Growth_Model_Part2_AK_Model

Growth_Model_Part2_AK_Model - Disclaimer: These notes were...

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Disclaimer: These notes were prepared based on lectures of Prof Sala-i-Martin’s 2008 Fall Course of Intermediate Macro-W3213. Contents of these notes might not match completely with the current teachings in class. An updated version would be available later in the semester. 2.8 Endogenous Growth: The AK model. Suppose that α=1 . In other words, imagine that ° = ±² . Everything we said still goes through. The Fundamental equation of the Solow Swan model is: ? ² = ³² ² = ?±² ?− 1 ? + ´µ 2.8 Now put α=1. This gives the equation as ? ² = ³² ² = ?± − ? + ´µ 2.9 How does it look like graphically? , ? + ´ ? ² > 0 ? + ´ k Fig 2.6 Note here both the saving line and the depreciation line ? + ´ are independent of k, so we represent both as horizontal lines. As long as > ? + ´µ growth rate of per capita capital ? ² is positive, as shown in Fig 2.6. This model predicts that there is growth for ever. The growth rate in this model depends only on the parameters of the model and we do not need to assume that something is growing exogenously. In this case growth is explained from within the model so it an endogenous model of growth. Note: In the AK model there is no diminishing return to per capita capital,[ ¶· ¸ = ± and 2 Y K 2 = 0 ] so it is not a neoclassical production function. Comparative static exercise: If increase savings rate from s to ?′ , then growth increases forever as shown in the Fig 2.7.
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The savings line shifts up horizontally to ?′° and growth rate increases to ? ± . , ? + ² ?′° ? ± > 0 ? ± > 0 ? + ² k Fig 2.7 If we decrease the population growth rate from n to ²′′ that shifts the depreciation line down and growth increases forever to ? ± ′′ . , ? + ² ? ± > 0 ? ± ′′ > 0 ? + ² ? + ²′′ k Fig 2.8 In the AK model growth rate in the long run does not become zero as in the neoclassical model. So
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this model is able to predict that countries can grow forever, a fact found to hold in reality. Criticisms of AK model: This model DOES NOT PREDICT ANY FORM OF CONVERGENCE since all countries grow at some constant rate given by the parameters of the model. Conditional convergence is found to hold empirically. The inability of the AK model to explain conditional convergence is definitely a shortcoming. Another criticism is regarding the treatment of labor as a form of capital, as the nature of human capital is distinctly different from physical capital. We need to consider special nature of human capital: 1) Everybody is born with zero human capital or skill. 2)
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This note was uploaded on 11/10/2011 for the course ECON 3100 taught by Professor Sala-i-martin during the Spring '11 term at Columbia.

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Growth_Model_Part2_AK_Model - Disclaimer: These notes were...

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