In economics, costs or production costs are the amount of money that is invested in a certain activity that entails the production of a good, a service or the development of an activity with social value. Minimizing production costs is a basic rule in any production system; It allows to determine the optimal combination of work and capital, the one that produces a good or service with the lowest possible cost. In other words, minimizing costs means determining the most profitable production method to produce goods and services while maintaining a certain level of quality. Therefore, when designing a financial strategy, it is important to understand what minimizing costs is and how it is done.

## The productive system

In the planning of a production process or in the evaluation of changes in one in progress, the employer has a certain range of flexibility in basic aspects of its structure, such as the number of workers to hire, the size of the facilities and the selection of the technology to implement. In economic terms, in long-term planning the entrepreneur can modify both the amount of capital and the amount of work.

Therefore, in the long-term production function, two parameters can be modified: capital and labor. Let us remember that the production function of a certain production system is the amount of product that can be generated based on the basic parameters of the system; in the short run, the production function only depends on the amount of labor, but in the long run it also depends on capital.

## The incidence of the production process

The design of the production system can be modified to produce a certain amount of product with a certain quality. Let’s look at a simple example. If the production system aims to produce sweaters, it is possible to think of two different designs of production systems. One might be to hire people who know how to knit and buy needles, while the other would be to buy or rent automatic knitting machines. An economic evaluation of the productive systems shows that the capital investment in the first case is very small, only knitting needles, and implies a great amount of work; it is a labor intensive design. In the second case, a large capital investment is needed and the incidence of labor is small, so it is a capital-intensive design.

In real situations, the combinations of possibilities in the design of the productive system are usually complex and require a detailed analysis. The way to choose the best combination of design parameters of the production system is its optimization, that is, minimizing the cost of production.

One possible way to perform this analysis is to record all the combinations of labor and capital that would produce the desired amount of output, calculate the cost of each of the combinations, and choose the process that involves the least cost. This procedure is complex and sometimes not even feasible. The simplest alternative is to adopt a general criterion to minimize costs, as we see below.

## Minimize costs

The criterion for the application of the procedure of minimizing costs is to determine levels of capital and labor in such a way that the marginal product of labor divided by the cost of labor, the total salary, is equal to the marginal product of capital divided by the rent of capital. invested. Let us remember that in economics the marginal product of a parameter refers to the variation of that parameter associated with an increase in the product by one additional unit to the quantity that is being produced; in this case, this would be the labor and capital needed to increase the quantity being produced by one unit.

An intuitive way of looking at this criterion is to think that the production system is more efficient, and therefore costs are minimized, when the increase in product per cost unit is the same for labor and capital. In other words, the same return is obtained per unit of money spent on the two most relevant factors of a productive system: the cost of labor and the capital invested. This criterion could also be extended if other parameters of the productive system were considered or if more than two inputs were considered.

## What happens if the cost is not minimized

Let’s delve into the concept of the cost minimization criterion and see what happens in a situation where the criterion is not met. Consider a production system in which the marginal product of labor divided by the cost of labor is greater than the marginal product of capital divided by the income from that capital. In this situation, the money spent on labor generates more product than the one spent on capital, and therefore the employer would try to shift costs from capital to labor, since this would allow him to obtain more product with the same cost. Or, alternatively, get the same product at a lower cost.

It is a general criterion in economics that the marginal product associated with these parameters is decreasing, which is why the transfer of capital spending to work at a point will no longer produce the same result. A combined effect is produced in both variables that tends to compensate; Since the marginal product is decreasing in both labor and capital, the increase in labor spending makes its marginal product less and less, and as capital spending decreases, the marginal product associated with capital spending increases. This gradual compensation process is completed, and therefore is interrupted, when the marginal product of each parameter per unit of expenditure is the same. And this is the criterion postulated to minimize the cost. Therefore,

## Font

Mankiw, N. Gregory. *Principles of economics* . Second edition. mcgrawhill

Puig, Martha. *Introduction to microeconomics. *University of Barcelona, Spain, 2006.