I need answers

11/3 Q4. Consider a country that produces cloth and food with labor L and capital K. The produc- tion function for cloth industry is given by Qe = K2L!/2 and for the food industry Q5 = k1 The country has an initial endowment of 150 units of capital and 100 units of labor. (a) Derive the the ratio of labor to capital used in both industries as a function of the cost of labor relative to capital i.e. w/r and represent these functions in a graph w/r on the y-axis and L/K on the x-axis. Which of the two goods is labor intensive, which is capital intensive? (b) Suppose that w=r = 10. Determine the allocation of labor (Le and L) and the allocation of capital (K. and K/) in the two sectors. What quantities of cloth and food does the country produce? (c) Suppose that the capital stock has increased by 10% to 165 units, but that the factor prices have remained constant. What is the new allocation of labor and capital in the two sectors? What are the new production levels of cloth and food? (a) The Rybczynski theorem states that in an economy producing two goods, and assuming that relative product prices are constant, growth in the country's endowment of one factor of production with the other factor unchanged, results in an increase by a greater proportion in the output of the good relatively intensive in that factor and a decrease in the output of the other good. Is your result from (e) consistent with the Rybczynski theorem?