Literature Review

The purpose of this chapter is to introduce the neo classical theoretical framework which is the basic foundation for the convergence theorem of economic growth. Further, we will see the other major theorems studying growth convergence.

The Neo-Classical Growth Model

“The art of successful theorizing is to make the inevitable simplifying assumptions in such a way that the final results are not very sensitive…and it is important that crucial assumptions are reasonably realistic” (Solow,1956)

The Solow-Swan model, as it is alternatively called is explained in the following 10 equations as done in Barro, Sala-i-Martin(1999)

We start by assuming a simplified, Robinson Crusoe type economy where producer and consumer are the same person who owns the inputs as well as the technology to transform inputs to output. The inputs are broadly classified into physical capital, K(t), and labour, L(t). Let`s also assume technology has no or little change over time.

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The production function, thus derived, will be of the following form

Y(t) = F[K(t), L(t)],1

where Y(t) is output at time period t. We further assume a one-sector production model in which output Y(t) is a homogenous good which can either be used for consumption ,C(t), or for Investment I(t) to create new units of Physical Capital K(t). The Capital depreciates at the constant rate δ > 0 We also assume that the economy is closed which implies the output equals income and saving equals investment in all periods, t. Further, we assume a constant, positive savings rate s(). Hence, the net increase in physical capital at a point in time equals gross investment less depreciation

Ḱ = I – δ K = s · F(K, L) – δ K,2

where á¸° is net increase in capital and 0 ≤ s ≤ 1. Equation 2 determines the dynamics of physical capital K for a given level of labour force L. The labour force L(t) varies in accordance with the population growth, worker participation rates and time worked by an average worker. For the simplicity of the model, we assume that population grows at a constant, exogenous rate, Ä¹/L = n ≥ 0 and that everyone works at same intensity. If the number of people is normalized at time 0 to 1 and the work intensity per person is normalized to 1, then the population and labour force at time t equal to

L(t) = e^nt3

If L(t) is given from equation 3 and technological progress is absent, then equation 2 determines the time paths of capital, K, and output,Y. Hence the production function becomes