problem in Robert_C._FeenstraAdvanced_International_Trade 2003 Chp 8

8.3 Building on problem 5.3 in chapter 5, consider the CES utilityr func- tion written as in (8.2), U= 2.9;,53, 9=o 1)/o where a, = f(z,-)8 is a transformation of the quality of each product, and can be treated as a parameter, 2' = 1, . . . , N. (a) Maximize this subject to the budget constraint, 23:1 pg,- E I, to obtain an expression for the demands 5,- as a function of prices and income. (b) Use these expressions to show that 66/61),- = Bag/61),, 3' # j. (c) Also show that equation (8.9) holds, which we rewrite as M M _ Z Blnc, +(_1 O) prf :3 1.216111%: _