(Homogeneous Bertrand Duopoly with Asymmetric Costs) Consider firm 1, located in country 1, which faces competition from a foreign firm (firm 2) in its home market. Both firms produce homo- geneous products and face the following market demand function in country 1: The cost functions for Firms 1 and 2 are: P 10 Q1 Q2 C(Q1) C(Q2) = 4Q1 = 4Q2 The two firms compete as Bertrand duopolists. Currently firm 2 can enter country 1 without incurring any tariffs. Firm 1 can spend money lobbying its home government to impose a per unit tariff, t> 0, on the imports from country 2, i.e. making firm 2 pay $t for each unit that it sells in country 1. a. What is the maximum amount that firm 1 is willing to pay to lobby for a positive tariff on firm 27 b. Define the social welfare in country 1 as consumer surplus in country 1 plus the producer surplus (profits) of firm 1 plus any tariff revenues collected from the foreign firm. Assume there is no lobbying. Does the government of country 1 have an incentive to levy a positive tariff on firm 2? Why or why not.