Section 4

Market Equilibrium

A market reaches equilibrium at the price where the amount buyers want to purchase exactly equals the amount sellers want to offer. At that price, and only that price, everyone who wants to trade at the going rate can do so — no one is left holding unwanted stock, and no one is left empty-handed.

Think of a farmers-market stall selling tomatoes. If the price is set too high, the seller goes home with boxes still full; if it is set too low, the queue stretches out the door and the tomatoes are gone by 9 a.m. The price that clears the stall — leaving neither leftover supply nor unmet demand — is the equilibrium price.

What happens away from equilibrium

In this market, quantity demanded is $Q_d = 100 - 2P$ and quantity supplied is $Q_s = -20 + 4P$ . At $P = 30$ , buyers want $Q_d = 100 - 2(30) = 40$ units but sellers offer $Q_s = -20 + 4(30) = 100$ units. That leaves 60 units unsold — a surplus (more supplied than demanded). Sellers who cannot move their stock have every reason to cut the price, and the price falls.

At $P = 10$ , the picture reverses: buyers want $Q_d = 100 - 2(10) = 80$ units but sellers offer only $Q_s = -20 + 4(10) = 20$ units. That 60-unit gap is a shortage (more demanded than supplied). Frustrated buyers compete for the limited stock and bid the price up. In both cases the price moves toward the same destination: $P^* = 20$ .

Supply and demand: equilibrium at P* = 20, Q* = 60

The demand curve slopes down — buyers want less as the price rises. The supply curve slopes up — sellers offer more as the price rises. The two curves cross at

P^* = 20

Q^* = 60

: the market's equilibrium. At any other price, one side of the market cannot do what it wants, and that pressure pushes the price back toward the crossing point.

How to find the equilibrium price

Setting quantity demanded equal to quantity supplied is the whole method for finding the equilibrium price and quantity — everything else is algebra.

Step 1
$Q_d = Q_s$
Equilibrium means buyers and sellers agree on quantity: the number of units changing hands is the same from both sides of the market.
Step 2
$a - bP = c + dP$
Substitute both linear equations. Here $a$ and $c$ are the intercepts of the demand and supply schedules, and $b$ and $d$ are their slopes with respect to price.
Step 3
$P^* = \frac{a - c}{b + d}$
Collect the $P$ terms on one side and divide. The numerator $a - c$ is the gap between the two curves' price-axis intercepts; the denominator $b + d$ is their combined responsiveness to price. A larger gap between intercepts raises the equilibrium price; steeper slopes (more price-sensitive buyers and sellers) lower it.
Step 4
$Q^* = a - bP^*$
Plug $P^*$ back into either equation to recover the equilibrium quantity. Both equations give the same answer — that is precisely what equilibrium means: the quantity demanded and the quantity supplied are identical.

A worked example with real numbers

With $Q_d = 100 - 2P$ and $Q_s = -20 + 4P$ , set the two expressions equal and solve step by step.

Step 1
$100 - 2P = -20 + 4P$
Set quantity demanded equal to quantity supplied. Both sides represent the number of units traded at price $P$ .
Step 2
$120 = 6P$
Add $2P$ to both sides and add $20$ to both sides. The left side collects the constant gap between the intercepts ( $100 - (-20) = 120$ ); the right side collects the total slope ( $2 + 4 = 6$ ).
Step 3
$P^* = 20, \quad Q^* = 100 - 2(20) = 60$
Divide both sides by 6 to get $P^* = 20$ . Substitute back: $Q_d = 100 - 2(20) = 60$ . You can verify with supply: $Q_s = -20 + 4(20) = 60$ . Both sides agree, confirming the answer.

The three-step exam recipe

Most exam questions on market equilibrium follow the same structure. Work through these three steps in order, and include the verification check to catch algebra slips before they cost marks.

1
Set $Q_d = Q_s$
Write down the quantity-demanded and quantity-supplied expressions and set them equal to each other. This single equation encodes the definition of equilibrium.
2
Solve for $P^*$
Collect all price terms on one side and all constants on the other, then divide. The result is the equilibrium price $P^*$ .
3
Substitute back to find $Q^*$
Plug $P^*$ into either the demand or the supply equation to get $Q^*$ . As a check, substitute into both equations — if they give different quantities, there is an algebra error somewhere above.