How in the world do you do this?

The demand and supply equations for a certain item are given by

D = –5p + 40

S = –p^2 + 30p – 8

Find the equilibrium price

Top 1 Answers

A few days ago

Aquaboy

Favorite Answer

“Equilibrium price is the price at which the quantity demanded of a good or service is equal to the quantity supplied.” In other words, when D = S. I’m guessing ‘p’ is the price, so:

D = S

=> –5p + 40 = –p^2 + 30p – 8

=> p^2 – 5p – 30p + 40 + 8 = 0

=> p^2 – 35p + 48 = 0

Now use the quadratic formula to solve for the price, p:

p = [-b +/- √(b^2 – 4ac)] / 2a

=> p = {35 +/- √[(-35)^2 – 4(1)(48)]} / 2(1)

=> p = 33.57 or 1.43

Therefore, the equilibrium price should be $33.57, (in whatever currency you’re working with), since $1.43 would yield a negative supply and demand.

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How in the world do you do this?

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