Assume there are two firms, A and B, buying labor in a market. They each have a constant level of VMP = 15. They face an upward sloping supply curve, W = 2L, where L is the sum of the supply of labor purchased by firm A, LA, and by firm B, LB. Their profits are a function of their own amount of labor purchased. For example, Firm A's profits are pA(L) = VMP x LA - W x LA.
(a) What would be the level of the wage and employment in a competitive market?
(b) What would the level of the wage and employment be if they colluded and divided the profits evenly?
(c) What is the profit maximizing level of employment for firm A if both parties were to break the collusion agreement (i.e., what is the Cournot-Nash equilibrium level of employment)?
(d) What wage is paid by each duopsonist according to your answer to (c)?
(e) What is the level of profit each firm has as a result of their failure to commit to an agreement?
(f) Does each firm have more or less profit than in the case for question (b)?