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2014 | OriginalPaper | Chapter

10. Convergence in a Three-Factor Dynamic Model: Finite Versus Infinite Lives

Author : Partha Sen

Published in: Trade, Globalization and Development

Publisher: Springer India

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Abstract

In two-sector dynamic trade models with infinitely-lived agents in the presence of factor–price-equalization, convergence of aggregate capital-labor ratios and incomes does not occur. The Euler equation implies equal growth rate of consumption in all trading economies. With finite lives capital-labor ratios do get equalized. In a dynamic specific factors model, we show that factor–price-equalization occurs only in the long run with infinitely lived agents. With finite lives, even in the steady state there is no factor price equalization.

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The world economy, of course, is a closed economy and hence a decline in the return to capital accompanies any accumulation of capital.

In this we are following Sen and Shimomura (2012). Eaton (1987, 1988) used specific factors in an overlapping generations framework.

In a previous paper, capital was mobile between sectors. The presentation in this paper corresponds to a model of industrialization, where as capital is accumulated, industry grows and sucks out labor from agriculture.

Hence the description of this model as “a model of perpetual youth”.

It would be straightforward, if tedious, to extend the analysis to the case of the instantaneous utility function being of the CRRA variety but with an intertemporal consumption elasticity different from unity (as in Buiter (1988)).

Solving the differential equation in (18) (similarly for (19)) and imposing transversality conditions, we find that the price of land is given by the present discounted value of the marginal product of land, where the (time-varying) discount factor is the return to capital.

$$ q(t) = \int\limits_{t}^{\infty } {e^{{ - \int_{t}^{s} {[\alpha k^{\alpha - 1} (\nu ) - \delta z(\nu )]{\text{d}}v} }} } p\left( s \right)\beta m^{\beta - 1} \left( s \right){\text{d}}s $$

The specific factors L and M could be thought of as two kinds of labor. The interpretation that suits the analysis in Sect. 2 is to think of L as labor and M as some endowment of fruits. In Sect. 3.2, we introduce the valuation of the trees that bear these fruits (as in Eaton (1987), (1988)). In the earlier dynamic specific factors models, the capitals in the sectors were specific in the short run, while labor was mobile across sectors (Neary (1978)). In the long run, capital was also mobile across sectors, and the model collapsed into the familiar Heckscher-Ohlin model.

Where there is no chance of confusion, we do not explicitly write the time index.

Constant growth rates for L and M can easily be incorporated, as can exogenous technical progress.

Atkeson, A., & Kehoe, P. J. (2000). “Paths of development for early- and late-boomers in a dynamic heckscher-ohlin model.” Research Staff Report No. 256, Federal Reserve Bank of Minneapolis.

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Title: Convergence in a Three-Factor Dynamic Model: Finite Versus Infinite Lives
Author: Partha Sen
Publisher: Springer India
Book: Trade, Globalization and Development
Print ISBN: 978-81-322-1150-1

Electronic ISBN: 978-81-322-1151-8

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-81-322-1151-8_10