Introduction To produce goods, every firm needs inputs such as capital and labor. Mankiw (2005) refers to the set of tools that workers use in the production process, for example machinery such as computers, while labor refers to the hours that employees invest working. The production function refers to the output of a firm, an industry, or an entire economy for all combinations of inputs (Banaeian and Zangeneh, 2001). Economists use the production function to specify the relationship between labor and capital and according to Mankiw (2005). Production functions reveal the technology available to transform labor and capital into output. Tang (2008) highlighted the fact that productivity theory was proposed by Knut Wicksell in 1851, which contributed a lot to the works of Charles Cobb and Paul Douglas. The Cobb-Douglas production function was developed by Cobb and Douglas in 1928 and is a fundamental function even today in both macroeconomics and microeconomics. The Cobb-Douglas production function is normally used by economists to explain the correlation between the contributions of resources involved in production such as labor, capital and technology. The Cobb-Douglas production function and the constant elasticity of substitution functions play a significant role for analysis in economics. The Cobb-Douglas production function is still universally used for analyzing productivity and growth (Felipe and Adams, 2005). Felipe and Adam found it true that Paul Douglas is one of the economists who deserved the Novel Prize for his wonderful works. Cobb and Douglas suggested that the elasticity of substitution between capital and labor should be constant or equal to one even though they did not specify… half of the paper… worldbank.gov. (2011). Data on South Africa's gross domestic product and total employment. World Bank.http://www.southafricanreservebank.co.za. (2011). Data on South Africa's fixed capital stock. South African Reserve Bank Mankiw, NG. (1995). “The growth of nations”. Brookings Business Document. pp 275-326Mankiw, NG. (2005). Macroeconomics, international edition. Worth Publishers: New YorkMankiw, NG (2013) Principles of Macroeconomics 7th Edition. Congage Learning: United States of America Romer, P. M. (1986). Increasing returns and long-term growth. Journal of Political Economy Vol 94. Pp 1002-37 Romer, P. M. (1990). Capital, Labor and Productivity. Journal of Political Economy Vol. 98, no. 5: University of Chicago. Pp 339341 Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly economics journal. pp 65-94