Infrastructure Development, Comparative Advantage and Missing Trade

Abstract

Whether infrastructure development facilitates trade by establishing comparative advantage in a wider set of goods is examined in an extended continuum of goods Ricardian model as developed by Dornbusch, Fisher and Samuelson (1977). When infrastructure development is financed through income tax collection, more goods are traded and the export basket of at least one country becomes more diversified. But if it is financed by tariff proceeds, increased volume of trade and diversified export baskets are not certain outcomes.

An earlier version of the paper was presented at the Symposium in Honour of Kalyan K. Sanyal organized by the Centre for Advanced Studies, Department of Economics, Jadavpur University, in collaboration with the ICSSR, Easter Region, during April 19-20, 2012. I thank Brati Shankar Chakraborty, Sugata Marjit, Biswajit Mondal, Abhirup Sarkar, Alok Ray, Ajitava Raychauduri and other participants for their comments. The usual disclaimer applies, however.

Appendix

• I. Tax-financed Case

Using (11b), total differentiation of the relative cost condition (2a) for the Home country yields,

$$\begin{aligned} & g(L_{R}^{*} )d\rho + \rho g^{\prime}dL_{R}^{*} = -\frac{1}{{Z_{C}^{2} }}dZ_{C} \hfill \\ & \quad \Rightarrow \rho g(L_{R}^{*})\left[ {\hat{\rho } + \frac{{g^{\prime}L_{R}^{*}}}{g}\hat{L}_{R}^{*} } \right] = - \frac{1}{{Z_{C}^{{}}}}\hat{Z}_{C} \hfill \\ & \quad \Rightarrow \left[ {\hat{\rho } +\frac{{g^{\prime}L_{R}^{*} }}{g}\hat{L}_{R}^{*} } \right] = -\hat{Z}_{C} \quad \quad \left[ {{\text{using}}\,(2{\text{a}})}\right] \end{aligned} $$

(A.1)

Since under tax financed infrastructure development, $L_{R}^{*} = \tau^{*} L^{*}$, so for no change in the endowment of labour $\hat{L}_{R}^{*} = \hat{\tau }^{*}$. Using this and $\alpha^{*} \equiv \frac{{L_{R}^{*}\, g^{\prime}}}{g}$, (A.1) boils down to,

$$ \left[ {\hat{\rho } + \alpha^{*} \hat{\tau }^{*} } \right] = - \hat{Z}_{C} \Rightarrow \hat{\rho } + \hat{Z}_{C} = - \alpha^{*} \hat{\tau }^{*} $$

Similarly, total differentiation of the relative cost condition (4a) for the Foreign country yields,

$$\begin{aligned}& d\rho = \frac{1}{{Z_{C}^{*} }}g^{\prime}dL_{R} - \frac{1}{{\left({Z_{C}^{*} } \right)^{2} }}g(L_{R} )dZ_{C}^{*} \\ & \quad\Rightarrow \rho \hat{\rho } = \frac{1}{{Z_{C}^{*} }}g\left[{\frac{{L_{R} g^{\prime}}}{g}\hat{L}_{R} - \hat{Z}_{C}^{*} } \right]\\ & \quad \Rightarrow \hat{\rho } = \left[ {\frac{{L_{R}g^{\prime}}}{g}\hat{L}_{R} - \hat{Z}_{C}^{*} } \right] \\& \quad \Rightarrow \hat{\rho } = \left\lfloor {\alpha \hat{\tau } -\hat{Z}_{C}^{*} } \right\rfloor \Rightarrow \hat{\rho } +\hat{Z}_{C}^{*} = \alpha \hat{\tau }\end{aligned}$$

(A.2)

Now under tax financed infrastructure development, total differentiation of the trade balance condition (15) yields,

$$\begin{aligned} - \rho L&(1 - \tau )v^{\prime}(Z_{C} )dZ_{C} + (1 - \tau )[1 -v(Z_{C} )]Ld\rho - [1 - v(Z_{C} )]\rho Ld\tau\\ &= (1 - \tau^{*})v^{\prime}(Z_{C}^{*} )L^{*} dZ_{C}^{*} - v(Z_{C}^{*} )L^{*}d\tau^{*} \\ & \Rightarrow \rho L(1 - \tau )[1 - v(Z_{C})]\left[ { - \frac{{Z_{C} v^{\prime}(Z_{C} )}}{{[1 - v(Z_{C})]}}\hat{Z}_{C} + \hat{\rho } - \frac{\tau }{1 - \tau }\hat{\tau }}\right]\\ &= L^{*} (1 - \tau^{*} )v(Z_{C}^{*} )\left[ {\frac{{Z_{C}^{*}v^{\prime}(Z_{C}^{*} )}}{{v(Z_{C}^{*} )}}\hat{Z}_{C}^{*} -\frac{{\tau^{*} }}{{1 - \tau^{*} }}\hat{\tau }^{*} } \right]\end{aligned}$$

(A.3)

Then using $\delta \equiv \frac{{Z_{C} v^{\prime}(Z_{C} )}}{{1 - v(Z_{C} )}} > 0$, $\delta^{*} \equiv \frac{{Z_{C}^{*} v^{\prime}(Z_{C}^{*} )}}{{v(Z_{C}^{*} )}} > 0$ and the initial trade balance condition, this boils down to,

$$ \left\lfloor { - \delta \hat{Z}_{C} + \hat{\rho } - \gamma \hat{\tau }} \right\rfloor = \delta^{*} \hat{Z}_{C}^{*} - \gamma^{*} \hat{\tau }^{*} \Rightarrow \hat{\rho } - \delta \hat{Z}_{C} - \delta^{*} \hat{Z}_{C}^{*} = \gamma \hat{\tau } - \gamma^{*} \hat{\tau }^{*} $$

Solving these three equations of change by Cramer’s Rule yields the solution values given in (19)–(21) in the text.

• II. Tariff-financed Case

Proceeding as before from (24a) in the text we obtain:

$$\begin{aligned} & \rho g^{\prime}(L_{R}^{*} )dL_{R}^{*} + g(L_{R}^{*} )d\rho =\frac{1}{{Z_{C} }}dt - (1 + t)\frac{1}{{Z_{C}^{2} }}dZ_{C} \\& \quad\Rightarrow \rho g\left[ {\frac{{L_{R}^{*}g^{\prime}(L_{R}^{*} )}}{{g(L_{R}^{*} )}}\hat{L}_{R}^{*} + \hat{\rho}} \right] = \frac{(1 + t)}{{Z_{C} }}\left[ {\frac{t}{1 + t}\hat{t}- \hat{Z}_{C} } \right] \\ & \quad \Rightarrow \left\lfloor{\alpha^{*} \hat{L}_{R}^{*} + \hat{\rho }} \right\rfloor =\left\lfloor {\gamma \hat{t} - \hat{Z}_{C} } \right\rfloor \end{aligned} $$

(A.4)

From (27), we have,

$$\begin{aligned} & L_{R}^{*} dt^{*} + (1 + t^{*} )dL_{R}^{*} = v(Z_{C}^{*} )(t^{*}dL^{*} + L^{*} dt^{*} ) + v^{\prime}(Z_{C}^{*} )t^{*} L^{*}dZ_{C}^{*} \\ & \quad \Rightarrow (1 + t^{*} )L_{R}^{*} \left\lfloor{\gamma^{*} \hat{t}^{*} + \hat{L}_{R}^{*} } \right\rfloor = t^{*}L^{*} v(Z_{C}^{*} )\left\lfloor {\hat{L}^{*} + \hat{t}^{*} +\delta^{*} \hat{Z}_{C}^{*} } \right\rfloor \end{aligned} $$

(A.5)

Substitution of (A.5) in (A.4) yields,

$$ \hat{\rho } + \hat{Z}_{C} = \gamma \hat{t} - \alpha^{*} \hat{L}^{*} - \alpha^{*} (1 - \gamma^{*} )\hat{t}^{*} - \alpha^{*} \delta^{*} \hat{Z}_{C}^{*} $$

(A.6)

Similarly, from (25a) and (26) in the text we obtain respectively:

$$ \left[ {\alpha \hat{L}_{R} - \hat{Z}_{C}^{*} } \right] = \left[ {\gamma^{*} \hat{t}^{*} + \hat{\rho }} \right] $$

(A.7)

$$ \hat{L}_{R}^{{}} = \hat{L} + (1 - \gamma )\hat{t} + \delta \hat{Z}_{C}^{{}} $$

(A.8)

Substitution of (A.8) in (A.7) yields,

$$ \hat{\rho } + \hat{Z}_{C}^{*} = - \gamma^{*} \hat{t}^{*} + \alpha \hat{L} + \alpha (1 - \gamma )\hat{t} - \alpha \delta \hat{Z}_{C}^{{}} $$

(A.9)

Finally, total differentiation of the trade balance condition (28) yields,

$$ \begin{aligned} & \left[ { - (1 + t^{*} )v^{\prime}(Z_{C} )dZ_{C} + \left\{ {1 -v(Z_{C} )} \right\}dt^{*} } \right]\rho \frac{L}{{L^{*} }} + (1 +t^{*} )\left\{ {1 - v(Z_{C} )} \right\}\\ & \left[ {\frac{L}{{L^{*}}}d\rho + \frac{\rho }{{L^{*} }}dL - \frac{\rho }{{L^{*2} }}dL^{*} }\right] = (1 + t)v^{\prime}(Z_{C}^{*} )dZ_{C}^{*} + v(Z_{C}^{*} )dt\\ & \quad \Rightarrow (1 + t^{*} )\left\{ {1 - v(Z_{C} )}\right\}\rho \frac{L}{{L^{*} }}\left[ { - \frac{{Z_{C}v^{\prime}(Z_{C} )}}{{1 - v(Z_{C} )}}\hat{Z}_{C} + \frac{{t^{*}}}{{(1 + t^{*} )}}\hat{t}^{*} + \hat{\rho } + \hat{L} - \hat{L}^{*}} \right] \\&\quad = (1 + t)v(Z_{C}^{*} )\left[ {\frac{{Z_{C}^{*}v^{\prime}(Z_{C}^{*} )}}{{v(Z_{C}^{*} )}}\hat{Z}_{C}^{*} +\frac{t}{(1 + t)}\hat{t}} \right] \\ & \quad \Rightarrow \hat{\rho } =\hat{L}^{*} - \hat{L} + \delta \hat{Z}_{C} + \delta^{*}\hat{Z}_{C}^{*} + \gamma \hat{t} - \gamma^{*} \hat{t}^{*} \end{aligned} $$

(A.10)

Equations (A.6), (A.9) and (A.10) together solve for $\hat{\rho }$, $\hat{Z}_{C}$ and $\hat{Z}_{C}^{*}$as in the text.