LEC 2 ECON 314 01/09/2014
The Solow Model
Labour and capital are the two factors of production
In general we would also include land, but it is not included as in modern times, land is absorbed into
capital. Also, we have no transitioned into a manufacturing industry (machinery etc.) thus land is a
The level of technology is exogenously given
This is a big handicap to the model. The technology that you are using will never be improved through a
conscious decision by the firms in the system. There is no investment in knowledge/technology.
Technology is always at a set level.
There are constant returns to scale
If the factors of production (Land and Capital) are doubled then output is also doubled.
Each individual produces the same. E.g. if there are 4 apples in the economy and 4 individuals then
each person produces 1 apple. Thus each individual is responsible for ¼ of production. Can only divide
by N to lead to 1/N if we have CRS!
This is different from other situations ▯ e.g. 1 person makes 1 apple and 2 people produce 3 apples ▯
this is an example of increasing returns to scale ▯ THIS IS NOT IN THE SLOW MODEL!
The production function is a CobbDouglas production function
Constant returns to scale
If the factors of production are increased by a given number, the output increases by the same number
as well. Thus, if the production function is defined as:
Y = F(K,L)
α (1 α)
… Y = K L
CobbDouglas production function and CRS Y = AK L is a CobbDouglas production function
CRS requires, α + β = 1
Thus, the CobbDouglas production function used in
the Solow model, becomes Y = AK L
To reduce the above to a per capita production,
Y/L = A[K/L] [L/L]
→ y = Ak
A CobbDouglas production function is simply Y = K L where A and B are 2 constants.
The CD function can be manipulated to show CRS.
The main condition for CRS is that A+B = 1
Increasing return to scale is A + B > 1 ▯ NOT IN SOLOW.
We assume full employment in Solow model. Thus population = labour force.
Small k = (K/L) when this is the capital output ratio.
Eventually leads to Y = Ak ▯ this is what we will be working with in Solow! Where A is just a constant.
Solow is Diminishing marginal productivity of capital ▯ DON’T CONFUSE WITH DIMISH