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Appendix to Chapter 14

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International Trade Theory and Policy

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Abstract

If we consider the growth-trade relations in a dynamic context, the static equations of the basic neoclassical model treated in Chap. 19 must be supplemented by the following differential equations (a dot indicates the time derivative and the subscript i = 1, 2 refers to the countries)

$$\displaystyle{ \begin{array}{rlc} \mathop{L}\nolimits^{.}_{i}/L_{i}& = n_{i}, & \\ \mathop{K}\nolimits^{.}_{i}& = S_{i}, & \\ S_{i}& = s_{i}I_{iA} = A_{i,}^{D}&0 < s_{i} < 1. \end{array} }$$
(28.1)

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Notes

  1. 1.

    In Sect. 14.1 we adopted the opposite assumption, and warned the reader that in that case stability requires other conditions (for example that concerning the elasticity of substitution). Since the formal proof of stability would be further complicated, we prefer here to adopt the traditional capital-intensity condition.

  2. 2.

    That is, in the interval of incomplete specialization. For a more detailed analysis of the existence and uniqueness of equilibrium in this and all other possible cases, see, e.g., the already cited works of Kemp (1969b), Oniki and Uzawa (1965), and Bardhan (1970).

References

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Gandolfo, G. (2014). Appendix to Chapter 14. In: International Trade Theory and Policy. Springer Texts in Business and Economics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37314-5_28

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  • DOI: https://doi.org/10.1007/978-3-642-37314-5_28

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