1. Suppose an economy can producer two goods, X and Y. Production of good X uses labor and capital Ky, which is specific to the X sector. Production of good Y uses labor and land Ty , which is specific to the Y sector. Labor is freely mobile across both sectors. The production functions are: X sector: Qx = AxlSKI- Y sector: Qy = AyLyTy Qx = output of good X; Qy = output of good Y; a. (10 points) Derive an expression for the production possibilities frontier, the PPF. Hint: solve the production functions for Ly and Ly, then use the full-employment condition on labor to get the PPF. Note your answer should be in the form of Qy as a function of Qx- For pars (b) and (c), assume Ax = Ay = 1; a = =; Kx = 10; Ty = 20; Px = Py = 2; and L = 50 (total labor supply) b. (10 points) Calculate how much labor is employed in each sector. That is, calculate the values of Ly and Ly. Hint: use the condition that the value of the marginal products of labor must be equal across sectors then solve for Ly. C. (4 points) Suppose the price of good Y, Py, rises, while the price of good X remains unchanged. What happens to the amount of labor employed in the X sector? Hint: differentiate