Abstract
In the current section, as a frame of reference, the Solow model will be sketched out briefly, offering the real analysis of a growing economy. Firms manufacture a single product by making use of capital and labour. For ease of exposition, consider a Cobb-Douglas technology Y = Kα Nβ with α > 0, β > 0 and α + β = 1. Output can be devoted to consumption and investment Y = C + I. Households save a certain fraction s = const of income S = sY. Savings are invested I = S, thereby adding to the stock of capital \( \dot{K} \) = I. Moreover let labour grow at the natural rate \( \dot{N} \)/N = n = const. Now it is convenient to state this in per capita terms. Output per head y = Y/N is a well-known function y = kα of capital per head k = K/N. Next take the time derivative of k = K/N and rearrange adequately \( \dot{k}\ \) = \( \dot{K} \)/N − (K/N)(\( \dot{N} \)/N). Then substitute \( \dot{K} \) = I = S = sY and \( \dot{N} \)/N = n, observing y = kα, to arrive at:
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© 1992 Physica-Verlag Heidelberg
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Carlberg, M. (1992). Solow Model. In: Monetary and Fiscal Dynamics. Studies in Contemporary Economics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-47689-1_26
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DOI: https://doi.org/10.1007/978-3-642-47689-1_26
Publisher Name: Physica-Verlag HD
Print ISBN: 978-3-7908-0619-9
Online ISBN: 978-3-642-47689-1
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