2. Consideran economy with J countries producing J different country-specific goods, as in the Armington economy of lecture note 2. Consumers everywhere have the prefer ences shown in question 1, with

XJ. In country, there are > 0 consumers, each endowed with one unit of labor. Everyone supplies laboristically There is a linear labor-only technology for producing country-specific good, and the productivity of this technogy is Write for the amount of good supplied by country Countries can fly wade all goods a. Explain why the relative prices for all and are the equilibrium prices for this economy. You can appeal to what you batore about hamothetic utily tamctioans without goaling, tacugh the tull ootruction of the competitive equilibrium (i) Tetecmine the ratio of pe-capital income tlor any poalir of countries i and i Show that per-capita income in country i declines relative to per-capita income in country if the population of country i incases relative to that of country >1, what happens to relative per-capita incomes when one country becomes more productive relative to the other? Answer the question for the caser(0,1) d. Real income is nominal income divided by the price index P Use the relative prices obtained in a to show that BR/M **(()) Show that per-capita income in country falls if its population increases Now that >1. Show that meal per-capita income in country jsises when this country becomes more productive. One can show that it may tall if <1, but you are not asked to show that he