Explain how the neoclassical growth model can be extended to enhance our understanding of economic growth.
AIM AND OBJECTIVE
The aim of this essay is to clarify how the neoclassical growth model can be used to explain economic growth by taking into account two new inputs: Natural Resources (R) and Land (T) by substantiating it with relevant research.
THE NEOCLASSICAL GROWTH MODEL
According to the Neoclassical Solow Model, economic growth arises due to influences outside economy. As an exogenous growth model it focus on four variables: output (Y), capital accumulation (K), Technology (A) and labor or population growth (L) in order to explain economic growth.
In 1798, Malthus raised the issue that once population growth had outpaced agricultural production subsistence-level conditions would result and hence, convinced other economists that natural resources, production and other environmental considerations are critical in the long run.
THEORETICAL ASSUMPTIONS OF THE MODEL
The analysis of the Cobb-Douglas function is now extended to include natural resources (R) and land (T).
The analysis of the Cobb-Douglas function is now extended to include natural resources (R) and land (T). Thus the production function, now, becomes: Y(t)=K〖(t)〗^α R〖(t)〗^β T〖(t)〗^γ [A(t)L (t)]^(1-α-β-γ) where,
α>0, β>0, γ>0, α-β-γ<1
Whereas the dynamics of capital, labor and the effectiveness of labor are the same as before,
i.e. K ̇(t)=sY(t)-δK(t), L ̇(t)=nL(t) and A ̇(t)=gA(t) it is important to consider the new assumptions that concern the newly added inputs.
As such, because the amount of land is fixed and in the long run the quantities used in production cannot be increased, it is assumed that T ̇(t)=0.
Resources used in production are fixed as well and after being used in production the available quantities must decline. As such, regardless of evidence pointing out that resource use has been rising, it is assumed that R ̇(t)=-bR(t), b>0.
THE NEW EQUATION OF MOTION FOR CAPITAL AND THE BALANCED GROWTH PATH
With new inputs in the production function, focusing on K/AL as a way to analyze the economy is no longer effective as it no longer converges to a given value.
It is assumed that A, L, R and T each grow at a constant rate. In order to achieve a balanced growth path, both K and Y must grow at a constant rate as well.
It is implied by the equation of motion for capital K ̇(t)=sY(t)-δK (t), that the growth rate of K is
(K ̇(t))/(K(t))=s (Y(t))/(K(t))-δ, meaning that in order for the growth rate of K to be constant so has Y/K to be which leads to the inevitable assumption that Y=K.
By taking logs of both sides in the production function, it is possible to find when this condition is satisfied.
ln〖Y(t)〗=α ln〖K(t)〗+β ln〖R(t)〗+γ ln〖T(t)〗+(1-α-β-γ)[ln〖A(t)〗+ln〖L(t)〗 ]
By differentiating both sides of this expression with respect to time and being aware that the time derivative of the log of a variable is the...