The question is as follow:

3. (HeckscherOhlin Model: Autarky) Consider a. economy, Mexico, with two goods (footballs F and soccer balls S), and two factors of production (high skilled labor H and low skilled labor L}. Suppose that footballs and soccer balls are produced with production function: or = Hfi'w (4} Qs= HgL\" \"' (51 where a = 1/2,:1' = 1/4. The total endowment of high and low skilled workers in the country is HF+H5=H, LH+LS=L. (6) Which product is more skill-intensive? The optimal production decision in these two industries implies that the ratio technical rate of substitution is the same in the two industries. i.e. MPHF _ MPHS MPLF _ MPLS' Where M PH F is the marginal product of high-skill worker in the football industry, and other variables are similarly dened. (7) i. Write down the explicit form of Equation (7), given the demand function. ii. Given endowment K and L, derive the equilibrium production possibility frontier (PPF) for this economy, using the equation derived in (i) together with equation (6} and the two production functions. Suppose the output price ratio is xed at 3, nd the equilibrium output for F and S in the graph with PPF. If the output prices increases to 25. How does this affect the purchasing power of high-skilled and low-skilled workers? sPlease explain this based our discussion in class. If Mexico introduces many high-skill workers from the United States and the total amount of high-skilled workers is doubled to 2H. i. How will this change the shape of PPF? Please explain clearly using either words as we did in class, or using the mathematical formula you derived above. ii. How will this affect the outputs of each product? Please show it in the gure