Q.The demand function for a product is $Q_d = 100 - 2P$ and the supply function is $Q_s = -20 + 3P$, where $P$ is the price per unit. Find the equilibrium price and quantity.

Market equilibrium occurs where the quantity demanded equals the quantity supplied at the same price.

At market equilibrium, quantity demanded equals quantity supplied at the same price, so we set $Q_d = Q_s$:

Collecting the $P$ terms on one side and the constants on the other:

So the equilibrium price is $P_e = 24$.

Finding the equilibrium quantity, substitute $P=24$ into the demand function:

Dual check using the supply function:

$Q_s = -20 + 3(24) = -20 + 72 = 52$ …

A common arithmetic slip is moving a term to the wrong side with the wrong sign — e.g. writing $100-20 = 3P+2P$ instead of $100+20=3P+2P$. Always add t …