1. (6 marks] Consider Krug'man's general equilibrium model of trade regionalism presented in section 12.6 of the textbook Letting e be consumers' common uniform elasticity of substitution between products, b be the number of symmetric trading blocs and t be the common uniform ad-valorem tariff levied by each trading bloc, normalized welfare of each trading bloc is given by: I? [5-1 + (1 bi)(1 + swan ' WQ?! 1'! 5'3 = b-1+(1 b'1)(1+r)" Since welfare is normalized, then the maximum value of ME, I, b) is 1. For this question, students might nd it easier to work with ln[w(e, r. 5)] (Le. the natural logarithm of normalized welfare] instead of ME. I, 5') directly. a. Show that normalized welfare is maximized if there is free trade [i.e. either there are no tariffs or there is only' one trading bloc) or if the number of trading blocs becomes arbitrarily large. In other words, Show the following: (i) w( e. 0, b) = l ; [ii] ME. I, 1) = l; and (iii) Me. I, b) i 1 as b 9 00. b. Letting b\" > 1 be the normalized welfare-minimizing number of trading blocs, derive the expression for b' as a function of e and r. Determine the value of b', rounded to the nearest integer, for the following cases: [i] E = 5 and I = 43.3%; and (ii) 5' = 7 and r = 37.1%