#[Demand function][Función de demanda]#
A
demand function expresses demand $q$ (the number of items demanded) as a function of the unit price $p$ (the price per item). It is usually the case that demand decreases as the unit price increases.
#[A
linear demand function is a demand function of the form][Una función de demanda
lineal es una función de demanda de la forma]#
$q(p) = mp + b$ \gap[40] \t
Also, as we expect demand to decrease as the price increases, it is normally that case that $m$ is negative.
Example
#[If the demand function for T shirts, measured in the number of shirts sold per day, is $q(p) = -4p + 90$, then setting the price at \$10 would result in daily sales of ][Si la función de demanda para playeras, medida en el número de playeras vendidas por dí, es $q(p) = -4p + 90$, entonces establecer el precio en \$10 resultaría en ventas diarias de]#
$q(10)$ \t ${}= -4(10) + 90$
\\ \t ${}= 410$ #[T shirts per day][playeras por día]#.
The slope $-9$ tells us that daily sales drop by 9 T shirts per \$1 increase in the price. The $q$-intercept tells us that, it the price were set at zero, then the semand for the T-shirts would amount to 500 per day.