Suppose a country produces two goods: wine and cloth. Suppose that each cask of wine always requires 4 labor units and 1 capital unit in its production and each bolt of cloth requires 2 and 5 units respectively of labor and capital. This is regardless of the factor prices.

Refer to the data in the above question. Portugal and England both have the same technology described above. England has 100 workers and 160 capital units, and Portugal has 100 workers and 70 capital units.

(a) Suppose there is no trade between the two countries (i.e. both countries are under autarky). Calculate the outputs of wine and cloth in each of the two countries assuming that both labor and capital are fully utilized.

(b) Continue to assume that there is no trade between the two countries. Regard England as Home.

(i) Plot the PPF of England with Qcon the horizontal axis and Qwon the vertical axis. Provide the relevant coordinates and slopes and intercepts of each curve so as to fully define the curve.

(ii) What is the lowest value of Pc/Pwthat can sustain full utilization of both labor and capital?

(iii) What is the highest value of Pc/Pwthat can sustain full utilization of both labor and capital?

(Hint: Find a point on the PPF that touches a straight line with slope equal to Pc/Pw. The tangency point represents the production point of the economy. Then see how the production point shifts as Pc/Pwchanges.)

(c) Continue to assume that there is no trade between the two countries. Regard Portugal as Foreign.

(i) Plot the PPF of Portugal with Q*con the horizontal axis and Q*won the vertical axis. Provide the relevant coordinates and slopes and intercepts of each curve so as to fully define the curve.

(ii) What is the lowest value of P*c/P*wthat can sustain full utilization of both labor and capital?

(iii) What is the highest value of P*c/P*wthat can sustain full utilization of both labor and capital?

(d) Suppose the two countries trade freely with each other. Suppose the equilibrium world relative price Pc/Pwunder free trade is equal to 0.75.

(i) What are the outputs of wine and cloth in England under free trade?

(ii) What are the outputs of wine and cloth in Portugal under free trade?

(iii) In equilibrium, the relative quantity supplied in the world must be equal to the relative quantity demanded. Suppose the relative demand curve is the same in both countries. What is the relative quantity of cloth to wine demanded in both countries in equilibrium?

(iv) Which country exports wine and which exports cloth? Why?

(e) The Heckscher-Ohlin theorem states that "An economy has a comparative advantage in producing, and thus will export, goods that are relatively intensive in using its relatively abundant factors of production, and will import goods that are relatively intensive in using its relatively scarce factors of production." Using your result in part (c), can you verify the Heckscher-Ohlin theorem?