3.3: Mathematical Representation of the Supply Curve

The supply function in economics describes the relationship between the quantity of a good that producers are willing to supply and the factors influencing that supply, particularly price.

Mathematically, a linear supply curve or the law of supply can be represented by the equation Qs = mP + b, where Qs is the quantity supplied, P is the price, m represents the slope (change in quantity supplied per unit change in price), and b is the intercept representing the quantity supplied at zero price. This equation can also be inverted to represent the price as a function of the quantity supplied.

The supply curve's vertical intercept, b, is known as the 'supply choke price' because it indicates the minimum price at which producers are willing to supply the goods. At this price, the quantity supplied is zero.

If the price falls below this level, suppliers will not provide any quantity of the good, effectively 'choking off' the supply. This point represents the threshold where producers find it unprofitable or infeasible to supply the goods due to cost considerations or other factors. Understanding this mathematical representation helps predict producers' behavior and how changes in price affect the quantity supplied.

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.