1. Chapter 3 Balancing Costs and Benefits McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

2. Last Chapter Review During the last chapter, we looked at the basic concepts concerning… Demand Supply Equilibrium Elasticity 3-2

3. Main Topics of Ch. 3: Balancing Benefits and Costs In chapter 1, one of the most basic principles of economics was that “Trade- offs are unavoidable”. In this chapter, we look at the basics of how we juggle these trade-offs to find the best choice. We will look at… Maximizing benefits less costs Thinking on the margin Marginal Benefit vs. Cost Sunk costs and decision-making 3-3

4. Maximizing Net Benefit Terms defined… Net benefit: total benefit minus total cost Total (economic) cost must include opportunity cost Opportunity cost: the cost associated with foregoing the opportunity to employ a resource in its best alternative use What is your opportunity cost to attend univ.? Right decision is the choice with the greatest difference between total benefit and total cost 3-4

5. Car Repair Example You own an old car that you use for delivering pizza, but now want to sell it. You know that if some repairs are made, the value of the car will increase. The more time the mechanic spends repairing the car, the more it will be worth. Also, the more time the mechanic spends, the more it will cost you. 3-5

6. Car Repair Example: Benefit Schedule The mechanic’s time is available in one- hour increments Maximum repair time is 6 hours The more time the car is repaired, the more it is worth Table 3.1: Benefits of Repairing Your Car Repair Time (Hours) Total Benefit ($) 00 1615 21150 31600 41975 52270 62485 3-6

7. Car Repair Example: Cost Schedule Table 3.2: Costs of Repairing Your Car Repair Time (Hours) Cost of Mechanic and Parts ($) Lost Wages from Pizza Delivery Job ($) Total Cost ($) 0000 114010150 235525380 364545690 41005751080 514401101550 619501502100 3-7 The mechanics time costs you money. Also, remember your opportunity cost with your pizza job!

8. Car Repair Example: Maximizing Net Benefit How should you decide how many hours is the “right” number to have your car repaired? Recall that every hour in the shop will bring both benefits and costs Choose the number of hours where benefits exceed costs by the greatest amount 3-8

9. Table 3.3: Total Benefit and Total Cost of Repairing Your Car Repair Time (Hours) Total Benefit ($) Total Cost ($) Net Benefit ($) 000 1615150 21150380 31600690 419751080 522701550 624852100 Car Repair Example: The Right Decision 3-9

10. Table 3.3: Total Benefit and Total Cost of Repairing Your Car Repair Time (Hours) Total Benefit ($) Total Cost ($) Net Benefit ($) 0000 1615150465 21150380770 31600690910 419751080895 522701550720 624852100385 Car Repair Example: The Right Decision 3-10

11. Table 3.3: Total Benefit and Total Cost of Repairing Your Car Repair Time (Hours) Total Benefit ($) Total Cost ($) Net Benefit ($) 0000 1615150465 21150380770 31600690910 419751080895 522701550720 624852100385 Best Choice Car Repair Example: The Right Decision 3-11

12. 465 Car Repair Example: Graphical Approach (Figure 3.1) Data from Table 3.3 are shown in this graph Costs are in red; benefits are in blue The best choice is where benefits > costs and the distance between them is maximized This is at 3 hours, net benefit = $910 Total Benefit, Total Cost ($) Repair Hours 123456 400 800 1200 1600 2000 2400 710 910 Best Choice 3-12

13. Maximizing Net Benefit: Finely Divisible Actions Many decisions involve actions that are more finely divisible E.g. mechanic’s time available by the minute In these cases, you can use benefit and cost curves rather than points or a schedule to make the best decision Underlying principle is the same: maximize net benefit 3-13

14. Car Repair Example: Finely Divisible Benefit Horizontal axis measures hours of mechanic’s time Vertical axis measures in dollars the total increase in your car’s value B(H)=654H-40H 2 Total Benefit ($) Hours (H) (a): Total Benefit 0123456 614 1602 2270 B 3-14

15. Car Repair Example: Finely Divisible Cost Vertical axis measures total cost in dollars Includes opportunity cost C(H)=110H+40H 2 0123456 150 690 1550 Hours (H) (b): Total Cost Total Cost ($) C 3-15

16. Car Repair Example: Finely Divisible Net Benefit Best choice is 3.4 hours of repair, maximizes net benefit Net benefit with finely divisible choices is greater than in previous example; more flexibility allows you to do better 836.40 1761.20 Total Benefit Total Cost ($) (c): Total Benefit versus Total Cost 0123456 Hours (H) 3.4 B C 924.80 3-16

17. Net Benefit Curve (Figure 3.3) Can also graph the net benefit curve Vertical axis shows B-C, net benefit Best choice is the number of hours that corresponds to the highest point on the curve, 3.4 hours 0123456 924.80 Hours (H) 3.4 Net Benefit ($) B – C 3-17

18. Thinking on the Margin Thinking like an economist Another approach to maximizing net benefits Capture the way that benefits and costs change as the level of activity changes just a little bit For any action choice X, the marginal units are the last  X units, where  X is the smallest amount you can add or subtract. Ie. the mechanic may charge by the hour, ½ hour or even by the minute. 3-18

19. Marginal Cost The marginal cost of an action at an activity level of X units is equal to the extra cost incurred due to the marginal units, divided by the number of marginal units 3-19

20. Car Repair Example: Marginal Cost Marginal cost measures the additional cost incurred from the marginal units (  H) of repair time If C(H) is the total cost of H hours of repair work, the extra cost of the last  H hours is  C = C(H) – C(H-  H) To find marginal cost, divide this extra cost by the number of extra hours of repair time,  H 3-20

21. Car Repair Example: Marginal Cost So the marginal cost of an additional hour of repair time is: Using the data from Table 3.2 (p65), if H= 3, we see: 3-21

22. Car Repair Example: Marginal Cost Schedule Table 3.5: Total Cost and Marginal Cost of Repairing Your Car Repair Time (Hours) Total Cost ($) Marginal Cost (MC) ($/hour) 00- 1150 2380230 3690310 41080390 51550470 62100550 3-22

23. Marginal Benefit The marginal benefit of an action at an activity level of X units is equal to the extra benefit produced due to the marginal units, divided by the number of marginal units 3-23

24. Car Repair Example: Marginal Benefit Marginal benefit measures the additional benefit gained from the marginal units (  H) of repair time This parallels the definition and formula for marginal cost 3-24

25. Car Repair Example: Marginal Benefit The marginal benefit of an additional hour of repair time is: Using the data from Table 3.1 (p65), if H= 3, we see: 3-25

26. Car Repair Example: Marginal Benefit Schedule Table 3.6: Total Benefit and Marginal Benefit of Repairing Your Car Repair Time (Hours) Total Benefit ($) Marginal Benefit (MB) ($/hour) 00- 1615 21150535 31600450 41975375 52270295 62485215 3-26

27. Marginal Analysis and Best Choice Comparing marginal benefits and marginal costs can show whether an increase or decrease in a level of an activity raises or lowers the net benefit Increase level if MB of doing so is greater than MC; if MC of last increase was greater than MB, decrease the level At the best choice, a small change in activity level can’t increase the net benefit Get as close to MB=MC as possible 3-27

28. Marginal Analysis and Best Choice Table 3.7: Marginal Benefit and Marginal Cost of Repairing Your Car Repair Time (Hours) Marginal Benefit (MB) ($/hour) Marginal Cost (MC) ($/hour) 0-- 1615>150 2535>230 3450>310 4375<390 5295<470 6215<550 Best Choice 3-28 No Marginal Improvement can be made. Why? Under what situation could this be improved?

29. Marginal Analysis with Finely Divisible Actions Can conduct the same analysis if choices are finely divisible by using marginal benefit and marginal cost curves Derive marginal benefit and marginal cost from total benefit and total cost curves Marginal benefit at H hours of repair time is equal to the slope of the line drawn tangent to the total benefit function at that point Usually called simply the “slope of the total benefit curve” at point D 3-29

30. Car Repair Example: Finely Divisible Marginal Benefit Let  H' = the smallest possible change in hours of car repair Adding the last  H‘ of repairs increases total benefit from point F to point D in Figure 3.4 (on the next slide), this equal to: Recall that marginal benefit (slope) is  B' /  H' Since the vertical axis measures hours of work and the horizontal axis measures total benefit, then marginal benefit equals “rise” over “run” between points F and D. 3-30

31. Relationship between Total Benefit and Marginal Benefit (Figure 3.4) Slope = MB Slope = MB = Slope = MB = Hours (H) Total Benefit ($) F E D 3-31

32. Relationship between Total Benefit and Marginal Benefit Tangents to the total benefit function at three different numbers of hours (H = 1, H = 3, H = 5) Slope of each tangent equals the marginal benefit at each number of hours Figure (b) shows the MB curve: note how the MB varies with the number of hours Marginal benefit curve is described by the function MB(H)= 654-80H 3-32

33. Relationship between Total Benefit and Marginal Benefit (Figure 3.5) Total Benefit ($) Hours (H) 0123456 614 1602 2270 B (a): Total Benefit Slope = MB = 574 Slope = MB = 414 Slope = MB = 254 0123456 254 414 574 Marginal Benefit ($/hour) MB (b): Marginal Benefit 654 Hours (H) 3-33

34. Relationship between Total Cost and Marginal Cost Parallels relationship between total benefit curve and marginal benefit When actions are finely divisible, the marginal cost when choosing action X is equal to the slope of the total cost curve at X 3-34

35. Relationship between Total Cost and Marginal Cost Tangents to the total cost curve at three different numbers of hours (H = 1, H = 3, H = 5) Slope of each tangent equals the marginal cost at each number of hours Figure (b) shows the MC curve: note how the MC varies with the number of hours Marginal cost curve is described by the function MC(H)= 110+80H 3-35

36. Relationship between Total Cost and Marginal Cost (Figure 3.6) 110 190 350 510 150 690 1550 Total Cost ($) (a): Total Cost(b): Marginal Cost 123456 Hours (H) 0 C Slope = MC = 190 Slope = MC = 350 Slope = MC = 510 0123456 Marginal Cost ($/hour) Hours (H) MC 3-36

37. Marginal Benefit Equals Marginal Cost at a Best Choice At the best choice of 3.4 hours, the No Marginal Improvement Principle holds so MB = MC At any number of hours below 3.4, MB > MC, so a small increase in repair time will improve the net benefit At any number of hours above 3.4, MC > MB, so that a small decrease in repair time will improve net benefit 3-37

38. Marginal Benefit Equals Marginal Cost at a Best Choice (Figure 3.7) Marginal Benefit, Marginal Cost ($/hour) Hours (H) MC MB 3.4 0123456 110 382 654 3-38

39. Slopes of Total Benefit and Total Cost Curves at the Best Choice MC = MB at the best choice of 3.4 hours of repair Therefore, the slopes of the total benefit and total cost curves must be equal at this point Tangents to the total benefit and total cost curves show this relationship 3-39

40. Slope of Total Benefit and Total Cost Curves (Figure 3.8) 0123456 Hours (H) Total Benefit Total Cost ($) B C 924.80 3.4 3-40

41. Marginal Anal. – 2 Steps to Finding the Best Choice Step 1: Identify any interior actions that satisfy the No Marginal Improvement Principle. MB=MC Step 2: Compare the net benefits of the best interior action to those from the boundary actions. Best choice is the one with the highest net benefit. 3-41

42. Marginal Anal. – Mechanic Ex. Step 1: MB=MC Marginal Benefit Eq. = MB(H)= 654-80H Marginal Cost Eq. = MC(H)= 110+80H 654-80H=110+80H H=3.4 ($924.80…remember…the total benefit equation is 654H-40H²) Step 2: Compare to boundary #s H=0 ($0) H=6 ($385 ~ rounded to nearest $5) …remember…the total benefit equation is 110H- 40H²) Which is the best choice? 3-42

43. Sunk Costs and Decision Making A sunk cost is a cost that the decision maker has already incurred, or A cost that is unavoidable regardless of what the decision maker does. Sunk cost examples….? Sunk costs affect the total cost of a decision Sunk costs do not affect marginal costs So sunk costs do not affect the best choice 3-43

44. Car Repair Example: Best Choice with a Sunk Cost Figure 3.9 shows a cost-benefit comparison for two possible cost functions with sunk fixed costs: $500 and $1100. In both cases, the best choice is H = 3.4: the level of sunk costs has no effect on the best choice Notice that the slopes of the two total cost curves, and thus the marginal costs, are the same 3-44

45. Best Choice with a Sunk Cost (Figure 3.9) 500 Hours (H) 3.4 0123456 C C´C´ B -175.20 424.80 Total Benefit, Total Cost ($) 1100 3-45

46. More Sunk Costs Knowing what will happen before the money is sunk can prevent you from even spending the initial money. Chunnel Example. 1987 est. cost = 3 B. Pounds 1987 est. revenue = 4 B. 1990 sunk cost = 2.5 B. 1990 est. addit. Cost = 2 B. Finish or abandon project? Why? 3-46

47. Summary Maximize benefits less cost Best choice yields the highest net benefit of all alternatives Thinking on the Margin Looking at marginal benefits can influence decision making No Marginal Improvement Principle… Sunk Costs The size of the sunk costs has no effect on the best choice. The act of sinking a cost can matter 3-47

48. Problem “If the cost of repairing your car goes up, you should do less of it.” Is this statement correct? If you think the answer is yes, explain why. If you think the answer is no, give an example in which the best choice is higher when the cost is higher. 3-48

49. Problems “If the cost of repairing your car goes up, you should do less of it.” If this statement correct? If you think the answer is yes, explain why. If you think the answer is no, give an example in which the best choice is higher when the cost is higher. In the absence of any other changes (specifically changes to benefits), this statement is correct. The only way that a higher cost could inspire a higher best choice would be if the benefits also increase, and if the benefits increased by more than the costs. (Note that if benefits and costs both increase by the same amount, the best choice should remain unchanged.) 3-49

50. Problems Chunnel Example. 1987 est. cost = 3 B. Pounds 1987 est. revenue = 4 B. 1990 sunk cost = 2.5 B. 1990 est. addit. Cost = 2 B. Finish or abandon project? Why? How much could the additional costs add up to before the Chunnel project would be abandoned…why? 3-50

51. Problem How much could the additional costs add up to before the Chunnel project would be abandoned…why? Once the investors expenses are incurred, they are sunk and no longer relevant to a decision to continue or no. If the cost of quitting is ₤0, the benefit of abandoning the project is also ₤0, since there would be no revenue earned. So, we need to compare the benefit to the cost of completing the project. The benefit of completing the project is ₤4 million in revenue that they expect to earn. If the cost of completing the project is ₤X million, then the net benefit is ₤(4 – X) million. So long as X < 4, this net benefit would be positive, making it greater than the net benefit of quitting. In other words, given that the initial ₤2.5 million is a sunk cost, investors will complete the project as long as they can break even starting from the present. 3-51