. 2. Suppose consumers in No countries home and foreign have the same preference for food and machines given by the following utility function U = CFIQCMIQ In the home country1 to produce one ton of food 1 workers is needed whereas to produce one machine requires l worker. In the foreign country, 3 workers produce one ton of food and 2 workers produce one machine. Home has 50 workers and foreign has 120 workers. Finally, let the price of machines be the numeraire in the economy. I. Solve for the equilibrium prices and quantities when countries are not allowed to trade. Which counu'y has the higher autarky price for food? II. Now suppose that countries are allowed to Irade. Compute the world relative price of food and wages in both countries. Ill. Explain the pattern of trade using the production possibility 'ontier for both countries. 1V. Show that both countries benet from trade