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A cost function is a function that relates the cost of producer goods (inputs) to the quantity of product that is manufactured , whose value indicates the cost of manufacturing a certain quantity of product given a set of prices of producer goods. . Often companies apply the cost function by using a cost curve, which seeks to minimize production costs to maximize production efficiency. There are a variety of applications of the cost curve, which include the evaluation of marginal costs , that is, those that are assumed when starting the production of an additional unit, and sunk costs , that is, already incurred and not recoverable.
In economics, companies use the cost function to determine what investments to make in the production process, both in the short run and in the long run .
Total costs and short-run average variable costs
To account for financial costs, that is, the cost of the investment made in the production process, which involves the supply and demand model of the current market, analysts divide short-term average costs into two categories: variable costs (costs associated with the number of units produced; it increases with production) and total costs (variable costs plus fixed costs, that is, those that do not depend on the number of units produced). The average variable cost model (usually labor) determines the cost per unit of output, where the worker’s wage is divided by the number of units produced.
In the average total cost model, the relationship between the cost per unit produced and the level of production is represented on a graph. It uses the unit price of physical capital per unit of time multiplied by the cost of labor per unit of time, and adds the product of the amount of physical capital used multiplied by the amount of labor used. Fixed costs (capital used) are stable in the short-run model, allowing the incidence of fixed costs to decrease as output increases based on labor used. In this way, companies can determine the opportunity cost of hiring more temporary workers.
Short and long run marginal curves
Relying on flexible cost functions is critical to successful financial planning. The short-term marginal cost curve (the cost of producing an additional unit at a certain level of production) describes the relationship between the incremental (or marginal) cost of production in the short term with the quantity of product manufactured. It holds technology and other resources constant, focusing on changes in marginal cost and the level of output. As can be seen in the following figure, the level of marginal cost is generally high at the beginning of the curve, with a low level of production, and it decreases as the level of production increases, reaching its lowest level; then it goes back up towards the end of the curve. This allows you to determine the lowest total average cost and moving average cost values. When this curve is above the average cost, the curve is considered rising; if the opposite occurs, it is considered descending (see the following figure).
On the other hand, the long-term marginal cost curve describes how each unit of production is related to the total aggregate cost that occurred in the long term; in the theoretical period in which all factors of production are considered variable to minimize total cost in the long run. Therefore, this curve allows us to calculate the minimum marginal cost that will increase the total cost per unit of additional production. Due to cost minimization over an extended period, this curve generally appears less variable, recording the factors that help mitigate negative fluctuations in cost.
