EB-08A00002A - Fine arts in Solow model: a clarification...

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Fine arts in Solow model: a clarification Jason (Jen-Shan) Kao Yeung-Nan Shieh Taiwan Institute of Economic Research Department of Economics, San Jose State University Abstract This paper shows that the Saito version of Solow growth model contains an error. It corrects this error. It further applies some built-in functions of Mathematica to the correct version of Solow economic growth model and derives some interesting graphs from the Solow convergent paths. We thank M. Wen and especially an anonymous referee for valuable discussions and comments. Any errors are sole responsibility of the authors. Citation: Kao, Jason (Jen-Shan) and Yeung-Nan Shieh, (2008) "Fine arts in Solow model: a clarification." Economics Bulletin, Vol. 1, No. 2 pp. 1-20 Submitted: January 11, 2008. Accepted: February 22, 2008. URL: http://economicsbulletin.vanderbilt.edu/2008/volume1/EB-08A00002A.pdf
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1. Introduction Recently, in Economics Bulletin , Saito (2007) applies some built-in functions of Mathematica to derive some interesting and important graphical illustrations of the famous Solow full employment equilibrium growth model. Saito’s graphical illustrations are based on the following differential equation: = (1 – s)f(k) – (n + δ )k (6) k where k = K/L , n = labor force growth rate, δ = depreciation rate, s = saving rate, and the dot indicates the rate of change over time. To utilize the algorithm for computing, Saito assumes that f(k) = k α for α є (0, 1) and evaluates whether | k* - k | is larger than ε or not. If | k* - k | > ε turns to “TRUE”, Saito proceeds to the next stage with capital accumulation according to k j+1 = k j + k j = k j + (1 – s)f(k j ) – (n + δ )k j (10) where k* (capital stock per labor at steady state) = [(1- s)/(n + δ )] [1/(1- α )] , k j = the capital stock per labor at j -th stage of computing for j = 0, 1, 2, …. , where k 0 is the positive initial capital stock per labor. Once | k* - k | > ε turns to “FALSE”, then the computing stops. However, equations (6) and (10) contain an error. They are different from the basic differential equation of Solow growth model. Since the purpose of Saito (2007) is to offer alternative analyzing tools in teaching economic growth theory, it is necessary to provide a correct version of Solow growth model. The purpose of this paper is to correct the error in equations (6) and (10). Using the correct version of Solow’s differential equation, this paper further applies Saito’s numerical examples to obtain some different graphical illustrations based on Solow’s convergent paths. 2. Solow growth model The Solow full employment equilibrium growth model considers an economy that produces a single consumption-investment good. This economy can be described by the following system of five equations, in which the government sector is ignored for the sake of simplicity. Y = C + I
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EB-08A00002A - Fine arts in Solow model: a clarification...

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