Question

The weekly demand and supply functions for Sportsman 5 × 7 tents are given by
p = −0.1x^2 − x + 33
p = 0.1x^2 + 2x + 13
respectively, where p is measured in dollars and x is measured in units of a hundred. Find the equilibrium quantity. Find the equilibrium price.

Answer 1

The equilibruim point of a demand and supply function is the point at which the quantity demanded is equal to the quantity supplied.

Given the demand function as
$p = -0.1x^2 - x + 33$
and the supply function as
$p = 0.1x^2 + 2x + 13$

The equilibruim quantity is obtained as follows:
$-0.1x^2 - x + 33=0.1x^2 + 2x + 13 \\ \\ \Rightarrow0.2x^2+3x+46=0 \\ \\ \Rightarrow x=-7.5\pm13.18i$

There is no real equilibruim quantity and price for the given demand and supply function.