Consider two countries, A and B, that produce two goods, X and Y. The production of each good requires a fixed quantity of labor and capital. Country A has 300 units of labor and 600 units of capital, while country B has 400 units of labor and 400 units of capital. The production function for each country is given by:

QA = 3LA^(1/2)KA^(1/2)
QB = 4LB^(1/3)KB^(2/3)

where QA and QB are the quantities of goods X produced by country A and B respectively, LA and LB are the quantities of labor used by country A and B respectively, KA and KB are the quantities of capital used by country A and B respectively.

a) Calculate the autarky relative price of good X in each country.

b) Which country has a comparative advantage in the production of good X?

c) What is the world relative price of good X in terms of the relative price of labor?

d) Assuming free trade, what are the quantities of good X produced and consumed in each country, and what is the gain from trade?

e) Suppose that the autarky relative price of good X in country A is 2.5. If the terms of trade are such that country A trades 1 unit of good X for 1.75 units of good X from country B, what is the gain from trade for country A?