Assume that all of the assumptions of the Heckscher-Ohlin theorem hold. Home and the Rest of the World produce X and Y with the following technologies:

QX = min{S, 1/3 U}, QY = min{ 1/2 S, 1/2 U}

where U is unskilled labor and S is skilled labor. QX and QY denote the quantity of X and Y respectively.

Home has a skilled labor supply of 2,000 (hours) and an unskilled labor supply of 4,000 (hours).

(A) What is the range for the relative price of X such that Home produces both X and Y ? Which good is produced if the relative price is outside of this range? Draw the PPF of Home. Assume for (b)-(g) that the price range is such that both goods are produced.

(B) Calculate the production and consumption quantities of X and Y under autarky at Home.

(C) Draw the relative supply function at Home; that is, draw how much suppliers are willing to supply QX QY given PX PY.

(D) Suppose that the relative demand of X is given by this relationship: QD x QD Y = 2 ∗ PY PX , where QD x and QD Y indicate the quantity of X and Y demanded, respectively. Draw the RD together with the RS function. Calculate the equilibrium price under autarky. Show the equilibrium point on the graph.

(E) Write down the unit costs of producing one unit of X and one unit of Y as a function of an hourly wage of unskilled workers (wu) and an hourly wage of skilled workers (ws). Solve for the wages in terms of the output prices under perfect competition.

(F) Now assume that Home hosts some skilled migrant workers such that the supply of skilled labor increases to 2,500. Draw the new PPF. How much X and how much Y will Home produce after this change? How does the allocation of skilled and Page 2 unskilled labor change across the two sectors? Calculate the change. Do the skillintensity of the two sectors change? Which theorem of the Hecksher-Ohlin Model is relevant here?

(G) Suppose the Rest of the World has a skilled labor supply of 10,000 (hours) and an unskilled labor supply of 40,000 (hours). Explain the trade patterns. What will Home export and import? Why?

(H) How does the free trade PX PY compare with the autarky relative price of X at home? (You do not need to calculate the exact new price, you need to write whether PX PY will increase, decrease or stay the same.) Explain. What happens to the real wages with this change in the relative prices? Who gains? Who loses? Using the wage equations you derive for (e), explain your answer. Which theorem of the Hecksher-Ohlin Model is relevant here?