Ouput is based on the production function, which relates output YY to the size of the capital stock and of the labor force LL:

Y=F(K,L)Y = F(K, L)

where KK is the total value of all physical capital in the economy, such as machines, tractors and office buildings, LL is the total number of workers in the economy and YY is real output.

The model assumes constant returns to scale, meaning that the prodction function satisfies the following property:

zY=F(zK,zL)zY = F(zK, zL)

If we scale both the amount of capital and labor by some constant zz, 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:

Y=KαL(1α)Y = K^\alpha L^{(1- \alpha)}

where α\alpha determines the relative importance of capital and labour. To understand α\alpha intuitively, change it's value using the slider below.

α\alpha

0.30
01

As you can see, decreasing α\alpha increases the relative importance of labour LL, and increasing α\alpha increases the relative importance of capital KK.


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