Before 1800, technological progress was relatively slow. The result was that output per worker hardly increased at all, but population grew. In 1798, Thomas Malthus wrote an essay on population that presented a pessimistic picture of economic growth. He said that when food is ample, population grows exponentially. Because there are diminishing returns to labor in food production, exponential population growth leads to starvation, and population falls again.
Here is a numerical example of a two-equation Malthusian model.
[food production] Yt = 1000 + Lt
where t is generation t.
[population growth] Lt = 600 + 100*(Yt-1/Lt-1)2
NB: population growth of this generation is related to food supply and population of the previous genration.
This generation's food production, Yt, increases linearly with this generation's labor supply (population). However, the next generation's labor supply increases with the square of this generation's ratio of food to population.
You can solve these two equations for values of Y and L that will be stable. These are called the equilibrium values. In this case, they are 2000 for Y and 1000 for L. If L is 1000, then according to the food production equation, Y will be 2000. If Y is 2000, then population will grow to be 1000. The food/population ratio is 2.
What happens if we start out with 2000 units of food, but disease causes the population to fall to 900? You can use the calculator below to see what happens if population starts out too low or too high. If you click on "calculate" the economy will move forward in time one generation. Keep clicking on "calculate" and you will see Y and L oscillate back and forth until they converge to their equilibrium values. You can try starting out with different values of Y and L and see the convergence process from different starting points.
Next, suppose that we get better technology in food production, so that the food production equation becomes
Yt = 1200 + Lt
What happens to the equilibrium values of Y, L, and Y/L? Use the calculator below to find out. Keep clicking on calculate until the values stop changing.
What is the equilibrium level of food? What is the equilibrium level for the population? What is the equilibrium ratio of food to population?
At first, with the population at 1000, the technological improvement brings food production to 2200, and the ratio of food to population rises to 2.200. However, in the final equilibrium, because of population increases, the ratio of food to population is only 2.136. This is the Malthusian effect by which population growth dissipates technological advances. In fact, prior to 1800, the Malthusian effect was so strong that there was very little progress in average output per capita; instead, nearly all of the inventions and technological advances until 1800 served primarily to increase population. This is still the case today in underdeveloped countries. All the output is consumed, there is no capital accumulation.