Economic growth is simply defined as an increase of income per person. Our aim in this chapter is to explain, first without any formalization, the process by which such an increase may be achieved in a given country. The necessity for a more formal approach will emerge in a natural way.

This will lead to a precise model, from which unambiguous inferences can be made. In particular, we will be able to answer the following questions: what are the necessary conditions for an economy to grow? And if those conditions are met, will income per person always increase, or will it tend toward a limit?

The growth process: an intuitive approach

In a given country, at the beginning of a given year t, society has two fundamental factors of production at its disposal. First, it has inherited from the past a stock of capital, that we may call Kt . This is the value of all equipment that has been accumulated by society and preserved until that instant: it includes the value of land, factories, machinery, transport infrastructure, and so forth. The second production factor is labour, which we will always consider as a given proportion of population; we will thus assume that a measure of this labour force is the population itself, denoted Lt . It is endowed at time t with a given technological knowledge, also inherited from the past.

Together with the capital at its disposal, this work force will produce within a given time span (a year for instance) an output which we call the gross domestic product. Part of this product is used to replace that part of the capital stock that has decayed within the time span considered; that part is usually referred to as the depreciation of capital. The remainder is called the net domestic product, to which corresponds an equal income accruing to society. It is denoted Yt , and called total income. Note that capital Kt and labour Lt are stocks, that is amounts observed at one point of time, in our case at the beginning of the first day of year t.