1. We have so far been concerned with an economy where the labour force increases, independently of the real wage rate and other economic factors, at a given constant rate. As we can easily discern by inspecting historical experiences, the rate of growth of the population has not been stationary in many countries, but has been influenced inter alia by the level of income per man, the level of capital per man (the number of hospitals, the number of rooms per man, etc.), the level of some specific economic activities (the production of medicines, etc.), and so on. These influences would certainly be very complicated ones; we begin this part by taking only the effect of the real-wage rate upon the growth rate of population into account. 1
The following parable due to Volterra would be valid in a closed economy at the crudest stage. 2 In an isolated region there live two types of animals, say, giraffes and lions. We assume that grasses upon which giraffes feed are always available in sufficient amounts; lions exclusively feed upon giraffes. If only a few lions live in the region, the number of giraffes will continually increase; there will be no food problem for lions, so that they will grow at a rapid rate. Sooner or later the number of giraffes will then begin to diminish; therefore many lions will starve and giraffes will again be able to propagate themselves.
This cyclical poverty of lions results from the following two basic assumptions. (i) The rate of growth of giraffes that clearly takes on a positive value in the absence of lions will become smaller as the number of lions becomes larger and will remain negative for very large numbers of lions. (ii) The rate of growth of lions, on the other hand, is evidently negative in the absence of giraffes but will increase with the enlargement