The Malthusian Trap and Growth Theory

In almost all posts here on DM we highlight in some way or another the potential negative effects of a declining population in either regions or whole countries. Particularly, we have argued in the context of Italy and notably Japan that declining and ageing population are likely to have an impact ... but an impact on what? Well quite frankly let us just call it 'growth' in its widest economic sense. Now, (and very briefly) in economics we have two broad measures of looking at the growth of the economy; short term and long term. The short term definition of growth in economic output centers around business cycle analysis where actual output grows either above or beyond a trend path. In terms of growth in the long run we are interested in the rate and change of real income of real output which centers around the idea of the steady state which in fact is the long-run equilibrium in growth theory.

A causal, yet very important link between the two approaches and perspectives is that the Neo-classical notion of steady state growth co-incides with the idea of trend growth. Simply put, in this framework the potential output of an economy grows over time along a steady state path determined exogenously by the rate of technological progress. Ok ... let us leave that for a moment, now you at least have the basics should you not know of it in advance. In this post I shall try to do a small synopsis of growth theory and apply the idea of the Malthusian trap to one of the poorest countries in the world.

In a general sense the reality and evidence have obviously surpassed the core idea of Malthus' theory but still the main thesis of Malthus helps us understand something very interesting about which properties we put into our (economic) models. In short; what are our intial assumptions when we try to create an argument. So let us set the scene with the standard Solow model for growth ... where Y is potential output, A is technological progress (the Solow residual), f is the function for Capital (K) and Labour (L) as inputs to growth.


Y = A x f (K,L)

Now, in terms of showing the Malthusian trap in this model we simply apply Malthus' theory to our function of capital and labour. Malthus' greatest concern was the effects of a growing population working a fixed supply of land. In short, Malthus' calculations and estimations showed how agricultural output would grow less quickly than population growth which again lead to the policies of restraining the reproduction rate and lowering the TFR. So what happens in our growth model then?

In a Malthusian trap context it has become customary to ammend the Solow production function to incorporate land (S, for space), since this is obviously a key (and constrained) variable in an agricultural context. We thus have;

Y = A x f (K,L,S)

Now S obviously remains constant. Let's take an initial situation of starvation and see what happens. In this initial environment people consume all income and we can assume that savings are zero which again makes investment zero finally making K eventually tend to zero as well. The crucial point is that the production function has diminishing returns to labour which means that the addition of extra labour brings down productivity ... so, should we look at Rwanda for a while?

'Jean Damascene Ntawukuriryayo who was speaking during a live television talk show about population issues appealed to Rwandans to be more responsible and to avoid accidental pregnancies.

“With a current birth rate of 3 %, the future of Rwanda remains at stake. This means all Rwandans should keep their reproductive tendencies in check,” he counselled. “Uncontrolled pregnancies are a challenge to our population. Parents should not have children if they are unable to provide accommodation, food, clothing, healthcare, and education.”'

In the end I have two objectives here ...

1. The idea of a Malthusian trap is long gone in the developed world where we in fact are in the other side of the ditch with our concern of declining and ageing populations. However, the theory still applies wherever and whenever we find the crucial properties mentioned above to be true. The real question here is obviously how to escape the Malthusian trap. Staying in the comfortable ivory tower of theory we could say that the developed world today escaped by increasing K and A but it is the how which is important here I guess.

2. In many ways the model depicted above is so very simple but I am quite sure that one of the future battlegrounds of macroeconomics will be to explain even further what drives economic growth. Remember, it is all about assumptions and which subsequent properties we feed into our model. I mean, even the question of economies of scale/returns to scale will set your path before you even begin, as will the issue of exogenous vs endogenous growth. My essential argument is that the derived knowledge from cross-disciplinary research in economics, health, and demographics will represent important contributions to this question.