Pre Calc Market Equilibrium

Question

The weekly demand and supply functions for Sportsman 5 ✕ 7 tents are given by

p = −0.1x² − x + 76 and

p = 0.1x² + 2x + 56

respectively, where p is measured in dollars and x is measured in units of a hundred.

Find the equilibrium quantity (in hundred units).

Find the equilibrium price (in dollars)

Answer 1

-x^2/10 -x +76 = x^2/10 +2x +56

x^2/5 + 3x - 20 = 0

x^2 +15x - 100 = 0

(x+20)(x-5) = 0

x=5 = 500 tents, (ignore the negative solution)

P = 25/10 + 10 + 56 = 68.5 = $65.50 = equilibrium price

or plug 5 into the other equation, & get the same equilibrium price

P =- - 2.5 - 5 + 76 = 68.5