Consider a set of ???? 2 countries that attract firms to their countries by engaging in tax competition. The number of firms, Mk, that moves to country ???? is:

ms: = 9 at}: +Ejkt'a where tk is a xed fee (a tax) imposed on each rm (independent of its prot) in country it , t; is the corresponding fee (tax) ofcountryj (j =f= It), 9 and a are positive parameters, and k = 1,2, , N. Suppose that each country must provide certain services and amenities to a rm in its jurisdiction at cost of $r: per rm. The fees (taxes) are also in dollars. Each country's objective is to maximize its total tax revenue or income from fees. (i) Find the Nash equilibrium taxes. [Note: impose appropriate conditions on 9 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 lnction? Prove your