A cost function is an economic formula that reflects the action of input prices and output prices. Another definition for this function is finding the cost of materials for producing a specific quantity of goods. The different methods for determining a cost function start with a few basic formulas. These include the average cost, break-even point, and marginal cost formulas. Many other more technical examples exist to determine this function, though the methods involve heavy calculus formulas.
The average cost function starts with computing total cost for a given level of production. This formula is fixed cost plus variable cost multiplied by the quantity produced. The average cost places the previous formula as a numerator and divides it by the total production output. The result is an average per-unit cost for the specific level of production. Companies can use this basic formula to assess the average cost for goods produced in different batches run through the same production process.
An important use of the cost function is to find the break-even point in terms of units for a given production process. This point represents the number of units a company must sell in order to cover all production costs. The formula here is per-unit revenue less per-unit cost multiplied by quantity, the variable in the equation. The end result is a figure that represents the quantity to produce in order to break even in economic terms. Many alterations can exist in this formula to match the company’s needs.
Marginal cost function is a specific formula designed to compute the change in cost for producing one additional unit. Formulas exist for both the cost side and revenue side of this process. To define the marginal cost for producing an additional unit or units, an accountant divides the change in output into the change in total cost. The formula is similar for the revenue side, where the change in total revenue is divided by the change in output. The comparison between the two determines if producing more units will either bring in more revenue or simply add more costs to the business.
The goal of most cost function analysis is to reach a point where marginal revenue equals marginal cost. At this point, the company maximizes its revenue and is unable to add more profit by producing more goods. This is not always a reachable goal, depending on many internal and external factors that affect the process.