Do not use chatgpt or other AI tools, if i found out then i will downvote. Thanks Consider a firm with the production function () = and assume = 1. (a) Find labor demand of a firm that is competitive on both labor and commodity market. Draw thelabor demand curve.

(b) Suppose that the inverse labor supply curve is () = 2. Find a competitive equilibrium employ- ment and wage rate. Mark the equilibrium in the graph.

Consider the case of Monopsony:

(c) Find a total labor cost of a monopsony that recognizes its impact on wage rate () = ()

and calculate marginal labor cost ().

(d) Explain why marginal cost of labor () is above wage () for any . Draw () and

() curves.

(e) Set up a profit function of a monopsony and derive the optimality condition. Explain why the

optimality condition holds.

(f) Find optimal level of labor and wage . Mark them in a graph and compare with the competitive

outcome from ). Is the result intuitive? Explain.