monopolist faces a market demand

A monopolist faces a market demand curve that is given by P = 1,050 – 50Q.

PQTRMRTCATCMC
$1,0500$0$0
1$625.00
2$637.50
3$650.00
4$662.50
5$675.00
6$687.50
7$700.00
8$712.50
9$727.00
  1. Fill in the blanks in the table, which shows the monopolist’s costs and revenue situations.
  2. With reference to the table, what is the profit-maximizing output level (Qm) for the monopolist? What price (Pm) will she charge at that output level? Indicate the rule that you employed to find the answer.
  3. With the profit-maximizing decision that you obtained in part 1.b above, what is the monopolist’s profit? Show how you obtained your answer.
  4. In a LARGE diagram sketch the information from the table that you filled out in part 1.a (but do not include the TR and TC numbers in your diagram). Mark Pm and Qm in the diagram. Shade the area that represents the monopolist’s profit. Indicate which area represents the deadweight loss that is attributable to the monopolist’s behavior.
  5. Suppose the MC-column in the table in part 1.a above represents the aggregated MC-curves of all the firms in a perfectly competitive industry. Also assume that the P- and Q-columns together represent the market demand facing this competitive industry. What would be the equilibrium price (Pc) and equilibrium quantity (Qc) in that competitive market?
  6. What is the magnitude of the Dead Weight Loss?
  1. Suppose that a monopolist can identify two distinct groups of customers, students and non-students. The demand by students Qds is given by   Qds = 60 – 5Ps  and the demand for non-students Qdn is given by Qdn = 30-3Pn.   The total demand for the firm’s product—both students and non-students

(Qdtot = Qds + Qdn) is then Qdtot= 90 -8Ptot.  The firm’s cost is $7.00 per unit regardless of the number produced and there are no fixed costs.  (assume you can’t sell fractions of units).

  1. Fill in the blanks in the tables, which show the monopolist’s costs and revenue situations. (hint: solve for the inverse demand equations)
  2. With reference to the table, what is the profit-maximizing output level and price to charge the students?
  3. With reference to the table, what is the profit-maximizing output level and price to charge the non- students?
  4. How much profit is made off of students?  (remember Profit=TR-TC)
  5. How much profit is made off of non-students?
  6. How much profit is made if the firm can price discriminate (profit from both students and non-students)

Now suppose the monopolist is unable to segment the market between students and non-students, which means it only sees the total demand curve of Qtot= 90 -8Ptot.

  1. Fill in the blanks in the tables, which show the monopolist’s costs and revenue situations.
  2. With reference to the table, what is the profit-maximizing output level and price to charge all customers?
  3. How much profit does the monopolist make when it cannot price discriminate?
  4. Compare the profit when the monopolist can price discriminate and when it cannot.

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