chap003-balacing costs and benefits
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microeconomicsTRANSCRIPT
Chapter 3
Balancing Costs and Benefits
McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Main Topics
Maximizing benefits less costsThinking on the marginSunk costs and decision-making
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Maximizing Net Benefit
Net benefit: total benefit minus total costTotal cost must include opportunity costOpportunity 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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Car Repair Example:Benefit Schedule
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
($)
0 0
1 615
2 1150
3 1600
4 1975
5 2270
6 2485
3-4
Car Repair Example:Cost Schedule
Table 3.2: Costs of Repairing Your Car
Repair Time
(Hours)
Cost of Mechanic and Parts
($)
Lost Wages from Pizza Delivery Job
($)
Total Cost
($)
0 0 0 0
1 140 10 150
2 355 25 380
3 645 45 690
4 1005 75 1080
5 1440 110 1550
6 1950 150 2100
3-5
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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Table 3.3: Total Benefit and Total Cost of Repairing Your Car
Repair Time (Hours)
Total Benefit ($)
Total Cost ($)
Net Benefit ($)
0 0 0
1 615 150
2 1150 380
3 1600 690
4 1975 1080
5 2270 1550
6 2485 2100
Car Repair Example:The Right Decision
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Table 3.3: Total Benefit and Total Cost of Repairing Your Car
Repair Time (Hours)
Total Benefit ($)
Total Cost ($)
Net Benefit ($)
0 0 0 0
1 615 150 465
2 1150 380 770
3 1600 690 910
4 1975 1080 895
5 2270 1550 720
6 2485 2100 385
Car Repair Example:The Right Decision
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Table 3.3: Total Benefit and Total Cost of Repairing Your Car
Repair Time (Hours)
Total Benefit ($)
Total Cost ($)
Net Benefit ($)
0 0 0 0
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
Car Repair Example:The Right Decision
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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
1 2 3 4 5 6
400
800
1200
1600
2000
2400
710
910
Best Choice
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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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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-40H2
Total Benefit ($)
Hours (H)
(a): Total Benefit
0 1 2 3 4 5 6
614
1602
2270
B
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Car Repair Example:Finely Divisible Cost
Vertical axis measures total cost in dollars
Includes opportunity cost
C(H)=110H+40H2
0 1 2 3 4 5 6
150
690
1550
Hours (H)
(b): Total Cost
Total Cost ($)
C
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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 BenefitTotal Cost($)
(c): Total Benefit versus Total Cost
0 1 2 3 4 5 6
Hours (H)
3.4
B
C924.80
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Net Benefit Curve(Figure 3.3)
Can also graph the net benefit curve
Vertical axis shows B-C, net benefit
Best choice is the number of hours that corresponds to the highest point on the curve, 3.4 hours
0 1 2 3 4 5 6
924.80
Hours (H) 3.4
Net Benefit($)
B – C
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Thinking on the Margin
Thinking like an economistAnother approach to maximizing net
benefitsCapture the way that benefits and costs
change as the level of activity changes just a little bitFor any action choice X, the marginal units
are the last X units, where X is the smallest amount you can add or subtract
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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
X
XXCXC
X
CMC
)()(
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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 hour 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
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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:
H
HHCHC
H
CMC
)()(
3103806901
)13()3(
CCMC
3-19
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)
0 0 -
1 150 150
2 380 230
3 690 310
4 1080 390
5 1550 470
6 2100 550
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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
X
XXBXB
X
BMC
)()(
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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
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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:
H
HHBHB
H
BMC
)()(
450115016001
)13()3(
BBMC
3-23
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)
0 0 -
1 615 615
2 1150 535
3 1600 450
4 1975 375
5 2270 295
6 2485 215
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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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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 - -
1 615 > 150
2 535 > 230
3 450 > 310
4 375 < 390
5 295 < 470
6 215 < 550
Best Choice
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Marginal Analysis withFinely 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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Marginal Benefit
Using Calculus
This is the slope of the Total Benefit Curve B(H).
dHHdB
HMB
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 is B' /H'
)()( HHBHBB
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Slope = MB
'HH
)'HH(B
'H
''HH H
''B
''H
'H/'B
)''HH(B
)H(B
'B
Slope = MB =
Slope= MB = ''H/''B
Hours (H)
Total Benefit ($)
Relationship between Total Benefit and Marginal Benefit (Figure 3.4)
F
E
D
3-30
Relationship between Total Benefit and Marginal Benefit
Tangents to the total benefit function at three different numbers of hours (H = 1, H = 3, H = 5)
Slope of each tangent equals the marginal benefit at each number of hours
Figure (b) shows the MB curve: note how the MB varies with the number of hours
Marginal benefit curve is described by the function MB(H)= 654-80H
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Relationship between Total Benefit and Marginal Benefit (Figure 3.5)
Total Benefit ($)
Hours (H)
0 1 2 3 4 5 6
614
1602
2270
B
(a): Total Benefit
Slope = MB = 574
Slope = MB = 414
Slope = MB = 254
0 1 2 3 4 5 6
254
414
574
Marginal Benefit ($/hour)
MB
(b): Marginal Benefit
654
Hours (H)
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Relationship between Total Cost and Marginal Cost
Parallels relationship between total benefit curve and marginal benefit
When actions are finely divisible, the marginal cost when choosing action X is equal to the slope of the total cost curve at X
Using Calculus
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dHHdC
HMC
Relationship between Total Cost and Marginal Cost
Tangents to the total cost curve at three different numbers of hours (H = 1, H = 3, H = 5)
Slope of each tangent equals the marginal cost at each number of hours
Figure (b) shows the MC curve: note how the MC varies with the number of hours
Marginal cost curve is described by the function MC(H)= 110+80H
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Relationship between Total Cost and Marginal Cost (Figure 3.6)
110
190
350
510
150
690
1550
Total Cost ($)
(a): Total Cost (b): Marginal Cost
1 2 3 4 5 6
Hours (H)
0
C
Slope = MC = 190
Slope = MC = 350
Slope = MC = 510
0 1 2 3 4 5 6
Marginal Cost ($/hour)
Hours (H)
MC
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Using Calculus to find Best Choice
Net Benefit = Total Benefit – Total CostMaximize Net Benefit (NB(H)).Using Calculus;
HMCHMBdHHdC
dHHdB
dHHdC
dHHdB
dHHdNB
0
Using Calculus to find Best Choice
So, at the maximum; MB(H) = MC(H). MB(H)= 654-80HMC(H)= 110+80HSolving, we obtain H* = 3.4.
Marginal Benefit Equals Marginal Cost at a Best Choice
At the best choice of 3.4 hours, the No Marginal Improvement Principle holds so MB = MC
At any number of hours below 3.4, MB > MC, so a small increase in repair time will improve the net benefit
At any number of hours above 3.4, MC > MB, so that a small decrease in repair time will improve net benefit
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Marginal Benefit Equals Marginal Cost at a Best Choice (Figure 3.7)
Marginal Benefit, Marginal Cost ($/hour)
Hours (H)
MC
MB
3.4
0 1 2 3 4 5 6
110
382
654
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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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Slope of Total Benefit and Total Cost Curves (Figure 3.8)
0 1 2 3 4 5 6
Hours (H)
Total BenefitTotal Cost($) B
C924.80
3.4
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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 costsSo sunk costs do not affect the best
choice
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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 $1100.
In both cases, the best choice is H = 3.4: the level of sunk costs has no effect on the best choice
Notice that the slopes of the two total cost curves, and thus the marginal costs, are the same
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Best Choice with a Sunk Cost (Figure 3.9)
500
Hours (H) 3.4
0 1 2 3 4 5 6
C
C´
B
-175.20
424.80
Total Benefit,Total Cost($)
1100
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