**Economic growth models are mathematical models, based on a theoretical framework, structured with the aim of explaining the progress of production and the level of income in an economy over time.**

In other words, economic growth models seek to explain, through mathematics, why countries or economies grow at a certain rate of change. This, with foundations in economic theory.

These mathematical models, from a formal point of view, began to be developed in the middle of the 20th century. However, since the beginning of economics as a science, with Adam Smith, it was already a topic of discussion as to why certain economies grew at a faster rate than others.

## Characteristics of economic growth models

Among the characteristics of economic growth models we can highlight:

- His study is part of the field of macroeconomics.
- They take into account assumptions, for example, that there is no unemployment and that all available capital is used.
- In its development, the production function is fundamental, what variables we include in it and how these are related to the level of production. That is, if it is a Cobb-Douglas function or a linear function, for example.
- These models are important, above all, in the long term because, if a country’s economy grows at a high rate, so will its per capita income level. Likewise, there may be economies that remain stagnant at a certain income level, and this will be reflected in other economic indicators such as the level of employment or poverty.
- For its development, mathematical tools such as derivatives and logarithms are used.
- They allow us not only to explain the determinants of the level of production, but also give us the possibility of making projections. This, through econometrics.
- They are important for taking economic policy measures.

## Types of economic growth model

There are mainly two types of economic growth model:

**Of endogenous growth:**These follow the paradigm of the neoclassical school. They have the drawback that they are not capable of solidly explaining the growth of an economy in the long run. This, unless an external shock, such as a technological leap, is included. The Solow model is perhaps the best known of its kind. This model concludes that economies grow, at increasingly smaller rates, until they reach a point where they cannot grow any more.**Of exogenous growth:**They are characterized in that they are capable of explaining long-term economic growth on their own, without introducing an external event. An example is the AK model, where the economy grows at a constant rate in the long run, which is not the case in the Solow approach.

## examples

Some examples of economic growth models are:

- Solow and Swan model.
- AK model.
- Ramsey model of rational choice.
- Barro model with a focus on fiscal policy.
- Lucas model of human capital.