Mathematical Representation of the Supply Curve

Mathematically, the law of supply can be represented using a linear function Q_s equals m times P plus b.

Here, Q_s is the quantity supplied, m is the quantity change per unit price change, P is the price, and b is the quantity supplied at zero price.

Suppose the quantity of tomatoes supplied increases by 200 pounds for every additional dollar in price. The supply function can be written as Q_s=200P-200.

The supply function can also be inverted to represent the price as a function of the quantity supplied.

For the above example, the inverse supply function shows that the farmer doesn't supply tomatoes for a price of less than one dollar per pound.

The point where the quantity supplied equals zero is known as the supply choke price, represented as the vertical intercept on the supply curve.

Understanding the mathematical function of the supply curve is crucial for predicting producers' behavior in response to price changes.