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

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

3. Solving the Problems The Answers Suppose Q = 50 – P TC = 5Q Q22.5 P$27.50 Revenue$618.75 Cost$112.50 Profit$506.25

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

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

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

7. Solving the Problems 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

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

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

10. Solving the Problems The Revenue Function Q = 50 – P P = 50 –Q R= PQ= (50-Q)Q R= 50Q-Q 2

11. Solving the Problems Marginal Revenue R= 50Q-Q 2

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

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

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

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

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

17. Solving the Problems Finding P Since Q = 50 – P P = 27.5 Q22.5 P$27.50 Revenue$618.75 Cost$112.50 Profit$506.25

18. Solving the Problems Revenue Revenue = PQ Q22.5 P$27.50 Revenue$618.75 Cost$112.50 Profit$506.25

19. Solving the Problems Cost TC = 5Q Q22.5 P$27.50 Revenue$618.75 Cost$112.50 Profit$506.25

20. Solving the Problems Profit π=Revenue- Cost Q22.5 P$27.50 Revenue$618.75 Cost$112.50 Profit$506.25

21. Solving the Problems Problem II QuantityPriceCost 0 6 11511 21316 31121 4826 5731 6636 7541

22. Solving the Problems The Answers Q3 P11 Revenue33 Cost21 Profit12

23. Solving the Problems A spreadsheet approach QPRevenue =PQ Marginal Revenue CostMarginal Cost Profit 0 1 2 3 4 5 6 7

24. Solving the Problems A spreadsheet approach QPRevenue =PQ Marginal Revenue CostMarginal Cost Profit 0 6 1 15 11 2 13 16 3 11 21 4 8 26 5 7 31 6 6 36 7 5 41

25. Solving the Problems A spreadsheet approach QPRevenue =PQ Marginal Revenue CostMarginal Cost Profit 0 0 6 115 11 2132616 3113321 483226 573531 6636 753541

26. Solving the Problems A spreadsheet approach QPRevenue =PQ Marginal Revenue CostMarginal Cost Profit 0 0 6 115 115 2132611165 311337215 4 832 26 5 5 7353 315 66361 5 7535415

27. Solving the Problems A spreadsheet approach QPRevenue =PQ Marginal Revenue CostMarginal Cost Profit 0 0 6 115 115 2132611165 311337215 4832265 57353315 66361 5 7535415

28. Solving the Problems A spreadsheet approach QPRevenue =PQ Marginal Revenue CostMarginal Cost Profit 0 0 6$6 115 115$4 2132611165$10 311337215$12 4832265$6 57353315$4 66361 5$0 7535415$6

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