The Home Market Effect in International Arms Trade Online Appendix A Theoretical model: Derivations and proofs

I model two types of goods: a continuum of differentiated civilian industries, whose products are demanded by consumers, and a differentiated military sector, whose goods are demanded by the government exclusively. There is a large country and a small country. Each has one factor of production: labor. The large country has a mass L > 1 of workers, each supplying one unit of labor inelastically and earning wage w. The small country’s labor endowment and wage are normalized to 1 (so w∗L∗ = 1). Each country’s military budget ME (ME∗) is extracted from workers through an income tax f (f∗), so that workers will have after-tax income Y = wL(1− f) = wL−ME (Y ∗ = 1− f∗ = 1−ME∗) to spend on civilian goods, while governments spend ME (ME∗) on military goods.