Competition in the traditional sector does not matter for the 'Core-Periphery' model

We modify Paul Krugman's (1991) 'Core-Periphery' model by replacing the traditional competitive sector with a monopolistically competitive one. We show that the structure of spatial equilibria remains the same as in the original model. This result continues to hold true under Cournot or Bertrand oligopolistic competition with free entry in the traditional sector. The key factor that explains why the nature of competition in the traditional sector does not matter for the spatial equilibria is constant expenditure shares-due to nested Cobb-Douglas and CES preferences-which imply that trade in the traditional sector is independent from its sectoral characteristics.