Please, I need help for this exercise.

Consider a world with two countries (the U.S. and Mexico) and two goods (baseballs and soccer balls). Suppose that there are 10 workers in the U.S. and 8 workers in Mexico. Each worker in the U.S. can make either 1 soccer ball or 2 baseballs, whereas each worker in Mexico can make either 1 soccer ball or 1 baseball. Workers in all countries have the same Cobb-Douglas preferences U = (S)^1/2(B)^1/2 where S is the quantity of soccer balls consumed and B is the quantity of baseballs consumed.

(a)Which country has comparative advantage in soccer balls? Which country has absolute advantage in soccer balls (that is, which country could make more soccer balls if it specialized in soccer balls)?

(b)Draw the world relative supply curve with p^S/p^B on the y axis and Q_S/Q_B on the y axis. In what range of relative prices prices will both countries fully specialize? What will Q_S/Q_B be when both countries specialize? Indicate these clearly on your graph.

(c)Derive the world relative demand curve. First calculate relative demand in Mexico bysolving for demand for each good in terms of total Mexico Y ^M p^S,p^B, then take the ratio of these two equations. Then do the same for the US. Are these the same? If so, then the world relative demand is the same as each country's relative demand. [Hint: Use the rule about expenditure shares with Cobb-Douglas preferences. Also, if relative demand is the same in both countries, then world relative demand is also the same.] What about the preferences we assumed makes relative demand not depend on Y ^M or Y ^US?

(d)Assume both countries are fully specialized. What would world relative supply be? At this levelof world relative consumption, what would prices have to be to make world relative demand equal this relative supply level? Based on your answer to (b), is complete specialization an equilibrium?

(e)Assume Mexico specializes in soccer balls, while the U.S. produces both baseballs and soccer balls.What would p^S/p^B have to be if this is the case?

(f)At this level of p^S/p^B , what is world relative demand? Would a specialized Mexico and a diversified U.S. be able to supply an amount that sets relative supply equal to demand?

(g)Suppose production technology stays the same, but Mexico's population increases to 80.

i.Is it possible that there will be a change in which country produces both goods and whichone specializes? You do not need to solve the whole problem again, but show in a graph with a RS and RD curve how things might change.

ii.Is it possible that a country that was specialized in just one good can become specializedin just the other good if its population changes, but technology in both countries stays the same? Why?