Los Modelos Matemáticos Como Una Estrategia de Enseñanza en la Economía.///Mathematical Models as a Teaching Strategy in Economics.

There is a gap in the professional community of certain areas in terms of the story about the usefulness of mathematics in their area of specialization; We see an example of this in those who enter administration and accounting careers. I have noticed that a good percentage of them think that they are going to relate less to mathematics in their undergraduate studies; I, as a teacher in that field, have been a witness, since I have heard that speech, and furthermore, I have discussed it with my students.

Perhaps this is because during their previous studies they have been victims of little encouragement in terms of discovering how interesting this subject is and how useful it is for solving specific issues in the context of those who study it; On the other hand, by developing mathematical skills applicable to the solution of real situations, coherent and logical thinking is developed, which should be the objective of any individual training process.

The objective of this post is to show how mathematical concepts can be introduced in the context of interest of those who study it, with the aim that students develop affection and recognize the importance of mathematics in their area of study.

Let's look at the following example in the context of economics, where we can introduce the concept of a mathematical model using linear equations.

A manufacturer can produce waterbed frames at a cost of $10 each and has calculated that he sells 50-x units per month at price x per unit. a) Express the manufacturer's monthly profit as an equation or mathematical model as a function of price x.

The problem describes the situation of a manufacturer who makes and sells waterbed frames, each of which costs $10 to manufacture.

The first column indicates the number of frames produced and the second column shows the cost of producing that number of frames.

Through the table we have developed a mathematical model that allows us to describe the manufacturer's cost in this problem, so that, if we call the cost by the letter C, we can state that:

On the other hand, the manufacturer produces his product in order to sell and obtain income: in this case, the manufacturer produces his product with the purpose of selling it at x dollars, if we call p the selling price, then:

The manufacturer's revenue I will be determined by developing a new table in order to obtain a mathematical model:

So far, we have identified, in the context of the problem posed, two very important indicators:

We need to find a mathematical model for the manufacturer's Profit or Profit, let's call U the profit or Profit and let's elaborate a new table taking into consideration the previous tables:

From the table we obtain the mathematical model that denotes the Profit ''U'' of the waterbed frame manufacturer.

Which corresponds to the answer to part a of the problem, i.e., we have obtained a mathematical model for the manufacturer's utility U as a function of sale x.

For example, if we want to determine the manufacturer's profit when waterbed frames are produced and sold at $20, we substitute x for 20 in the model and evaluate as follows:

All images are from Pixabay, the content is entirely original to the author. The problem was taken from the text: Calculus For Social Science and Management. Laurence D. Hoffmann.