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

2. Main Topics Maximizing benefits less costs Thinking on the margin
Sunk costs and decision-making
1. Maximizing benefits less costs. Economic decisions generate benefits and costs. The best choice maximizes the difference between benefits and costs.
2. Thinking on the margin. Marginal benefits and marginal costs measure incremental benefits and costs.
3. Sunk costs and decision making. Sometimes a decision must be made after costs have been incurred; these costs are sunk costs. Sunk costs should be ignored when making economic decisions.
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3. Maximizing Net Benefit
Net benefit: total benefit minus total cost
Total cost must include opportunity cost
Opportunity cost: the cost associated with foregoing the opportunity to employ a resource in its best alternative use
Right decision is the choice with the greatest difference between total benefit and total cost
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4. Car Repair Example: Benefit Schedule
Table 3.1: Benefits of Repairing Your Car
Repair Time
(Hours)
Total Benefit
($) 1
615 2
1150 3
1600 4
1975 5
2270 6
2485
Mechanic’s time is available in one-hour increments
Maximum repair time is 6 hours
The more time the car is repaired, the more it is worth
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5. Car Repair Example: Cost Schedule
Table 3.2: Costs of Repairing Your Car
Repair Time (Hours)
Cost of Mechanic and Parts
($)
Lost Wages from Pizza Delivery Job
Total Cost 1
140 10
150 2
355 25
380 3
645 45
690 4
1005 75
1080 5
1440
110
1550 6
1950
2100
Note that there are two different kinds of costs incurred here: One is an indirect kind of cost in that you cannot work at your pizza delivery job while you car is in the shop. The other kind of cost is more direct: you hire the mechanic and buy parts.
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6. 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
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7. Car Repair Example: The Right Decision
Table 3.3: Total Benefit and Total Cost of Repairing Your Car
Repair Time (Hours)
Total Benefit ($)
Total Cost ($)
Net Benefit ($) 1
615
150 2
1150
380 3
1600
690 4
1975
1080 5
2270
1550 6
2485
2100
The next slide includes the net benefit figures, in case the instructor wants to pause here to ask students to compute net benefit before revealing the numbers.
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8. Car Repair Example: The Right Decision
Table 3.3: Total Benefit and Total Cost of Repairing Your Car
Repair Time (Hours)
Total Benefit ($)
Total Cost ($)
Net Benefit ($) 1
615
150
465 2
1150
380
770 3
1600
690
910 4
1975
1080
895 5
2270
1550
720 6
2485
2100
385
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9. Car Repair Example: The Right Decision
Table 3.3: Total Benefit and Total Cost of Repairing Your Car
Repair Time (Hours)
Total Benefit ($)
Total Cost ($)
Net Benefit ($) 1
615
150
465 2
1150
380
770 3
1600
690
910 4
1975
1080
895 5
2270
1550
720 6
2485
2100
385
Best Choice
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10. 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 1 2 3 4 5 6
400
800
1200
1600
2000
2400
710
910
465
Best Choice
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11. 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 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
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12. Sample Problem 1 Identifying costs
What are the costs of buying a concert ticket if you have to wait in line for 2 hrs?
Ticket master
What is the cost of watching a movie for two hours?

13. Car Repair Example: Finely Divisible Benefit
Total Benefit ($)
Hours (H)
(a): Total Benefit 1 2 3 4 5 6
614
1602
2270 B
Horizontal axis measures hours of mechanic’s time
Vertical axis measures in dollars the total increase in your car’s value
B(H)=654H-40H2
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14. Car Repair Example: Finely Divisible Cost1 2 3 4 5 6
150
690
1550
Hours (H)
(b): Total Cost
Total Cost ($) C
Vertical axis measures total cost in dollars
Includes opportunity cost
C(H)=110H+40H2
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15. 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
(c): Total Benefit versus Total Cost
Total Benefit
Total Cost
($) B C
924.80
836.40 1 2 3
3.4 4 5 6
Hours (H)
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16. Net Benefit Curve (Figure 3.3)
Can also graph the net benefit curve
Vertical axis shows B-C, net benefit
Best choice is the number of hours that corresponds to the highest point on the curve, 3.4 hours
Net Benefit
($)
924.80
B – C 1 2 3
3.4 4 5 6
Hours (H)
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17. Sample Problem 2 (3.1)
Suppose that the cost of hiring your mechanic (including the cost of parts) is $200 an hour up to four hours (she charges for her time in one-hour increments). Your benefits and other costs are the same as in tables 3.1 and 3.2. Construct a table like Table What is your best choice?

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 DX units, where DX is the smallest amount you can add or subtract
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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
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20. Car Repair Example: Marginal Cost
Marginal cost measures the additional cost incurred from the marginal units (DH) of repair time
If C(H) is the total cost of H hour of repair work, the extra cost of the last DH hours is DC = C(H) – C(H-DH)
To find marginal cost, divide this extra cost by the number of extra hours of repair time, DH
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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, if H= 3, we see:
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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) - 1
150 2
380
230 3
690
310 4
1080
390 5
1550
470 6
2100
550
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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
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24. Car Repair Example: Marginal Benefit
Marginal benefit measures the additional benefit gained from the marginal units (DH) of repair time
This parallels the definition and formula for marginal cost
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25. Car Repair Example: Marginal Benefit
The marginal benefit of an additional hour of repair time is:
Using the data from Table 3.1, if H= 3, we see:
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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) - 1
615 2
1150
535 3
1600
450 4
1975
375 5
2270
295 6
2485
215
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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 level
At the best choice, a small change in activity level can’t increase the net benefit
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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) - 1
615
>
150 2
535
230 3
450
310 4
375
<
390 5
295
470 6
215
550
Best Choice
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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 point
Usually called simply the “slope of the total benefit curve” at point D
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30. Car Repair Example: Finely Divisible Marginal Benefit
Let DH' = the smallest possible change in hours of car repair
Adding the last DH‘ 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 is DB' /DH'
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.
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31. Relationship between Total Benefit and Marginal Benefit (Figure 3.4)
Slope = MB D
Slope = MB = E
Slope
= MB = F
Hours (H)
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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)= H
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33. Relationship between Total Benefit and Marginal Benefit (Figure 3.5)
Hours (H) 1 2 3 4 5 6
614
1602
2270 B
(a): Total Benefit
Slope = MB = 574
Slope = MB = 414
Slope = MB = 254
254
414
574
Marginal Benefit ($/hour) MB
(b): Marginal Benefit
654
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34. Relationship between Total Cost and Marginal Cost
Parallels relationship between total benefit curve and marginal benefit
When actions are finely divisible, the marginal cost when choosing action X is equal to the slope of the total cost curve at X
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35. Relationship between Total Cost and Marginal Cost
Tangents to the total cost curve at three different numbers of hours (H = 1, H = 3, H = 5)
Slope of each tangent equals the marginal cost at each number of hours
Figure (b) shows the MC curve: note how the MC varies with the number of hours
Marginal cost curve is described by the function MC(H)= H
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36. Relationship between Total Cost and Marginal Cost (Figure 3.6)
110
190
350
510
150
690
1550
Total Cost ($)
(a): Total Cost
(b): Marginal Cost 1 2 3 4 5 6
Hours (H) C
Slope = MC = 190
Slope = MC = 350
Slope = MC = 510
Marginal Cost ($/hour) MC
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37. Marginal Benefit Equals Marginal Cost at a Best Choice
At the best choice of 3.4 hours, the No Marginal Improvement Principle holds so MB = MC
At any number of hours below 3.4, MB > MC, so a small increase in repair time will improve the net benefit
At any number of hours above 3.4, MC > MB, so that a small decrease in repair time will improve net benefit
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38. Marginal Benefit Equals Marginal Cost at a Best Choice (Figure 3.7)
Marginal Benefit, Marginal Cost ($/hour)
Hours (H) MC MB
3.4 1 2 3 4 5 6
110
382
654
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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
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40. Slope of Total Benefit and Total Cost Curves (Figure 3.8)
($) B
924.80 C 1 2 3
3.4 4 5 6
Hours (H)
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41. Sample Problem 3 (3.8)
Suppose you can hire your mechanic for up to six hours. The total benefit and total cost functions are B(H)= 400H1/2 and C(H) = 100H. The corresponding formulas for marginal benefit and marginal cost are MB(H) = 200/H1/2 and MC(H) = What is your best choice?

42. 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 costs affect the total cost of a decision
Sunk costs do not affect marginal costs
So sunk costs do not affect the best choice
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43. 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 $1100.
In both cases, the best choice is H = 3.4: the level of sunk costs has no effect on the best choice
Notice that the slopes of the two total cost curves, and thus the marginal costs, are the same
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44. Best Choice with a Sunk Cost (Figure 3.9)
Total Benefit,
Total Cost
($) B C
424.80
1100
500 1 2 3
3.4 4 5 6
Hours (H)
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45. Sample Problem 4
Let’s say you run a bakery. If you are month-to-month on your lease, is your next month’s rent a sunk cost? What if you are currently in the middle of a one-year lease?
It will cost you $5,000 to purchase a new oven. Is this a sunk cost?