Economics Dynamics Problems 146

Economics Dynamics Problems 146 - L t 1 But if population...

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130 Economic Dynamics Figure 3.20. 3.12 Solow growth model in discrete time We have already established in chapter 2, example 2.9, that a homogeneous of degreeoneproductionfunctioncanbewritten y = f ( k ),where y istheoutput/labour ratio and k is the capital/labour ratio. In discrete time we have 13 y t = f ( k t 1 ) where y t = Y t / L t 1 and k t 1 = K t 1 / L t 1 . Given the same assumptions as example 2.9, savings is given by S t = sY t and investment as I t = K t K t 1 + δ K t 1 , where δ is the rate of depreciation. Assuming saving is equal to investment in period t , then sY t = K t K t 1 + δ K t 1 = K t (1 δ ) K t 1 Dividing both sides by L t 1 , then sY t L t 1 = K t L t 1 (1 δ ) K t 1 L t 1 = K t L t ± L t L t 1 ² (1 δ ) K t 1
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Unformatted text preview: L t 1 But if population is growing at a constant rate n , as is assumed in this model, then L t L t 1 L t 1 = n i.e. L t L t 1 = 1 + n 13 A little care is required in discrete models in terms of stocks and ows (see section 1.3). Capital and labour are stocks and are deFned at the end of the period. Hence, K t and L t are capital and labour at the end of period t . lows, such as income, investment and savings are ows over a period of time . Thus, Y t , I t and S t are ows over period t ....
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.

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