A coal mine operates with a production function Q = L/2, where L is the quantity of labor it employs and Q is total output. The firm is a price taker in the output market, where the price is currently 32. The firm is a monopsonist in the labor market, where the supply curve for labor is w = 4L.
a) What is the monopsonist's marginal expenditure function, MEL?
b) Calculate the monopsonist's optimal quantity of labor. What wage rate must the monopsonist pay to attract this quantity of labor?
c) What is the deadweight loss due to monopsony in this market?