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Question 3 (50 Points) Consider an economy that produces only steel and corn where it requires 10 units of labour and 5 units of capital to produce a ton of steel while it requires 2 units of labour and 4 units of capital to produce a ton of corn. Suppose that the price of steel is $1000/ton and the price of corn is $500/ton. Also, consider that the economy's total resources are initially 350 hours of labour and 250 units of capital. i. Draw the production possibility frontier with steel on the vertical axis and corn on the horizontal axis. (10 points) ii. Write down the unit cost of producing one ton of steel and one ton of corn 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 (Ps) and corn (Pc). Solve for the factor prices w and r. (10 points) iii. Suppose Ps increases to $1150/ton (from the initial situation). What happens to those factor prices you found in (ii) when the price of steel rises? Who gains and who loses from this change in the price of steel? Are these changes consistent with the Stolper- Samuelson theorem? (15 points) iv. Now suppose that the labor supply increases to 380 hours. Derive the new production possibility frontier. Assuming that the economy produces at a point such that all the resources are fully utilized, how much steel and corn will the economy produce after this increase in its labour supply? Are the changes in the production levels consistent with the Rybczynski theorem? (15 points) 2

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