An aggregate production function shows the maximum amount of real output that can be produced from any given amount of factor inputs. A simple aggregate production function can be written mathematically as:
Y = A(K,L)
Where Y is real output, A is technology, K is the quantity of capital and L is the quantity of labour.
Most economic models will assume that the aggregate production function exhibits decreasing marginal returns. For example, assuming capital is fixed in the short-run, as the quantity of labour in the economy increases, there are more workers employed, firms produce more, output rises and the economy moves along its production function. In the long-run, however, it is possible for the aggregate production function to shift. An increase in productivity and/or an increase in the quantity of capital will shift the aggregate production function upwards and increase production.