Consider a firm which is a monopolist in the output market and monopsonist in the factor market. The monopolist's production function is y = f(x) = x/2 where x denotes the quantity of the factor and y denotes the quantity of the output.
The inverse demand function for the monopolist's output is p(y) = 210 - 3y and the inverse factor supply function is w(x) = 10 + 4x.
a) Find the quantity of output to maximize the firm's profit. What quantity of the factor does the firm use, what price of the output does it charge, and what price does it pay for the factor?
b) Find the values of p, w, x, and y that correspond to the competitive equilibrium