In the pair of supply and demand equations below, where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price. p = - x2 - 3x + 80 and p = 7x + 5

Equilibrium quantity = 5

Equilibrium price = 40

Explanation:

given:

p = - x²-3x+80

p = 7x+5

For the equilibrium quantity the price from both the functions will be equal

thus, we have

-x² - 3x + 80 = 7x+5

⇒ x² + 3x + 7x + 5 - 80 = 0

⇒x² + 10x - 75 = 0

now solving for x

x² - 5x + 15x - 75 = 0

x (x-5) + 15 (x-5) = 0

therefore, the two roots of the equation are

x = 5 and x = - 15

since the quantity cannot be in negative

therefore, the equilibrium quantity will be = 5

now the equilibrium price can be found out by substituting the equilibrium quantity in any of the equation

thus,

p = - (5) ² - 3 (5) + 80 = 40

or

p = 7 (5) + 5 = 40