"In an efficient market all identical goods must have only one price." So states the aptly named law of one price. In the real world, however, one may easily verify that identical products are often sold for different prices. This thesis develops an extension of the Bertrand model in economics to include spatially localised competition to explain this price variation, which is then studied through simulation methods and theoretical analysis. Our model studies the effect that local heterogeneities in the environment experienced by sellers have on successful pricing strategies. Taking inspiration from models of evolutionary dynamics, we define the fitness of a seller and evolve seller prices through selection and mutation. We find three distinct steady states in our model related to the probability that a seller experiences competition for a buyer, mediated by the number of bankrupt sites in the system. When competition-free sales are unlikely, the system collapses on to a single price. If temporary monopoly situations do exist sellers can accumulate capital and variation in prices is stable. In this scenario, sellers spontaneously separate into two classes: cheap sellers – requiring sales to every potential buyer; and expensive sellers – requiring only occasional sales. Finally, we find an intermediate regime in which there is a single highly favoured price in the system which oscillates between high and low extrema. We study the properties of these steady states in detail, building a picture of how globally uncompetitive sellers can nonetheless survive if competition is strictly local. We show how the system builds up correlations, leading to niches for expensive sellers. These niches change the nature of the competition and allow for long-term survival of uncompetitive sellers. Not all expensive prices are equally likely in the steady state and we analyse why (and where) peaks in the price distribution appear. We can do this exactly for the early time dynamics of the model and extend the argument more qualitatively to the steady state. This latter analysis allows us to predict, for an observed steady distribution, the minimum price an expensive seller should charge to guarantee profit. The oscillatory ‘steady state’ is qualitatively reminiscent of boom and bust cycles in the global market. We study methods to suppress the oscillations and suggest ways of avoiding catastrophic crashes in the global economy – without negatively affecting the ability of outliers to make large profits.

There are three main chapters in the dissertation which fall in the areas of industrial organization and international economics. After the introduction and the literature review, I present two different models that highlight how the degree of substitutability between differentiated products on a market affects a new entrant's entry decisions. I further extend the benchmark model to discuss the implications of the government trade policy on the competition strategies. The last chapter investigates how the bilateral trade flows in various industries between the United States and China respond to Yuan/Dollar exchange rate fluctuations and a few other key variables. In the second chapter, I extend the Singh and Vivies (1984) model and the Hackner (2000) model by allowing for a multi-product duopoly, a domestic incumbent and a foreign entrant, with asymmetric costs in producing two differentiated products: high- and low-quality. If they engage in Cournot competition, in the subgame perfect Nash equilibrium, the foreign entrant will choose to supply both products when two varieties are more heterogeneous. If two varieties are more homogeneous, the foreign entrant tends to supply only one product. After extending the model to consider the tariff imposed on foreign imports, the simulation results suggest that, to increase domestic welfare, the government should allow cost-effective foreign entrants to enter, but keep cost-ineffective ones out of the domestic market. In the third chapter, I provide a thorough analysis of the Bertrand model with a setup that is similar to the Cournot model. When firms compete on prices, the SPNE differs significantly from that of the Cournot model. Depending on the relative marginal cost between two firms, there are circumstances under which the foreign entrant would choose to only enter into the low- or the high-quality market regardless of the degree of substitutability between two varieties. Furthermore, when the domestic government imposes a tariff on the foreign imports, the foreign entrant's entry decision changes with the tariff level. In the last chapter, unlike the existing literature which mainly look at the relationship between the exchange rate and the trade balance at the aggregate level, I attempt to investigate the short-run and the long-run impact of the Yuan/Dollar exchange rate on the US trade balance at the commodity level using a new methodology, the Autoregressive Distributed Lag Bounds Testing approach. As most articles found no short-run and long-run relationship between the exchange rate and the trade balance at the aggregate level ("aggregation bias"), I argue that different commodities may respond to the exchange rate fluctuations differently. Therefore, this study would offer us a better understanding on which US industries are more vulnerable to the Yuan/Dollar exchange rate fluctuations and which ones are strong players against Chinese competitors. In addition, I further explore other possible contributors to the US trade deficit such as income levels, China FDI inflow, and the US FDI outflow. / Economics