Consider the labor allocation problem for the specific factors model in the medium run. Assume that PC = $120, PE = $60, MPLC = 500 – LC/10, MPLE = 400 – LE/20, and LC + LE = 4000 persons per week.
- Solve for the allocation of labor which would equate WC = WE, solve for the equilibrium weekly wage rate, and show your results on a labor allocation diagram.
- Using the area method for the labor allocation graph, solve for the total gross profits (i.e., returns to capital) in each sector. Check your answers by solving for output of each (taking the integral of the MPL), multiply by price to get revenue, and subtract total wages to get profit.
- Suppose that PC falls by half, to $60. Show this on your diagram.
- Assume that in the very short-run, after PC falls, labor is immobile. How will wages change in each sector?
- Assume instead that wages are sticky in the very short-run, after PC falls. What will happen to employment in each sector? What will be the temporary unemployment rate, as a percentage of the total labor endowment?
- Now assume that nominal wages are flexible and labor is mobile. Solve for the new labor allocation after PC falls, and then solve for the new equilibrium wage rate, and the new amounts of total gross profits in each sector. By what percentage did each change, and how does this compare to the change in PC?