# Malthusian Growth Model

A concise write-up on Malthusian growth model (exponential growth model), put forth by Rev. Thomas Malthus, which has formed the basis for the development of various population growth models over the last couple of centuries.

Abhijit Naik

**Thomas Malthus**

Not many people in the world would boast of being as influential and controversial as Rev. Thomas Malthus. In fact, he influenced some of the greatest minds in history like naturalists Charles Darwin and Alfred Russel Wallace, economist John Maynard Keynes, etc. Malthus authored the book 'An Essay on the Principle of Population' wherein he gave a detailed account of population dynamics. In his theory of population, Malthus stated that the growth of human population was quite different from the growth of food which was required to feed this population. He also pointed towards the fact that human population grew geometrically or exponentially, while the food supply meant to feed this population increased arithmetically or linearly, and stated that this was a perfect recipe for a disaster waiting to happen in form of overpopulation.

**Malthusian Growth Model**

Malthusian growth model, also referred to as the exponential growth model, was a growth model put forth by demographer Thomas Malthus, which stated that the population increases or decreases at a rate which is directly proportional to the size of the population. For instance, if the population of 500 individuals increases to 543 individuals in a period of 10 years, the population of 5000 individuals would increase to 5430 individuals in the same period, the population of 50000 would increase to 54300, and so on. The Malthusian law of population - also known as the exponential law, is considered to be the first principle of population dynamics.

**Formula**

Every growth model has variables and parameters, and Malthusian model is no exception. In this model, the variable is population, a number in which you need to take keen interest, and the parameter is population growth rate - which is known to you beforehand. While variables are known to change in course of time, parameters are mostly constant - but do have the tendency to change at times.

P(t) = P_{0}e^{rt} |

'P_{0}' indicates Initial Population'r' indicates growth rate or Malthusian Parameter 't' indicates time |

Malthusian growth model can be applied when it comes to population of large animals when the same is not kept in check by the environment. More importantly, this growth model is not just restricted to demography, but also finds application in the field of economics wherein interest compounding continuously adds to the balance of the savings account while the rate of interest remains constant.

Even though Thomas Malthus was an influential person back then, his take on population dynamics was met with severe criticism by scholars like Karl Marx and William Godwin. His critics often argued that Malthus was either not able to recognize or turned blind eye to human potential of increasing food supply by resorting to developments in the field of science and technology. Though the assumption that stressed on the inability of the society to become perfect did put this growth model under the scanner, the fact that it still forms the basis of various population growth models - one of the best examples being the logistic growth model, speaks volumes about its popularity.