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\begin{document}
\title{Infrastructure Provision between Landlocked and Transit Countries and Strategic Trade Policy }
\author{Normizan Bakar and Zalila Othman}
\date{}
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\begin{abstract}
This paper analyses the infrastructure provision in the landlocked country and coastal country. The government of the landlocked country has incentives investing and subsidizing in transport infrastructure and the coastal government has a possibility to impose a toll fee on the landlocked firm exports. Establishing the three-stage-game, this paper shows that the transportation infrastructure capital investment policies are negative for the coastal country and positive for the landlocked country. Furthermore, it demonstrates that the persecution policy, toll fees, is positive.
\end{abstract}
\textbf{Keywords:} Landlocked country, Coastal country, Transportation cost, Strategic trade policy
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\section{Introduction}
This chapter focuses on the rivalry between landlocked and coastal countries and the use of public infrastructure provision for strategic trade policy\footnote{Infrastructure includes a ``hard'' dimension such as road, ports, highways, and a ``soft'' dimension such as custom management and other institution aspects as defined by \cite{Portugal-Perez2012}.}.
\section{Basic Model and Assumptions}\label{modelofinfra}
Consider two countries, landlocked and coastal countries, and a firm in each. The two firms, the landlocked firm (LF) and the coastal firm (CF) produce homogeneous goods, sell in the third market and maximize their respective profit by determining the quantity (export). There is no consumption in the producing countries.
We assume that both governments provide the transport facilities, i.e. roads and highways. The transportation facilities or infrastructures in the landlocked country can only be accessed by the LF while the transportation facilities located in the transit country provided by its government can be utilized by both firms. The governments bear the cost of provision and determine the volume (level) of the infrastructure, strategically. Regarding the transit regime in the transit country as discussed the previous chapter, the transit government take the opportunity to earn revenues by setting a user rate. Hence, the transit country's government may discriminate the landlocked country's firm by solely imposing the transit tariff on the landlocked firm. Thus, the landlocked firm pays the transit charge but the coastal firm pays nothing.
Although in general the total transportation cost is the sum of various transportation modes' costs, for simplicity in this model it is assumed that the shipping costs of both firms are similar, thus, the land transport cost is the sole cost concerned. It is also assumed that the land transport cost depends on the infrastructure provision. Furthermore, the transit fee depends on the level of infrastructure provision of the coastal country.
Let's denote the land transport cost by $t$ and $t^{*}$ for the LF and CF, respectively. The level of infrastructure of the two countries is denoted as $k$ and $k^*$\footnote{In \cite{Conrad1997}, it is assumed that the infrastructure is an amount of stock.}. The land transport costs of the LF and CF are denoted as $t(k,k^*)$ and $t^*(k^*)$, respectively. The LF's transportation has been affected by both countries' level of infrastructures, $k $ and $k^*$ while the CF's transportation cost only depends on the transit country's level of infrastructure. Assume that the land transport costs is a decreasing function of the level of infrastructure in which a change in the level of infrastructure decreases the transportation cost. It is also crucial to note that the infrastructure cost does not affect the marginal cost or the production cost as in \cite{Conrad1997}\footnote{As in equation \ref{profitfunctionmodelconrad1997}, the infrastructure element is introduced into the production cost. Meanwhile, in our model, the infrastructure affects the additional transportation cost as in the following equation \ref{profitLF}.}. Furthermore, within this assumption it shows that the change in the infrastructure level in the rival country yields a positive spillover to both firms and not only to the local firm. Hence, the marginal transportation cost has the following characteristic:
\begin{equation} \label{landtransportcost}
t'(\kappa)<0, \;and, \; t^*{'}(k^*)<0
\end{equation}
where $\kappa =k+k^*$ is the total amount of infrastructure in the landlocked and transit countries that the LF employs. For simplification, we assume that the level of infrastructures of two countries can be added as $\kappa$. The derivatives, $t'=\dfrac{dt}{d\kappa}$ and $t^{*'}=\dfrac{dt^*}{dk^*}$ are the marginal transportation cost of the LF and CF, respectively. We assume that transit fee is an increasing function of an infrastructure level $k^*$ and supposedly that the following characteristic:
\begin{equation}\label{tauandk*}
\tau'(k^*)>0
\end{equation}
Under the assumption and features presented above, the profits of the landlocked firm and coastal firm, $\Pi$ and $\Pi^*$, are defined as:
\begin{equation} \label{profitLF}
\Pi=p(x+x^*)x-t(k,k^*)x-\tau(k^*) x-cx
\end{equation}
\; and \;
\begin{equation} \label{profitCF}
\Pi^*=p(x+x^*)x^*-t^*(k^*)x^*-c^*x^*
\end{equation}
where $t$ and $t^*$ are transport cost functions, $\tau$ is a unit transit fee and $c$ and $c^*$ are production costs. Meanwhile, $p(x+x^*)$ is the indirect demand function. The transit fee, $\tau$ contracts the LF's total profit compared to the CF's total profit.
Equation \eqref{profitCF} and equation \eqref{profitLF} show that infrastructure provision is incorporated endogenously and directly affecting transport costs as well as profits. Furthermore, these functions, equation \eqref{profitLF} and equation \eqref{profitCF}, are different compared to those in previous studies \citep[e.g.,][]{Biugheas2003} which assumed a reduction in production cost.
Similar to the previous model (in Chapter 2 and 3), the current model includes the direct collection that the coastal (or transit) country may impose on its rival country's firm. However, it is assumed that the landlocked government is assumed does not collect any transit fee from the landlocked firm. For simplicity, this model also omits the tax collection variable. The model does not focus on the infrastructure finance issues but mainly shed a light on the use of infrastructure as a strategic trade policy and a source of transit revenue. Hence, taking into consideration that all products are exported to the third country, the economic welfare of the landlocked and coastal countries are respectively given by
\begin{equation} \label{welfareL}
W=\Pi-kx
\end{equation}
and
\begin{equation} \label{welfareC}
W^*=\Pi^*+\tau(k^*)x-k^*X
\end{equation}
where $X=x+x^*$ is total exports, $kx$ and $k^*X$ are the total infrastructure cost for each country, respectively, while $\tau x$ is the total transit fees. At the welfare determination level, we assume that the level of infrastructure of both countries can be represented by the unit cost of the infrastructures, $k$ and $k^*$, respectively. Hence, we may calculate the pecuniary optimal level of infrastructure.
Equation \eqref{welfareL} shows that the welfare of the landlocked country consists of the LF profit and infrastructure expenditure. On the other hand, equation \eqref{welfareC} consists of the CF profit, transit fees revenue and infrastructure expenditure. The total transit fees revenue, $\tau x$, directly depends on the volume of the LF exports. The rise in export of the landlocked firm increases the transit revenue. However, the total cost of infrastructure provision, $k^*X$, also directly depends on the total export, $x+x^*$. Intuitively, equation \eqref{welfareC} shows that the coastal government gains a benefit as a transit country by imposing the fee on its neighbor's export.
The game is designed in two stages where the firms and the governments act to maximize their profits and welfare, respectively. In the first stage, the landlocked and coastal governments set the infrastructure provision and transit fee simultaneously. We assume that the coastal government determines the infrastructure provision and transit fee simultaneously in the first stage. In the second stage, the LF and CF set their output given the political decision made in the first stage. The solution of the game requires a sub-game perfect equilibrium by backward induction.
Equation \eqref{outputdifference} shows the difference of market share between the LF and CF. Hence, the sign depends on the difference in total transportation costs of each firm as follows:
\begin{equation}\label{differentbetweenoutputiniframodel}
x-x^*
\begin{cases}
<0, &\textit{if} \ \ t^*>(t+\tau) \\
=0, & \textit{if} \ \ t^*=(t+\tau) \\
>0, & \textit{if} \ \ t^*<(t+\tau)
\end{cases}
\end{equation}
\begin{remark}
In general, the landlocked firm's market share directly depends on the transit and transportation costs.
\end{remark}
The effects of the infrastructure level $k$ and $k^*$ can be calculated by totally differentiating equation \eqref{focprofitCF} and equation \eqref{focprofitLF} with respect to $x$, $x^*$, $k$, and $k^*$, and yield:
\begin{subequations}
\begin{align}\label{socmodelinfrax}
\Pi_{xx}dx+\Pi_{xx^*}dx^*+\Pi_{xk}dk=0 \\\label{socmodelinfrax*}
\Pi^{*}_{x^{*}x}dx+\Pi^{*}_{x^*x^*}dx^*+\Pi^{*}_{x^*k}dk=0
\end{align}
\end{subequations}
Since $\Pi_{xk}=t'(k,k^*)$ and $\Pi^{*}_{x^*k}=0$, these equations, equation \eqref{socmodelinfrax} and equation \eqref{socmodelinfrax*}, can be put in matrix form and solved, using Cramer's rule.
\begin{equation} \label{totaldifferentoffocprofits}
\begin{bmatrix}
\Pi_{xx} & \Pi_{xx^*} \\
\Pi^*_{x^*x} & \Pi^*_{x^*x^*}
\end{bmatrix}
\begin{bmatrix}
dx \\
dx^*
\end{bmatrix}
=
\begin{bmatrix}
t'(k,k^*)dk \\
0
\end{bmatrix}
\end{equation}
\end{equation}
where equation\eqref{outputoninfra difference} shows that a rise in the infrastructure provision reduces the geographical disadvantages. The infrastructure provision reduces the transport costs and indirectly increases the output. Therefore, the total output (export) of the LF is bigger than the CF. Equation \eqref{outputoninfra total exports} shows that the total exports to the third country increase.
Similarly, the effect of the coastal country's infrastructure provision $k^*$ on the total output can be calculated by totally differentiating equation \eqref{focprofitCF} and equation \eqref{focprofitLF} with respect to $x$, $x^*$, and $k^*$, which yield:
\begin{subequations}
\begin{align}\label{socmodelinfraxonk*}
\Pi_{xx}dx+\Pi_{xx^*}dx^*+\Pi_{xk^*}dk^*=0 \\\label{socmodelinfrax*onk*}
\Pi^{*}_{x^{*}x}dx+\Pi^{*}_{x^*x^*}dx^*+\Pi^{*}_{x^*k^*}dk^*=0
\end{align}
\end{subequations}
Since, $\Pi_{xk^*}=t'(k,k^*)+\tau '(k^*)$ and $\Pi^{*}_{x^{*}k^*}=t^{*'}(k^*)$, these equations, equation \eqref{socmodelinfraxonk*} and equation \eqref{socmodelinfrax*onk*}, can be put in matrix form and solved, using Cramer's rule.
\begin{equation} \label{totaldifferentoffocprofits}
\begin{bmatrix}
\Pi_{xx} & \Pi_{xx^*} \\
\Pi^*_{x^*x} & \Pi^*_{x^*x^*}
\end{bmatrix}
\begin{bmatrix}
dx \\
dx^*
\end{bmatrix}
=
\begin{bmatrix}
t'(k,k^*)+ \tau'(k^*)dk^*\\
t^*{'}(k^*)dk^*
\end{bmatrix}
\end{equation}
Taking into consideration equation \eqref{landtransportcost}, equation \eqref{socsatisfaction}, and $\tau'(k^*)>0$, the effects of a change in the CG's infrastructure provision on outputs of both firms are as follows:
\begin{equation} \label{cginfraonoutputlf}
x_{k^*}=\frac{(t'(k,k^*)+\tau'(k^*))\Pi^*_{x^*x^*}-t^*{'}(k^*)\Pi_{xx^*}}{D}<0
\end{equation}
and
\begin{equation} \label{cginfraonoutputcf}
x^*_{k^*}=\frac{t^*{'}(k^*)\Pi_{xx}-(t'(k,k^*)+\tau'(k^*))\Pi^*_{x^*x}}{D}>0
\end{equation}
The results of the three comparative analyses show that the coastal country is always at an advantage position as it may discriminate the landlocked firm with the transit fee. In practice as the coastal government may control the transit fee, it may use the transit fee strategically to protect its firms in the international market. Hence, this reflects the difficulties that are inherent in the global initiative focusing on the landlocked countries and their transit partners. As long as the transit counterpart influencing the transit agreement favors its local welfare then the landlocked firm may have difficulties to access into international markets.
The effects of these policies on the landlocked firm profit can be calculated by taking a total differentiation of $\pi$ with respect to each policy variable, which yields:
\begin{subequations}
\begin{align}\label{pionk}
\Pi_k &= x(p'x^*_{k}-t') >0\\\label{piok*}
\Pi_{k^*} &=x(p'x^*_{k^*}-t'-\tau') <0 \\\label{piontau}
\Pi_{\tau}&=x(p'x^*_{\tau}-1)<0
\end{align}
\end{subequations}
We have the above equality since $p'<0$, taking into consideration equation \eqref{landtransportcost}, equation \eqref{tauandk*}, equation \eqref{tollonoutputs}, equation \eqref{cginfraonoutputcf}, and equation \eqref{outputandinfrastructure}. However, equation \eqref{piok*} is unstable as it depends on the difference between marginal transit fee to the other variables. Hence, the landlocked firm profit may rise with a change in the transit country's infrastructure.
The effects of these policies on the transit firm profit can be calculated by taking a total differentiation of $\pi^*$ with respect to each policy variable, which yields:
\begin{subequations}
\begin{align}\label{pi*onk}
\Pi^{*}_{k} &= x^*p'x_k <0\\\label{pi*ok*}
\Pi^{*}_{k^*} &=x^*(p'x_{k^*}-t')>0 \\\label{pi*ontau}
\Pi^{*}_{\tau}&=x^*(p'x_{\tau}-1)>0
\end{align}
\end{subequations}
From equation \eqref{landtransportcost}, equation \eqref{tauandk*}, equation \eqref{tollonoutputs}, equation \eqref{cginfraonoutputcf}, equation \eqref{outputandinfrastructure}, and $p'<0$ we may determine the sign. Hence, the provision of infrastructure by the landlocked country reduces the profit of the coastal country and \eqref{pi*onk} is similar to the export subsidy policy in \cite{Brander1985}.
Obviously, the imposition and provision of the above policies by both governments allow their local firm to gain a better market share and profit but inversely affect the rival firm. Proposition \ref{propositionmodelinfrakesanpolisikeatasprofit} summarizes the effects of the policies on profits.
\begin{proposition}\label{propositionmodelinfrakesanpolisikeatasprofit}
An increase in the landlocked (coastal) infrastructure provision increases (decreases) the landlocked firm profit while an increase in the coastal transit fee increases the coastal firm profit and reduce the landlocked firm profit.
\end{proposition}
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