1. Consider a set of N 2 2 countries that attract firms to their countries by engaging in tax competition. The number of firms, mk, that moves to country k is: mk = 0 - atk + Zitkti, where tx is a fixed fee (a tax) imposed on each firm (independent of its profit) in country k , t; is the corresponding fee (tax) of country j (j # k), 0 and a are positive parameters, and k = 1,2, ..., N. Suppose that each country must provide certain services and amenities to a firm in its jurisdiction at cost of $c per firm. The fees (taxes) are also in dollars. Each country's objective is to maximize its tax revenue net of costs. (i) Find the Nash equilibrium taxes. [Note: impose appropriate conditions on 0 and a to ensure that these equilibrium taxes are positive]. (ii) What is the effect of an increase in the number of countries on the equilibrium tax in (i)? Prove your answer and give the intuition. (iii) What is the sign of the slope of a country's best-response function? Prove your