The Production Function

The quantity of real GDP supplied in an economy is a function of the quantity of labour (L), quantity of capital (K), and total factor productivity (A). This is called the production function.

Y = A x F(L, K)

Total factor productivity, A, is the production unaccounted for by capital or labour. It is related to the available production technology.

We can also express this function as output or real GDP per worker:

Y/L = A x F(K/L)

Y/L is the output per worker while K/L is the physical capital per worker. We can either increase physical capital per worker or improve technology to increase labour productivity.

The production function exhibits diminishing marginal productivity for every input. As we increase the quantity of an input, the output increases but at a decreasing rate. For example, as the amount of physical capital per labour increases, the output from additional unit of capital keeps decreasing. This is the reason why sustainable growth cannot be achieved just by investing more capital. Growth in all factors is necessary for long-term growth.