Endogenous Growth Theory Notes
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Pip Reeve HT 10 T6 'Except under very special circumstances, endogenous growth theory either predicts explosive growth or convergence to a neo-classical steady state'
In a model of endogenous growth, the long run growth rate of the output per worker is determined within the model, using microeconomic foundations, as opposed to being determined by some exogenous rate of technological progress, or an exogenous savings rate. In this essay I will show a variety of endogenous growth theory models which tend to conclude that in some cases there will be explosive growth and in others there will be convergence to a neo-classical steady state.
I will begin by looking at a model of endogenous growth which focusses on research and development. Shaw suggests that knowledge can enter the production process in two ways. A new design allows the production of a new intermediate input. Also, an increase in the total stock of knowledge and therefore an increase in the productivity of human capital in the research sector. The second model I will discuss focuses more on the second method of knowledge entering the production process through an increase in the productivity of human capital due to an increase in the total stock of knowledge. Firstly, I will investigate the case where capital is excluded from the model, making the production function for output:
This, along with the equation for the production function for new knowledge:
allows us to calculate the growth rate of A, the stock of knowledge:
Taking logs of both sides and differentiating the two sides with respect to time gives the equation for the growth rate of gA:
The case where θ is less than one is an example of an endogenous growth theory which predicts convergence to a neo-classical steady state, a balanced growth path. In this case a higher savings or investment share does not raise the growth rate. The growth of per capita output is caused entirely by technological progress, however, it is endogenous because it arises from knowledge spillovers associated with capital accumulation. On the following graph, the economy will converge to g A*
whatever the initial conditions of the economy are. When g A reaches gA*, both Y/L and A will be growing steadily at the rate g A* which is the unique positive value of gA which is associated with a value of g.A equal to zero. gA* is defined as:
With these conditions, this model suggests that the long run growth rate of output per worker is an increasing function of the rate of population growth. This can be seen from the point of view of worldwide economic growth, as long as the stock of knowledge can be accessed worldwide, higher global population growth will lead to higher global income growth. When θ is less than one, the production of knowledge has increasing returns, so, without resource limitations, population growth is beneficial to the growth of the global stock of knowledge. Indeed positive population growth is in fact essential for sustained growth of output per worker as in the neo-classical steady state.
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