Consider a 2x2x2 Heckscher-Ohlin model with two countries, Australia and Japan. Australia produces two goods, wine and software. Production of wine is relatively labor intensive, and Australia is relatively capital abundant.

a. (6 marks) Using the production possibility frontier diagram, show how Australia can be better off once it engages in trade. Explain your answer.

b. (6 marks) Derive the Stopler-Samuelson and Rybczynski theorems, using fully labelled graphs to support your answers.

c. (6 marks) Suppose Australia imposes a tariff on importing goods, which raises the relative price of the import-competing sector's output. How does the Stolper-Samuelson theorem predict about changes in factor prices in Australia? Why? Explain your answer.

c. (6 marks) Suppose the amount of capital stock increased in Australia. What is the prediction of the Rybczynski theorem on changes in the production amounts of wine and software in Australia (use the production possibility frontier diagram to illustrate your answer, fully label and explain your diagrams).