Equilibrium Point of a Non-linear Supply and Demand

Quantitative Finance Level 1

For a given product, suppose that the formula for supply is Q s = 2 p 2 Q_s=2p^2 and the formula for demand is Q d = 300 − p 2 Q_d=300-p^2 . What's the equilibrium point?

10 300 \sqrt{300} 5 300 0

Christopher Williams by Christopher Williams , 33, USA

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1 solution

To solve for supply and demand equilibrium you must set Q d = Q s Q_d = Q_s , set the equation to 0 and find the roots . In this case: 2 p 2 = 300 − p 2 2p^2 = 300 - p^2
0 = 300 − p 2 − 2 p 2 = 300 − 3 p 2 0 = 300 - p^2 - 2p^2 = 300 - 3p^2 then divide both sides by negative three.
0 = p 2 − 100 0 = p^2 - 100
0 = ( p − 10 ) ( p + 10 ) 0 = (p - 10)(p+10)
p = 10 or p = − 10 p = 10 \text{ or } p=-10
We know that, in this case, price will not equal − 10 -10 , it will not be negative. So the equilibrium price is $ 10 \$10 . As a graph of the two equations would also show this intersection.

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