please help me with this problem

5. (14 marks) Suppose gizmos are produced in a perfectly competitive industry where two types of managers oversee the production. One type of the managers are called as alpha-type and the other as omega-type. There are only 100 alpha managers, whereas there is unlimited supply of omega 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 with an alpha manager at this salary is: IC Alpha ( 9 ) = 144 + -9 920 9= 0 where q is output in thousands of units and total cost is expressed in thousands of dollars per year. The long-run total cost of a firm with an omega manager at the annual salary of $144,000 is: TComega (q ) = 144 + 92 if 920 0 9=0 The market demand can be described by O(p)= 7200-100p , where p is the market price in dollars and O is the market quantity, expressed in thousands of units per year. a) Find the minimum efficient scale for a firm run by each type of a 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 omega managers would be operating at this equilibrium? Suppose that firms bid against each other for the services of alpha 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 an alpha manager)? d) What would be the long-run equilibrium price in this case? How many firms with omega- type managers would be operating at this equilibrium? Explain