand (or supply) function at the equilibrium price.

#[Example][Ejemplo]#

#[If the demand for Ludington's Wellington Boots is $q = -4.5p + 4000$ pairs sold per day and the supply is $q = 50p - 1995$ pairs per week (see the graph below), then the market equilibrium price is obtained when demand = supply:][Si la demanda de Botas Wellington de Ludington es $q = -4.5p + 4000$ pares vendidos por semana y la oferta es $q = 50p - 1995$ pares por semana (vea la gráfica más abajo), entonces se obtiene el precio de equilibrio del mercado cuando la demanda = la oferta:]#

$-4.5p+4000$ \t ${}= 50p-1995$ \\ $54.5p$ \t ${}=5995$ \\ $p$ \t ${}=\dfrac{5995}{54.5} = \$110.$

#[The equilibrium price is therefore \$110 and the equilibrium demand is $q = -4.5(110) + 4000 = 3505$ pairs. per week. What happens at prices other than the equilibrium price can be seen in the following figure:][Sigue que el precio equilibrio es \$110 y la demanda de equilibrio es $q = -4.5(110) + 4000 = 3505$ pares por semana. Lo que ocurre a precios distintos del precio de equilibrio se puede ver en la figura siguiente:]#