Consider the following case of a specific factor model

Question

Assignment:

Consider the following case of a Specific Factor model. There are two sectors, Manufacturing (M) and Services (S). Engineers (E) work only in Manufacturing, while Designers (D) only in Services. Unskilled workers (L) work in both sectors. There are 20,000 engineers in the country and 10,000 designers, as well as 50,000 unskilled workers. The country is open to trade. World market prices are 1 for Manufacturing output (pM = 1)and 2 for Services (pS = 2). The production technology employed in either sector is given by the production functions:

Q_M= Q_M(E, L_M)= E^_a L_M¹-^a

Q_S= Q_S(D, L_S)= D^aL_S¹-^a

 

where LM is the number of unskilled workers employed in Manufacturing and LS the number employed in Services. Assume perfect competition and full employment. Fix the labor share of value added paid as wages to the unskilled workers to 30%, so that α = 0.7.

(a) Compute the share of unskilled workers working in Manufacturing, out of their 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 given by

P= √ PS PM

Use it to compute real wages for all three groups.

(d) Redo your calculations from (a)-(c) if the number of unskilled workers decreases to 40,000 due to opportunities for seasonal work abroad. Who is better off? Who is worse off? (Real wages are the measure of welfare-relevant real-income.)

(e) Redo your calculations from (a)-(c) if the number of engineers decreases to 10,000, following a "brain drain" of technology specialists towards the West. Keep the number of unskilled workers at its initial value. Which groups are better or worse off? For engineers, consider only the welfare of those who stay.

(f) Go back to the initial values given in the text of the problem and redo your calculations for (a)-(c) under the assumption that the world market price of Services 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. Assume that the country is debating allowing in 5,000 refugees from a nearby country ravaged by civil war. 20% of the refugees are designers, the rest are unskilled. Who would be in favor or against this measure, going by economic interest alone? Would the measure pass a popular vote? (Assume everyone votes their narrowly-defined economic interest.)