The Production Function
Ouput is based on the production function, which relates output to the size of the capital stock and of the labor force :
where is the total value of all physical capital in the economy, such as machines, tractors and office buildings, is the total number of workers in the economy and is real output.
The model assumes constant returns to scale, meaning that the prodction function satisfies the following property:
If we scale both the amount of capital and labor by some constant , output will increase by that same constant. This assumption is considered realistic and will simplify our analysis.
A famous function which has this property is the Cobb-Douglas production function, which is formulated as follows:
where determines the relative importance of capital and labour. To understand intuitively, change it's value using the slider below.
As you can see, decreasing increases the relative importance of labour , and increasing increases the relative importance of capital .