Consider an economy that produces only steel and wheat where it requires 20 units of labour and 1 unit of land to produce a ton of steel while it requires 5 units of labour and 1 unit of land to produce a ton of wheat. Suppose that the price of steel is $750/ton and the price of wheat is $300/ton. Also, consider that the economy's total resources are initially 1200 hours of labour and 90 units of land.

1. Draw the production possibility frontier with steel on the vertical axis and wheat on the horizontal axis.
2. Write down the unit cost of producing one ton of steel and one ton of wheat as a function of the hourly wage rate (w) and the rental rate (r). In a competitive market, these costs will be equal to the prices of steel and rice. Solve for the factor prices w and r.
3. Suppose P_S increases to $900/ton (from the initial situation). State and prove the Stolper-Samuelson theorem.
4. Now suppose that the labor supply increases to 1,500 hours. State and prove the Rybczynski theorem.