2. Literature review 

With the development of optimization algorithms and data availability in recent decades, computable equilibrium models have been increasingly applied to the analysis of international resource commodity markets. In particular, due to the rapid growth of natural gas and electricity trade, many computable equilibrium models have been established to evaluate the impact from market structure transition and construction of new infrastructures on price and trade volume in these two markets. The early work on natural gas equilibrium models are stemmed from the studies on market power and competition patterns in the European gas market. Notable examples include GASTALE-Gas mArket System for Trade Analysis in a Liberalizing Europe (Boots et al., 2004), NATGAS-NATural GAS model (Zwart and Mulder, 2006). GASTALE explores the effect of producers’ strategic behaviors on gas price and trade volume. NATGAS focuses on the impact from the market structure (i.e., consumer surplus) through deriving more plausible demand functions for gas consumption. As for the North American gas market, Gabriel et al. (2005a) discussed the regional price differentials in the US market through building a large-scale linear complementarity gas equilibrium model. Gabriel et al. (2005b) further presented a general model for natural gas market and provided sufficient details, showing that the model is an instance of mixed nonlinear complementarity problem (NCP). This work is a milestone of natural gas market equilibrium analysis, as it provides a standard modeling framework and proves the existence of solution. Egging et al. (2010) extended the model to global market and developed the World Gas Equilibrium Model (WGM). In order to be more realistic, WGM updates the market power of gas producers in upsteam market and endogenizes the infrastructure investment. These models have been further extended to study (through considering) infrastructure constraints (Huppmann, 2013), supply securities in low-carbon energy system (Holz et al., 2016), impacts of new entrants on market power (Siddiqui et al., 2017), gas price indexation (Shi and Variam, 2017), etc.
   As for electricity market, Green and Newbery (1992) simulated the British electricity market based on a supply function equilibrium of oligopoly structure under uncertainty (Klemperer et al., 1989). Leuthold et al. (2005) built a spatial equilibrium model (ELMOD) for German electricity market. Weigt et al. (2006) extended the application scope of ELMOD to cover more European regions including France, Benelux, Western Denmark, Austria and Switzerland. Based on the previous work, Leuthold et al. (2012) made a summary for ELMOD and developed more thorough and specific assumptions so that the large-scale spatial equilibrium model of the European electricity market becomes applicable. As a classical framework, ELMOD has been extended to analyze the impact from development of transmission facilities between high voltage alternating current and direct current (Egerer et al., 2013), pricing scheme (Neuhoff et al., 2013; Egerer et al., 2016), electricity congestion management (Kunz et al., 2015), renewable energy reform (Janda et al., 2017), political impacts forecasting (Assembayeva et al., 2018), etc.
    It is noted that equilibrium analysis of nature gas and electricity market has already achieved many developments and applications. However, the iron ore international market is still an untouched field, which also exists the similar structural changes such as the development of transportation facilities, market restructuring and resource security policy making (Wilson, 2012). As few limited studies in this filed, Toweh and Newcomb (1991) presented a spatial equilibrium model to estimate the competitive prices and efficient trade flows in iron ore trade within the consideration of ex-post-computed transport cost. Wang et al. (2007) applied a CGE model to analyze the impact of world iron ore price fluctuation on Chinese economy from both macroeconomic indices (e.g., GDP and price of GDP) and industrial differentiation. Ye (2008) applied a multi-sector dynamic CGE model to estimate the impacts of iron ore boom on national economy performance.
   The above models are macro economy-based, which are not applicable to solve our problem because of the following reasons. First, they assume that the market is perfect competitive based on general equilibrium theory, which is not consistent with the reality. Germeshausen et al. (2018) suggested the existence of imperfect competition among iron ore producers. Second, these models are hard to solve the industrial-economy issues, e.g., the impact from the capacity change of industrial sector on the commodity trade, since they ignore the restrictions in the movement of productive endowments and commodities. Third, the shipping cost is treated as one part of exogenous trade costs, which make it impossible to explicitly evaluate the complex interaction between the shipping sector and the international iron ore trade. The shipping sector plays an important role in international iron ore trade. For example, Li et al. (2019) found that building a very large ship can be an effective strategy to low down the Brazil iron ore price, when the market chartering price of large size ship maintains high. However, this impact has never been discussed in an equilibrium modeling framework considering the strategies of various stakeholders in this industry. As mentioned by Robson et al. (2018), the computable equilibrium model will help to open the “black box” where the market mechanics are hidden.
   This study will enrich the previous literature of computable equilibrium models through 1) extending its application to international iron ore market, 2) breaking through the limitation of perfect competition assumption and 3) treating the shipping sector as one independent module, which enable the investigation of the interactions between iron ore trade and shipping market.