Economic Growth and Standard Neoclassical Model

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“Countries grow at different rates because they accumulate capital at different rates.” Is this true? Explain your answer.
Eyeballing any cross sectional data on growth across countries shows that countries grow at different rates. Many theories try to explain this phenomenon with emphasis with capital accumulation being one of them. I will start by developing the standard neoclassical growth model as developed by Solow(1956)[1]. I will then proceed to discuss the extensions that have been made to this basic model in an attempt to better understand actual growth figures, for e.g. the standard neoclassical model cannot explain the magnitude of international differences in growth rates. Mankiw[2] points out that “the model can explain incomes that vary by a multiple of slightly more than two. Yet income per person varies by a multiple of more than ten.”

Economic growth is conventionally measured with the percentage of increase in Gross Domestic Product(GDP). Statistics from the OECd shows the big divergence of GDP annual growth rates from 1998 to 2002 between countries. The top GDP growth rate countries were Ireland and China at 8.1% while the bottom GDP growth rate is that of Japan at only 0.2%. In the standard neoclassical model, GDP denoted by Y is a function of two factors of production capital, K and labour L and A representing the total factor productivity. The production function is as follows: Y=AF(K,L). Assuming constant returns to scale, diminishing marginal product to capital and Inada conditions, the production function can be rewritten as a Cobb Douglas function with α representing the share of capital. The production function becomes Y=Kα(AL)1-α. In order to simplify our analysis, we will use ‘per effective worker’ variables; y is output per effective worker(Y/AL) and k is capital per effective worker(K/AL). Simplifying the production function, we get y=kα.

Assume a closed economy, a constant savings rate s and a constant...
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