Consider a two-sector, two-factor economy. The two sectors are a Services sector 8 and a Manufacturing sector M. Workers in each sector are unable to work in the other sector, but capital can be used in either sector. The production functions for each sector are Y3 = ASKnga YM = AMKEJLV There is a fixed supply of labor in each sector LE and Li, and a fixed supply of capital in the economy K. a) Derive MPLS and MPKS, and show how these quantities change with Kg, LS, and A3 (just the sign of the relationship is sufficient). b) Explain how the Neoclassical assumption that factors are paid their marginal products (50 g = MPK) means that the demand curve for capital slopes down to the right. c) Suppose there is a manufacturing-biased productivity shock. That is. AM increases. Using a Neary Bucket model, show the full impact of this change on the economy. Who is made better off by this shock? Who is make worse off by this shock? d) Suppose there is an outflow of workers in the Services sector. That is, suppose the supply of service workers Lg decreases. Using a Neary Bucket model, show the full impact of this change on the economy. What happens to production in the Services sector? What happens to production in the Manufacturing sector? What happens to aggregate production in the economy (i.e. the sum of both sectors)