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Solving the Problems

Solving the Problems. Q = 50 – P TC = 5Q. Problem I. Suppose Q = 50 – P TC = 5Q. The Answers. Suppose Q = 50 – P TC = 5Q. The Detailed Solution. Find the value of Q at which MR = MC. Solving Problem I. Find the value of Q at which MR = MC Find MC Find MR. Marginal Cost.

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Solving the Problems

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  1. Solving the Problems Q = 50 – P TC = 5Q Lectures in Microeconomics-Charles W. Upton

  2. Problem I • Suppose Q = 50 – P TC = 5Q Solving the Problems

  3. The Answers • Suppose Q = 50 – P TC = 5Q Solving the Problems

  4. The Detailed Solution • Find the value of Q at which MR = MC Solving the Problems

  5. Solving Problem I • Find the value of Q at which MR = MC • Find MC • Find MR Solving the Problems

  6. Marginal Cost If TC = 5Q, MC = 5 Solving the Problems

  7. Marginal Revenue • 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 Solving the Problems

  8. The Inverse Demand Function Q = 50 – P P = 50 -Q Solving the Problems

  9. The Revenue Function Q = 50 – P P = 50 –Q R= PQ= (50-Q)Q Solving the Problems

  10. The Revenue Function Q = 50 – P P = 50 –Q R= PQ= (50-Q)Q R= 50Q-Q2 Solving the Problems

  11. Marginal Revenue R= 50Q-Q2 Solving the Problems

  12. Finding Marginal Revenue • The derivative of ax2 + bx + c is 2ax+b Solving the Problems

  13. Finding Marginal Revenue • The derivative of ax2 + bx + c is 2ax+b 50Q-Q2 Solving the Problems

  14. Finding Marginal Revenue • The derivative of ax2 + bx + c is 2ax+b 50Q-Q2 MR=50-2Q Solving the Problems

  15. Find MR = MC • MC = 5 • MR = 50- 2Q 50 – 2Q = 5 Solving the Problems

  16. Find MR = MC • MC = 5 • MR = 50- 2Q 50 – 2Q = 5 Q=22.5 Solving the Problems

  17. Finding P • Since Q = 50 – P P = 27.5 Solving the Problems

  18. Revenue Revenue = PQ Solving the Problems

  19. Cost TC = 5Q Solving the Problems

  20. Profit π=Revenue-Cost Solving the Problems

  21. Problem II Solving the Problems

  22. The Answers Solving the Problems

  23. A spreadsheet approach Solving the Problems

  24. A spreadsheet approach Solving the Problems

  25. A spreadsheet approach Solving the Problems

  26. A spreadsheet approach Solving the Problems

  27. A spreadsheet approach Solving the Problems

  28. A spreadsheet approach Solving the Problems

  29. End ©2004 Charles W. Upton Solving the Problems

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