chapter  14
6 Pages

Switching costs

Firms have no fixed costs and have constant marginal costs. The home firm’s marginal costs are normalized to zero, while c* represents the foreign firm’s marginal costs. Before moving to the trading equilibrium, let us briefly examine the equilibrium without the foreign firm’s entry. In this case, the home firm’s profit is represented by

Π = __

Π1 + __

Π2 = (a – bx1 – s)x1 + (a – bx2)x2,

where Πt represents profits in period t. We can obtain the equilibrium output as

_ x1 =

_ x2 =

2a – s_____4b , (14.1)

where an overbar indicates the equilibrium value without the foreign firm’s entry. Consumer surplus

follows:

CS2 = (2a – s)2_______16b , (14.2)

Π = __

Π1 + __

Π2 = (2a – s)2_______8b , (14.3)

Π = 3(2a – s) 2

________16b . (14.4)

Now, let us move to the case with the foreign firm’s entry. In this case, the analysis is simplified by considering the firm’s second-period reaction curves. We write R(y2) for the home firm’s reaction curve if consumers have no switching costs, and R´(y2) and R*(x2) when consumers have a switching cost s. The emboldened line in Figure 14.1 is the home firm’s reaction curve given x1 > 0.