Economics Dynamics Problems 146

# Economics Dynamics Problems 146 - L t − 1 But if...

This preview shows page 1. Sign up to view the full content.

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
This is the end of the preview. Sign up to access the rest of the document.

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 ﬂows (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 ﬂows over a period of time . Thus, Y t , I t and S t are ﬂows over period t ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online