1. We solve the 2 X 2 Ricardian model with a constant elasticity of substitution (CBS) demand. Assume that the demand in country 71 of the goods 3', gum, is the result of the utility maximiza tion: a 0-1-1 o----1:| h max [WW + (9.2) . S-t- pnlynl 'l' pn2y7b2 2 X7\" where n = N, S indexes the country, and X7, is the total expenditure of the country. 0 > 1 denotes the elasticity of substitution across goods. (a) Write down the Lagrangian function and solve for the optimal consumption bundle for country 71. (b) The ideal price index is dened as the cost of one unit of utility. Show that with CBS utility function, the price index takes the form: 1 13,, = [(me'\" + (pn2)l_'7] m (c) Under the assumption of free trade, law of one price holds so we have le 2 p31 2 p1, and p31 = p52 = 392. Solve for the world relative demand of the two goods. (d) Same as in the lecture, we assume the North has comparative advantage in goods 1, so: aNi 181