worth 40 marks

(HO model, with two goods and with two factors of production) Suppose that at current factor prices a ton of steel is produced using 20 hours of labor and 1acre of land, and a ton of rice is produced using only 5 hours of labor and 1 acre of land. Suppose that the economy's total resources are 600 hours of labor and 60 acres of land. Initially, P_S= $600/ton & P_r=$300/ton.

a. Draw the production possibility frontier with steel on the vertical axis and rice on the horizontal axis. ( 6 points)

b. Write down the unit cost of producing one ton of steel and one ton of rice 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. ( 7 points)

c. Now suppose that the labor supply increases to 900 hours. State and prove the Rybczynski theorem. ( 6points)

d. Suppose P_rincreases to $450/ton (from the initial situation).State and provethe Stolper-Samuelson theorem. (6 points)