Innovative Applications of O.R.Tariffs and quotas in world trade: A unified variational inequality framework
Introduction
World trade is essential to the global economy through the flow of goods from supply markets in countries to demand markets. Products as diverse as fresh produce and other agricultural and food products such as meat, fish and seafood, cereals, including rice and wheat, and dairy products, to steel and aluminum, and a variety of other commodities, are transported across national boundaries to points of demand. Given the importance of global trade for producers and consumers alike, governments, nevertheless, often turn to trade policies ranging from tariffs and quotas, and their combination, in the form of tariff rate quotas (TRQs), in order to reduce the impact of competitive foreign firms on their demand markets and to protect their less competitive domestic firms. For example, the Uruguay Round in 1996 induced the creation of more than 1300 new TRQs (cf. Skully, 2001). A TRQ (sometimes also referred to as a tariff quota) is a two-tiered tariff, whereby a lower in-quota tariff is applied to the units of imports until a quota or upper bound is reached and a higher over-quota tariff is applied to all subsequent imports (World Trade Organization, 2004), with, currently, World Trade Organization members having a combined total of 1425 tariff quotas in their commitments (Organization, 2018).
Given the relevance of trade policies to world trade, and that tariffs, in particular, are a major issue now in the news (cf. Paquette, Lynch, & Rauhala, Tankersley, 2018), the development of rigorous mathematical models that can capture trade policies used in practice today and that are computable, providing both equilibrium supply market prices and demand market prices, as well as product flows, is critical. Such models should be sufficiently general to be able to handle multiple supply and demand markets in different countries, trade flows on general networks, and to be able to handle nonlinear cost and price functions that are also asymmetric and flow-dependent.
Spatial price equilibrium (SPE) models, in particular, have attained prominence in the modeling, analysis, and solution of a wide spectrum of commodity trade problems, dating to the seminal contributions of Enke (1951), Samuelson (1952), Takayama and Judge (1971), and Takayama and Judge (1964). The need to develop extensions, over and above the original SPE models that were reformulated and solved using optimization approaches, especially quadratic programming ones, has also spearheaded advances through the use of methodologies such as complementarity theory as well as variational inequality theory (cf. Asmuth, Eaves, Peterson, 1979, Florian, Los, 1982, Dafermos, Nagurney, 1987, Dafermos, Nagurney, 1984, Friesz, Harker, Tobin, 1984, Harker, 1985, Nagurney, Aronson, 1988, Nagurney, Takayama, Zhang, 1995, van den Bergh, Nijkamp, Rietveld, 1996, Nagurney, 1999, Daniele, 2004, Nagurney, 2006, Li, Nagurney, Yu, 2018, and the references therein). In addition, spatial price equilibrium models, due to their practical applications in agricultural and energy and mineral markets, have been constructed to include policies such as ad valorem tariffs (Nagurney, Nicholson, Bishop, 1996a, Nagurney, Nicholson, Bishop, 1996b), price policies (Nagurney & Zhao, 1993), and goal targets (Nagurney, Thore, & Pan, 1996) using variational inequality theory, as well as quotas and other tariff schemes using complementarity theory (see, e.g., Rutherford, 1995, Nolte, 2008, Grant, Hertel, Rutherford, 2009, Johnston, van Kooten, 2017, and the references therein).
In this paper, we construct a general spatial price network equilibrium model consisting of countries and multiple supply markets and demand markets in each country under a tariff rate quota regime. Spatial price equilibrium models in which various policy interventions have been incorporated such as tariff rate quotas assume either regions or countries as supply and/or demand markets. Since different supply and demand markets may have, respectively, distinct supply and demand price functions, and trade policies such as tariff rate quotas can impose quotas over multiple countries, we believe that having a greater level of detail is meaningful. Furthermore, rather than assuming only a single path (essentially a link) between a pair of supply and demand market nodes, we allow for multiple paths, each of which is not limited to the same number of links. Different supply markets in a given country may have distinct transport mode options to demand markets in the same or other countries, and, therefore, such options can be represented as paths on the general network, with associated costs. We focus on tariff rate quotas (TRQs) since they have been deemed challenging to formulate and only stylized examples have been reported in an SPE framework (cf. Bishop, Nicholson, Pratt, & Novakovic, 2001). In addition, we construct variants of the general spatial price network equilibrium model with tariff rate quotas, to demonstrate how the latter can be easily adapted to handle unit tariffs, ad valorem tariffs, and/or strict quotas. We also note that, through the use of multiple paths, the evaluation of avenues for transshipment, as a means to avoid tariffs, a topic that has garnered a lot of attention in the popular press recently (cf. Bradshear, 2018), is made possible. Moreover, our framework allows for the investigation of the impacts of TRQs on domestic markets, on both producers and consumers alike, that are imposed on non-domestic markets.
This paper is organized as follows. In Section 2, we first present the general spatial price network equilibrium model with tariff rate quotas, and derive a variational inequality formulation of the governing equilibrium conditions. We then demonstrate in Section 3 how the model can be easily adapted to also handle unit tariffs, ad valorem tariffs, and/or quotas, using a variational inequality framework. In addition, we present several numerical examples for illustrative purposes. In Section 4 we provide qualitative properties and propose a computational scheme in Section 5, which yields closed form expressions at each iteration. A case study in Section 6 on the dairy industry, with a focus on cheese, is then constructed to illustrate the effectiveness of the modeling and computational approach and the type of insights that can be gained. A summary of results, along with conclusions, and suggestions for future research, are provided in Section 7.
Section snippets
The spatial price network equilibrium model with tariff rate quotas
We consider a spatial price equilibrium problem on a general network consisting of the set of nodes N and the set of links L. In classical spatial price equilibrium problems, the commodity supply prices, trade flows, and demand prices are achieved when the equilibrium conditions stating that: if there is a positive volume of trade of the commodity between a supply market and a demand market, then the commodity price at the demand market is equal to the commodity price at the supply market plus
Variants of the spatial price network equilibrium model
In this section, we present several variants of the model constructed in Section 2. This is being done in order to demonstrate the flexibility of the variational inequality formalism for policy modeling in the context of world trade.
First, an extension of the classical spatial price network equilibrium model is given, and from this model policies in the form of ad valorem tariffs and then quotas incorporated.
Without loss of generality, we let the set of paths P correspond to all the paths
Qualitative properties
In this Section we provide qualitative properties of the function F (cf. (23)) corresponding to the SPE model with TRQs, which are needed for convergence of the algorithmic scheme in Section 5. In addition, we provide existence results for a solution X* of the variational inequality (23).
In the following proposition we establish that if the supply price functions, the link cost functions, and minus the demand price functions are monotone in their respective vectors of variables, then the
The algorithm
In this Section, we present the algorithm to solve the variational inequality (23), equivalently (15), governing the spatial equilibrium model with tariff rate quotas and its variants that is presented in Section 3. The algorithm that we propose for the computation of the equilibrium pattern is the modified projection method of Korpelevich (1977).
The steps of the algorithm for the spatial price problem with tariff rate quotas are as follows:
Step 0: Initialization
Initialize with . Set t ≔ 1
A case study on the dairy industry
In this Section, we focus on a case study based on the dairy industry in the United States. In 2002, the dairy industry in the United States generated 20 billion dollars in sales value (Hadjigeorgalis, 2005). In recent years, the dairy industry in the United States has experienced a shift towards larger operations with more than 500 cows, in which the dairy farmers can hold more inventory and increase their production of milk. The large size operations accounted for nearly 60% of all milk
Summary, conclusions, and suggestions for future research
With numerous commodities from fresh produce to metals such as aluminum and steel, utilized in many product supply chains, criss-crossing the globe from points of production to locations of demand, world trade is essential for producers and consumers alike. Policy makers, as well as governments, in turn, are increasingly utilizing policy trade instruments in an attempt to protect domestic producers from competition. In fact, in the past year or so, the discussions of various trade policies,
Acknowledgments
The authors are grateful to the three anonymous reviewers of the original manuscript and to the Editor for their helpful comments and suggestions. The first author acknowledges support from the Radcliffe Institute for Advanced Study at Harvard University where she is a Summer Fellow and from the John F. Smith Memorial Fund at the University of Massachusetts Amherst.
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