A demand function is a mathematical function that describes the relationship between the quantity demanded of a commodity and the factors that influence it. It is generally characterized as a decreasing function of the quantity demanded, meaning that the unit price of the commodity decreases as the quantity demanded increases. The demand function is typically expressed as p = f(x), where p is the unit price of the commodity and x is the number of units of the commodity in question. The demand curve is the graphical representation of the demand function, which shows the relationship between the unit price of the commodity and the quantity demanded.

The demand function is an essential tool in economics, as it helps economists understand the relationship between the price of a commodity and the quantity demanded by consumers. It is used to assess market stability and market-clearing cost, and it specifies the quantities and prices that individuals or all customers are willing to buy and pay at any given time. The demand function can be used to calculate the revenue function, which describes the relationship between the revenue earned by a company and the quantity of the commodity sold.

Factors that influence the quantity demanded of a commodity include the price of the commodity, the incomes of consumers, the prices of related goods and services, the tastes or preference patterns of consumers, the expected price of the product in future periods, and the number of consumers in the market. The demand function can be expressed with respect to an individual customer or all consumers in the market.