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Productivity, Demand, and the Home Market Effect

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Abstract

The nature of causality between international trade and industrialization remains ambiguous. We consider a model of international trade that features the home market effect—where there are differences in income and productivity between sectors and between countries—to identify additional channels by which to determine the effects of international trade on industrialization. The introduction of non-homothetic preferences and differences in productivity can aid in interpreting of some apparent paradoxes within international trade, such as the commercial relations between more populated countries as China and India and large economies in term of their GDP as the U.S. Population size, demand composition, and productivity levels constitute the three main channels by which to determine the effects of international trade. Interactions among these channels define the results obtained, especially in terms of the countries’ industrialization levels. Additionally, we find that welfare levels under trade are always higher than those under autarky.

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Notes

  1. World Bank data (2013).

  2. Hereafter,thevariablesthatcorrespondtoforeignregionsbearasuperscriptasterisk.

  3. γ∗ > 1

  4. This consumption is equal across all countries, thus indicating that everybody needs the same minimum consumption of food to survive.

  5. γ represents the relationship between the population and labour—in other words, the dependency factor.

  6. The level of industrialization can also be measured by the amount of labour available in the manufactured goods sector (Desdoigts and Jaramillo 2009).

  7. The supernumerary income is defined as the wage minus subsistence consumption of X good.

  8. This is a simplified assumption that is widely used (Helpman and Krugman 1985; Krugman 1991, etc.) and which does not affect the essential argument of the model. Ottaviano and Thisse (2004) and Zeng and Kikuchi (2009) each shows that the HME and conclusions pertaining to differentiated goods persist, while bearing in mind transportation costs on homogeneous goods.

  9. $$\mathcal{L=}\left( \sum\limits_{i = 1}^{n}y_{i}^{\sigma }+\sum\limits_{j = 1}^{n^{\ast }}y_{j}^{\ast \sigma }\right)^{\frac{1}{\sigma }}-\lambda \left( \sum\limits_{i = 1}^{n}p_{i}y_{i}+\sum\limits_{i = 1}^{n}\widehat{p_{j}^{\ast }}y_{j}^{\ast }-\left( 1-\alpha \right) \left( \frac{w}{\gamma }-P_{x}\overline{X}\right) \right) $$

  10. The results can be modified relative to those of the closed economy, only if wages between the countries differ; this is a central element in the following section.

  11. D is determined by the zero-profit condition: \(D_{i}=D=\frac {\mu \sigma }{\left (1-\sigma \right ) \beta }\)

  12. Barrios et al. (2003) show evidence of this establishment of firms in the largest market.

  13. In the Appendix, we show that even when international trade reduces the degree of industrialization in a country, the welfare of the representative agent improves, because the international market offers a greater number of varieties.

  14. This is true so long as worker remuneration exceeds the survival consumption of the agricultural good; this is one of the assumptions made herein.

  15. See Appendix 1.

  16. See Kikuchi (2001) for more details on welfare levels in a monopolistic competition model. Candau and Fleurbaey (2011) show how this result is robust to heterogeneous preferences.

  17. It is always true that productivity is higher than the minimum level of consumption of homogeneous goods.

  18. These results are always true under the interest interval.

  19. These standard values are used in the studies of Krugman (1991), Martin and Ottaviano (1999), and Corsetti et al. (2007), among others.

  20. When productivity is equal among sectors, total productivity determines the wages of workers.

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Author information

Authors and Affiliations

  1. School of Business, Colegio de Estudios Superiores de Administración-CESA, Cra 6 #34-51, Bogotá, Colombia

    Iader Giraldo

  2. Economics Department, Universidad del Rosario, Cl 12c #4-69, Bogotá, Colombia

    Fernando Jaramillo

Authors
  1. Iader Giraldo
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  2. Fernando Jaramillo
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Corresponding author

Correspondence to Iader Giraldo.

Additional information

We wish to thank two anonymous referees and the editor for helpful comments and suggestions. We also thank Thierry Verdier, Matthieu Crozet, Cecilia García-Peñalosa, Alain Desdoigts, Hernando Zuleta, and Ricardo Argüello for their pertinent comments.

Appendix

Appendix

In this section, we demonstrate that welfare levels are always better after trade, relative to autarky levels. The next equation relates the utility levels under trade and under autarky:

$$ \frac{U}{U_{A}}=\left( \frac{n}{n_{A}}+\frac{n^{\ast }\tau^{\frac{\sigma }{ 1-\sigma }}}{n_{A}}\left( \frac{p}{p^{\ast }}\right)^{\frac{\sigma }{ 1-\sigma }}\right)^{\frac{(1-\sigma )(1-\alpha )}{\sigma }}. $$
(71)

Using Eqs. 17, 21, 33, 36, 37 and 38,

$$\begin{array}{@{}rcl@{}} \frac{n}{n^{A}} \!&=&\!\left( \frac{\frac{n}{n^{\ast }}}{\frac{n}{n^{\ast }} \!+\!\theta \frac{p^{\ast }}{p}}\right) \!+\!\left( \frac{\theta^{\ast }\frac{n}{ n^{\ast }}}{\frac{p^{\ast }}{p}\!+\!\theta^{\ast }\frac{n}{n^{\ast }}}\right) \frac{1}{Z}\!=\!\frac{1}{1\!-\!\theta^{\ast }}\!-\!\frac{\theta }{1\!-\!\theta }\left( \frac{1}{Z}\right) \end{array} $$
(72)
$$\begin{array}{@{}rcl@{}} \frac{n^{\ast }}{n^{A}} \!&=&\!\left[ \left( \frac{\theta }{\frac{n}{n^{\ast }} \frac{p}{p^{\ast }}\!+\!\theta }\right) \!+\!\left( \frac{1}{1\!+\!\theta^{\ast }\frac{n }{n^{\ast }}\frac{p}{p^{\ast }}}\right) \frac{1}{Z}\right] \!\frac{p}{p^{\ast } }\!=\!\theta \left( \! \frac{1}{\left( 1\!-\!\theta \right) Z}\!-\!\frac{\theta^{\ast }}{ 1\!-\!\theta^{\ast }}\!\right). \end{array} $$
(73)

Entering the final equations in (71), we have

$$ \frac{U}{U_{A}}=\left( \frac{1-\theta \theta^{\ast }}{1-\theta^{\ast }} \right)^{\frac{(1-\sigma )(1-\alpha )}{\sigma }}. $$
(74)

Given that 𝜃 < 1 ⇒ U > UA, welfare is always better after trade, relative to that under autarky.

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Giraldo, I., Jaramillo, F. Productivity, Demand, and the Home Market Effect. Open Econ Rev 29, 517–545 (2018). https://doi.org/10.1007/s11079-018-9476-1

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