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Applying the Monopoly Model

Applying the Monopoly Model. An Application. Lets do some simple applications, first mathematically and then using a spreadsheet. The Demand Functions. Q = 100 – 2P. The Demand Function. Q = 100 – 2P MC = 5. Step One. Q = 100 – 2P MC = 5 Find where MR = MC. Finding MR. R = PQ.

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Applying the Monopoly Model

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  1. Applying the Monopoly Model Lectures in Microeconomics-Charles W. Upton

  2. An Application • Lets do some simple applications, first mathematically and then using a spreadsheet. Applying the Monopoly Model

  3. The Demand Functions Q = 100 – 2P Applying the Monopoly Model

  4. The Demand Function Q = 100 – 2P MC = 5 Applying the Monopoly Model

  5. Step One Q = 100 – 2P MC = 5 • Find where MR = MC Applying the Monopoly Model

  6. Finding MR R = PQ Applying the Monopoly Model

  7. Finding MR R = PQ Q = 100 – 2P P = 50 – (1/2)Q R = [50-(1/2)Q]Q Applying the Monopoly Model

  8. Finding MR R = PQ Q = 100 – 2P P = 50 – (1/2)Q R = [50-(1/2)Q]Q R = 50Q – (1/2)Q2 Applying the Monopoly Model

  9. An Application Applying the Monopoly Model

  10. An Application • We must find the derivative of our equation R = 50Q – (1/2)Q2 Applying the Monopoly Model

  11. The derivative of ax2 + bx + c Derivative Review Applying the Monopoly Model

  12. The derivative of ax2 + bx + c is 2ax+b Derivative Review Applying the Monopoly Model

  13. The derivative of ax2 + bx + c is 2ax+b 50Q – (1/2)Q2 Derivative Review Applying the Monopoly Model

  14. The derivative of ax2 + bx + c is 2ax+b 50Q – (1/2)Q2 50- Q Derivative Review Applying the Monopoly Model

  15. Set MR = MC MR = 50 – Q Applying the Monopoly Model

  16. Set MR = MC MR = 50 – Q MR = MC 50-Q = 5 Q = 45 Applying the Monopoly Model

  17. Step Two • What price will the monopolist charge? Remember the inverse demand function P = 50 – (1/2)Q Applying the Monopoly Model

  18. Finding the Price • What price will the monopolist charge? Remember the inverse demand function P = 50 – (1/2)Q P = 50 – (1/2)(45) Applying the Monopoly Model

  19. Finding the Price • What price will the monopolist charge? Remember the inverse demand function P = 50 – (1/2)Q P = 50 – (1/2)(45) P = 27.5 Applying the Monopoly Model

  20. Finding Price • Working from the demand function Q = 100 – 2P Applying the Monopoly Model

  21. Finding Price • Working from the demand function Q = 100 – 2P 45 = 100 – 2P P = 27.5 Applying the Monopoly Model

  22. Last Steps Applying the Monopoly Model

  23. We Know Applying the Monopoly Model

  24. Revenue Applying the Monopoly Model

  25. Revenue Applying the Monopoly Model

  26. Revenue Applying the Monopoly Model

  27. Total Cost Applying the Monopoly Model

  28. Applying the Monopoly Model

  29. Applying the Monopoly Model

  30. An Application • Find the value of Q at which MR = MC Applying the Monopoly Model

  31. Review • Find MC Applying the Monopoly Model

  32. Review • Find MC • Find MR Applying the Monopoly Model

  33. Review • Find MC • Find MR • The Revenue Function is PQ Applying the Monopoly Model

  34. Review • Find MC • Find MR • The Revenue Function is PQ • Solve for the inverse demand function Applying the Monopoly Model

  35. Review • Find MC • Find MR • The Revenue Function is PQ • Solve for the inverse demand function • Substitute for P into the revenue function Applying the Monopoly Model

  36. Review • Find MC • Find MR • The Revenue Function is PQ • Solve for the inverse demand function • Substitute for P into the revenue function Applying the Monopoly Model

  37. An Application • Find the value of Q at which MR = MC • Find MC • Find MR • Solve for the inverse demand function • Substitute for P into the revenue function • Find the derivative Applying the Monopoly Model

  38. A spreadsheet approach • An alternative means of doing the problem is to build a spreadsheet. Lets work through that approach. Applying the Monopoly Model

  39. End ©2003 Charles W. Upton Applying the Monopoly Model

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