solow-1 - NOTES ON SOLOWS GROWTH MODEL HAKAN YILMAZKUDAY 1...

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NOTES ON SOLOW’S GROWTH MODEL HAKAN YILMAZKUDAY 1. Introduction The starting point for modern growth theory is the classical article of Ramsey (1928) 1 . His paper made a profound contribution to the literature about household optimization and intertemporally separable utility function which is widely used today as the Cobb-Douglas production function. However Ramsey’s approach was not widely used by the economists until the 1960s. Meanwhile, between Ramsey and 1960s, Harrod (1939) and Domar (1946) introduced a Keynesian growth model. According to their model, fixed proportions of inputs (say, capital and labor) should be used. The model had no problem at the steady state but there was the problem of instability in the absence of a steady state. This brought together the idea that the capitalist system is unstable. But, since the model was introduced just after the Great Depression, it made a sound in the literature. However this sound did not last for a long time. Solow (1956) criticized the Harrod-Domar model to analyze long-run problems with the usual short-run classical analysis. In his study, Solow, took all the assumptions as given in Harrod-Domar model except the assumption of fixed proportions of input. Here, neo-classical approach helped him to achieve this. This study on growth is known as Solow’s Growth Model. 1 See (Barro and Sala-i-Martin, 1995)
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2. Solow’s Growth Model The model is simplified in a variety of ways. First of all there is only a single good, (Y t ), in the economy. This good is produced, consumed and saved. So we can say that production is also the real income for individuals 2 . Some part of the income is consumed, (C t ), and the rest of it is saved, (S t ). Since the economy is a closed one, saving is assumed to be equal to investment (I t ). We know that the change in capital between two periods is known as investment 3 . If we denote capital by K, we can write: dK K sY dt ! ! ! (1) The good is produced by using labor (L t ) and capital (K t ). So we can present the production function as ( , ) Y F K L ! . Since Solow uses a neo- classical production model, it is convenient here to present the assumptions of such a model. According to Romer (1996) a production function is neo-classical if the following three properties hold. First of all K>0 and L>0, exhibits positive and diminishing marginal products with respect to each input.
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