Let the economy's production function be = (, ) where Y is real GDP, N is the population (and labour), K is the stock of capital, A is a measure of the state of technology, and f is the production function for the economy. (We make no distinction between labour

and population N and so standard of living and labour productivity are the same: ).

Let A = 1 and K = 100 (the actual numbers don't matter) and suppose the relationship between real GDP (Y) and population (N) (for a given stock of capital and state of technology) is shown in the diagram below.