In a market, Demand is the quantity of a good that buyers are willing to purchase at different prices.
Supply is the quantity that producers are willing to sell at those prices.
The two curves intersect at the equilibrium price and quantity.
Mathematically:
Demand: \$Q_d = a - bP\$
Supply: \$Q_s = c + dP\$
Where \$P\$ is price, \$a, b, c, d\$ are constants that shape the curves.
Some goods are used together. When the price of one good changes, the demand for the other changes too.
These goods are called complements.
Example: Coffee and sugar. If coffee becomes cheaper, people buy more coffee and, consequently, more sugar.
The joint demand function for two complements can be written as:
\$Q{joint} = f(PA, P_B)\$
where \$PA\$ and \$PB\$ are the prices of goods A and B.
| Good A | Good B | Joint Demand Function |
|---|---|---|
| Coffee | Sugar | \$Q{joint} = \alpha - \beta P{coffee} - \gamma P_{sugar}\$ |
| Printer | Ink Cartridges | \$Q{joint} = \delta - \epsilon P{printer} - \zeta P_{ink}\$ |
Think of complements like a pair of shoes: you can’t wear one without the other. If the shoe price drops, you’re more likely to buy the matching pair, boosting demand for both.