2. Consider the following case of a Specific Factor model. There are twosectors, Manufacturing (M) and Services (S). Engineers (E) work onlyin Manufacturing, while Designers (D) only in Services....

2. Consider the following case of a Specific Factor model. There are twosectors, Manufacturing (M) and Services (S). Engineers (E) work onlyin Manufacturing, while Designers (D) only in Services. Unskilledworkers (L) work in both sectors. There are 20,000 engineers in thecountry and 10,000 designers, as well as 50,000 unskilled workers.The country is open to trade. World market prices are 1 forManufacturing output (pM = 1) 1and 2 for Services (pS = 2). The production technology employed in eithersector is given by the production functions:QM = QM(E,LM) = E?L1M??QS = QS(D,LS) = D?L1S??where LM is the number of unskilled workers employed in Manufacturingand LS the number employed in Services. Assume perfect competition andfull employment. Fix the labor share of value added paid as wages to theunskilled workers to 30%, so that ? = 0.7.(a) Compute the share of unskilled workers working in Manufacturing,out oftheir total number.(b) Compute the wage of unskilled workers (wL), engineers (wE), and designers(wD).(c) Assume that everyone’s tastes are captured by the price index givenby?P=pS pMUse it to compute real wages for all three groups.(d) Redo your calculations from (a)-(c) if the number of unskilledworkersdecreases to 40,000 due to opportunities for seasonal work abroad.Who is better off? Who is worse off? (Real wages are the measureof welfare-relevant real-income.)(e) Redo your calculations from (a)-(c) if the number of engineers decreases to10,000, following a “brain drain” of technology specialists towards the West.Keep the number of unskilled workers at its initial value. Which groups arebetter or worse off? For engineers, consider only the welfare of those whostay.(f) Go back to the initial values given in the text of the problem and redoyourcalculations for (a)-(c) under the assumption that the world market price ofServices drops to 1.5 Who will gain and who will lose from this price change? (g) Go back to the initial values given in the text of the problem. Assumethat thecountry is debating allowing in 5,000 refugees from a nearby country ravagedby civil war. 20% of the refugees are designers, the rest are unskilled. Whowould be in favor or against this measure, going by economic interest alone?Would the measure pass a popular vote? (Assume everyone votes theirnarrowly-defined economicinterest.) 2