Please pay ATTENTION to the question, answer mathematically. DO NOT EXPLAIN TO ME WHAT A PPF IS. Please answer the question mathematically.-----> *****part i, ii, and iii are the most important***** Consider an economy that produces only rice and corn where it requires 4 units of labour and 4 units of land to produce a ton of rice while it requires 2 unit of labour and 6 units of and to produce a ton of corn. Suppose that the price of rice is $400/ ton and the price of corn is $320/ ton. Also, consider that the economy's total resources are initially 4000 hours of abour and 6000 units of land. i. Draw the production possibility frontier with rice on the vertical axis and corn on the horizontal axis. (10 points) ii. Write down the unit cost of producing one ton of rice 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 rice and corn. Solve for the factor prices w and r. (15 points) iii. Suppose the price of rice increases to $500 /ton (from the initial situation). State and prove the Stolper-Samuelson theorem. (10 points) iv. Now suppose that the labor supply increases to 5000 hours. State and prove the Rybczynski theorem. (15 points) Consider an economy that produces only rice and corn where it requires 4 units of labour and 4 units of land to produce a ton of rice while it requires 2 unit of labour and 6 units of and to produce a ton of corn. Suppose that the price of rice is $400/ ton and the price of corn is $320/ ton. Also, consider that the economy's total resources are initially 4000 hours of abour and 6000 units of land. i. Draw the production possibility frontier with rice on the vertical axis and corn on the horizontal axis. (10 points) ii. Write down the unit cost of producing one ton of rice 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 rice and corn. Solve for the factor prices w and r. (15 points) iii. Suppose the price of rice increases to $500 /ton (from the initial situation). State and prove the Stolper-Samuelson theorem. (10 points) iv. Now suppose that the labor supply increases to 5000 hours. State and prove the Rybczynski theorem. (15 points)