From a theoretical point of view there is no guarantee that interior equilibria are always stable. In fact, if the income effect is stronger enough than the competition effect, the model would be unstable because, as firms moved to a country, they would make that nation firms’ profits greater, which would attract even more firms. This means that to get stability, constraining the model parameters to a certain range is required. However, when there is just one interior equilibrium, the link between its uniqueness and its stability makes it unnecessary to add extra conditions to those already imposed. By means, if there is one and just one interior equilibrium, equations (18) and (19) guarantee non-corner solutions and stability. Figure 1 shows a choice of parameters for which there exists a stable interior equilibrium. The blue curve, which represents profits of a national firm, is up to the purple curve for every n right to the interior solution. In Appendix A.1., I show that this interior equilibrium is unique. Figure 1. From our discussion above, notice that the demand and supply sides together with profit equalization , jointly determine the equilibrium number of firms located at home. Therefore, given an N value that satisfies (22), they also determine the share of national firms over the world number of companies, . Using these equations, I claim the following propositions. Proposition 1: Under (22) and the non-corner solution conditions there exists a unique stable equilibrium where: See Appendix A.1. From this, it can very easily be shown that is increasing in if and only if . The reason is that in the equal trade cost case, if the national labor share is more than a half, there are more firms at home than abroad. Proposition 2: Under (22) and the non-corner solution conditions there exists a unique stable equilibrium where:
From a theoretical point of view there is no guarantee that interior equilibria are always stable. In fact, if the income effect is stronger enough than the competition effect, the model would be unstable because, as firms moved to a country, they would make that nation firms’ profits greater, which would attract even more firms. This means that to get stability, constraining the model parameters to a certain range is required. However, when there is just one interior equilibrium, the link between its uniqueness and its stability makes it unnecessary to add extra conditions to those already imposed. By means, if there is one and just one interior equilibrium, equations (18) and (19) guarantee non-corner solutions and stability. Figure 1 shows a choice of parameters for which there exists a stable interior equilibrium. The blue curve, which represents profits of a national firm, is up to the purple curve for every n right to the interior solution. In Appendix A.1., I show that this interior equilibrium is unique. Figure 1. From our discussion above, notice that the demand and supply sides together with profit equalization , jointly determine the equilibrium number of firms located at home. Therefore, given an N value that satisfies (22), they also determine the share of national firms over the world number of companies, . Using these equations, I claim the following propositions. Proposition 1: Under (22) and the non-corner solution conditions there exists a unique stable equilibrium where: See Appendix A.1. From this, it can very easily be shown that is increasing in if and only if . The reason is that in the equal trade cost case, if the national labor share is more than a half, there are more firms at home than abroad. Proposition 2: Under (22) and the non-corner solution conditions there exists a unique stable equilibrium where:
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