Consider an industry in which two types of managers run firm

Consider an industry in which two types of managers run firms, Genius and Ordinary. There is a fixed supply of 100 genius managers, whereas there is unlimited supply of ordinary managers. Both types of managers are willing to work for a salary of $144,000 per year. The long-run total cost of a firm that hires a genius manager at this salary is: TC(q)=144+1/2q^2 where q is output in thousands of units and total cost is expressed in thousands of dollars per year. The corresponding long-run marginal cost curve is: MC (q) =q where marginal cost is expressed as dollars per unit. The long-run total cost of a firm that hires an ordinary manager at the annual salary of $144,000 and the corresponding marginal cost are: TC(q)=144+q^2 and MC(q)=2q The market demand can be described byQ( p) = 7200 ?100 p , where p is the market price in dollars and Q is the market quantity, expressed in thousands of units per year. a) What is the minimum efficient scale for a firm run by an ordinary manager? By a genius manager? b) Suppose, at a long-run equilibrium, both types of managers are running the firms. What is the long-run equilibrium price? How many firms with ordinary managers would be operating at this equilibrium? Suppose that firms bid against each other for the services of genius managers. c) What would you expect the winning bid be (i.e., what is the maximum annual salary a firm would be willing to offer to a genius manager)? d) What would be the long-run equilibrium price in this case? How many firms with ordinary managers would be operating at this equilibrium? Explain

Solution

Qd = 7200-100P

P = 72-0.01Q

TR = 72Q-0.01Q²

MR = 72 -0.02Q

Firm is in equilibrium where MR = MC

For ordinary manager

72-0.02Q = 2Q

Q = 72/2.02For genius manager

Q = 35.64 units rounded off to 36 units.

72-0.02Q = Q

Q =72/1.02= 70.588 units

rounded off to 71 units