Overview
The endogenous growth model addresses some of the shortcomings of the Solow growth model. In particular, endogenous growth seeks to model the unexplained technology term of the Solow model, tying it back to choices of agents in the economy.
Setup
The model utilizes the following variables:
- Output - {% Y %}
- Labor - {% L %}
- Capital - {% K %}
- Technology - {% A %}
Sectors
There are two sectors in the model economy. A goods producing sector, and an R&D sector. Resources are divided between the two sectors, and the resource allocations are taken to be constant. {% a_L %} is the fraction of labor used in the R&D sector, and {% a_K %} is the fraction of capital used in the R&D Sector.
The production function used to model production in the economy is given as
{% Y = (A(t)(1 - a_L)L)^{1-\alpha} (1-a_K)K^\alpha %}
This equation uses the
Cobb Douglas
production function with constant returns to scale. It models technology as a multiplier to labor. That is, technology is seen as a factor that increases the productivity of
labor.
The rate of change of the technological factor is modeled as
{% \dot{A}(t) = B[a_L L(t)]^\gamma[a_K K(t)]^\beta A(t)^\theta %}
This is a Cobb Douglas production function again, but now without constant returns to scale. The term {% A(t)^\theta %}
means that the current level of knowledge can affect the rate of technological progress, but at a different multiplier than
the rate used for labor productivity.