This article solves a high frequency model of price arbitrage incorporating storage and trade when the amount of trade is limited by transport capacity constraints. In equilibrium there is considerable variation in transport costs, because transport costs rise when the demand to ship goods exceeds the capacity limit. This variation is necessary to attract shipping capacity into the industry. In turn, prices in different locations differ by a time varying amount. Thus while the law of one price holds, it holds because of endogenous variation in transport costs.
Coleman, Andrew (2009). ‘A model of spatial arbitrage with transport capacity constraints and endogenous transport prices’, American Journal of Agricultural Economics, Oxford University Press, Volume 91(1), Pages 42-56, DOI: https://doi.org/10.1111/j.1467-8276.2008.01183.x.