Geographic Pricing and Cross-Market Tariff Spillovers in a Differentiated Bertrand Duopoly

This paper studies how third-degree price discrimination impacts the Nash equilibrium of a duopolistic Bertrand model in differentiated markets. The model looks at two automobile producers, one based in the UK and the other based in the EU, competing in two different markets–Ireland and Britain market. The European Union producer faces a tariff only in the British market, while the United Kingdom producer faces no tariff in either of the markets. By calculating both firms’ best-response functions, this study compares the equilibrium prices and quantities under geographic price discrimination and a uniform price system. The results show that price discrimination results in the tariff increasing both producers' equilibrium prices in Britain, while leaving prices in the Irish market unchanged. This leaves the cost shock isolated in the British market. Additionally, the tariff increases the British producer’s equilibrium quantity demanded while reducing the EU producer’s quantity demanded. However, under uniform pricing, the tariff results in a cross-market spillover, increasing equilibrium prices in Ireland, set by both producers, despite the absence of a tariff in that market.