1. Cost Analysis and Estimation
Chapter 8

2. Chapter 8 OVERVIEW Economic and Accounting Costs
Role of Time in Cost Analysis
Short-run Cost Curves
Long-run Cost Curves
Minimum Efficient Scale
Firm Size and Plant Size
Learning Curves
Economies of Scope
Cost-volume-profit Analysis

3. Economic and Accounting Costs
Historical Versus Current Costs
Historical cost is the actual cash outlay.
Current cost is the present cost of previously acquired items.
Opportunity Costs
Foregone value associated with current rather than next-best use of an asset.
Replacement cost is expense of replacing productive capacity using current technology.
Explicit and Implicit Costs
Explicit costs are cash expenses.
Implicit costs are noncash expenses.

4. Economic and Accounting Costs
Explicit costs
- require an outlay of money,
payment to non owners for resources:
paying wages
paying rent
paying interest
Implicit costs
- do not require a cash outlay,
opportunity cost:
the owner’s time
lost wages
the owner’s property
forgone rental income
the owner’s money
forgone interest income

5. Economic and Accounting Costs
Shoe Co.
Revenue
$300,000
Worker Wages
$100,000
Explicit
Rent Expense
$50,000
Explicit
Leather Cost
$100,000
Explicit
Explicit Cost
$250,000
Accounting Profit
$50,000
Superintendent
$100,000
Principal
$50,000
Teacher
$30,000
Implicit
- $50,000
Economic Loss $0
Economic Profit
Economic Profit
$20,000
Accounting profit - total revenue minus total explicit costs
Economic profit - total revenue minus total costs (includes explicit and implicit costs)
Accounting profit ignores implicit costs and it’s always higher than economic profit.
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6. Economic and Accounting Costs
Short Run
- a time period when at least one input is fixed
Cost for a fixed input is termed Fixed Cost
Factory
Special equipment
Land
Long Run
- A time period when all inputs are variable
firms can build more factories, or sell existing ones
In the long run, ATC at any Q is cost per unit using the most efficient mix of inputs for that Q (the factory size with the lowest ATC)

7. Role of Time in Cost Analysis
Incremental Cost
Incremental cost is the change in cost tied to a managerial decision.
Incremental cost can involve multiple units of output.
Marginal cost involves a single unit of output.
Sunk Cost
Irreversible expenses incurred previously.
Sunk costs are irrelevant to present decisions.

8. Short-run Cost Curves Short-run Cost Categories
Total Cost = Fixed Cost + Variable Cost
For averages, ATC = AFC + AVC
Marginal Cost, MC = ∂TC/∂Q
Short-run Cost Relations
Short-run cost curves show minimum cost in a given production environment.

9. Short-run Cost Curves - Fixed Cost (TFC) 𝑀𝐶= ∆𝑇𝐶 ∆𝑄
costs that don’t vary as output changes
AV𝐶= 𝑇𝑉𝐶 𝑄
AT𝐶= 𝑇𝐶 𝑄
AF𝐶= 𝑇𝐹𝐶 𝑄
- Variable Cost (TVC)
costs that do vary as output changes
- Total Cost (TC)
TC = TFC + TVC
- Marginal Cost (MC)
the cost of producing one more output (Q) Q 1 2 3 4 5 6 7 8 9
TFC
TVC TC MC
AFC --
$10.00
$5.00
$3.33
$2.50
$2.00
$1.67
$1.43
$1.25
$1.11
AVC --
$4.00
$3.50
$3.67
$4.50
$5.60
$7.83
$10.57
$14.00
$18.00
ATC --
$14.00
$8.50
$7.00
$7.60
$9.50
$12.00
$15.25
$19.11
$10 $0
$10
$14
$17
$21
$28
$38
$57
$84
$122
$172
$10 $4 $7
$11
$18
$28
$47
$74
$112
$162 $4 $3 $4 $7
$10
$19
$27
$38
$50
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10. Short-run Cost Curves Calculation Equations at Q = 6
𝑀𝐶= ∆𝑇𝐶 ∆𝑄 = 𝑇𝐶 1 − 𝑇𝐶 0 𝑄 1 − 𝑄 0
$57−$38 6−5 = $19 1 =$19
𝐴𝐹𝐶= 𝑇𝐹𝐶 𝑄
$10 6 =$1.67
𝐴𝑉𝐶= 𝑇𝑉𝐶 𝑄
$47 6 =$7.83
𝐴𝑇𝐶= 𝑇𝐶 𝑄
$57 6 =$9.50
𝐴𝑇𝐶=𝐴𝐹𝐶+𝐴𝑉𝐶
$9.50=$
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11. Short-run Cost Curves $ MC $19.00 ATC AVC $9.50 $1.67 AFC $7.83 Q 1 24 5 6 7 8 9
The MC curve intersects the ATC curve at minimum average total cost.
when MC < ATC, ATC falls as Q rises
when MC > ATC, ATC rises as Q rises
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12. Short-run Cost Curves 𝑀𝐶= ∆𝑇𝐶 ∆𝑄 = 𝑤𝑎𝑔𝑒 𝑀𝑃 𝑙 = $75 25 =$3MC 10 25 50 65 75 80 $ Q
Minimum Marginal Cost corresponds to maximum Marginal Product
Suppose an accountant earns $75 / hour and her marginal productivity is:
$7.50
$3.00 MP
wage MC
Third hour 25
Fourth hour 15
Fifth hour 10
Sixth hour 5
$75 $3 $5
$7.5
$15 MP 1 2 3 4 5 6
Labor
Q / Labor 25 10
𝑀𝐶= ∆𝑇𝐶 ∆𝑄 = 𝑤𝑎𝑔𝑒 𝑀𝑃 𝑙
= $75 25 =$3
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13. Long-run Cost Curves
Long-run total cost curves show minimum total cost in an ideal environment.
Economies of Scale
Increasing returns to scale imply falling average costs.
Constant returns to scale implies constant average costs.
Decreasing returns to scale implies rising average costs.

14. Long-run Cost Curves $ Output Short Run Average Cost
Long Run Average Cost
Diseconomies to Scale
Economies to Scale
Constant Returns to Scale
Output

15. Cost Elasticities Econ. of Scale
Cost elasticity measures the percentage change in cost following a one percent change in output.
𝐸 𝑐 = %∆𝑇𝐶 %∆𝑄 = 𝜕𝑇𝐶 𝜕𝑄 ∙ 𝑄 𝑇𝐶
Cost elasticity measures returns to scale.
EC < 1 means increasing returns (falling AC).
EC = 1 means constant returns (constant AC).
EC > 1 means decreasing returns (rising AC).

16. Long-run Cost Curves $ Output Long Run Average Cost Min LRAC
Least Cost Plant
Output

17. Firm Size and Plant Size
Multi-plant Economies and Diseconomies of Scale
Multi-plant economies are cost advantages from operating several plants.
Multi-plant diseconomies are coordination costs from operating several plants.
Plant Size and Flexibility
Big plants can offer lower AC.
Smaller plants can make it easier to add and /or subtract capacity.

18. Firm Size and Plant Size
Constant costs
Declining costs
U-shaped costs $ $ $
𝑄 ∗
𝑄 𝐹
𝑄 ∗
𝑄 𝐹
𝑄 ∗
𝑄 𝐹

19. Firm Size and Plant Size
𝑃=$940−$0.02𝑄
𝑇𝑅= $940−$0.02𝑄 𝑄=$940𝑄−$0.02 𝑄 2
𝑀𝑅= 𝑑𝑇𝑅 𝑑𝑄 =$940−$0.04𝑄
𝑇𝐶=$250,000+$40𝑄+$0.01 𝑄 2
𝑀𝐶= 𝑑𝑇𝐶 𝑑𝑄 =$40+$0.02𝑄

20. Firm Size and Plant Size
𝑀𝑅=𝑀𝐶
$940−$0.04𝑄=$40+$0.02𝑄
$0.06𝑄=$900
𝑄=15,000
𝑃=$940−$0.02𝑄=$940−$ ,000 =$640
𝜋=$940𝑄−$0.02 𝑄 2 −($250,000+$40𝑄+$0.01 𝑄 2 )
𝜋=−$0.03 𝑄 2 +$900𝑄−$250,000
𝜋=−$ , $900(15,000)−$250,000
𝜋=$6,500,000

21. Firm Size and Plant Size
𝐴𝐶= 𝑇𝐶 𝑄 = $250,000+$40𝑄+$0.01 𝑄 2 𝑄
𝐴𝐶=$250,000 𝑄 −1 +$40+$0.01𝑄
𝑀𝐶=𝐴𝐶
$40+$0.02𝑄=$250,000 𝑄 −1 +$40+$0.01𝑄
$250,000 𝑄 −1 =$0.01𝑄
𝑄 2 = $250,
𝑄= $25,000,000 =5,000

22. Firm Size and Plant Size
Average cost is minimized at an output level of 5,000. This output level is the minimum efficient plant scale (MES). Because the average cost-minimizing output level of 5,000 is far less than the single plant profit maximizing activity level of 15,000 units, the profit maximizing level of total output occurs at a point of rising average costs. Thus a multi-plant alternative will reduce cost and increase profits.
𝑀𝐶=$40+$0.02𝑄=$40+$ ,000 =$640
𝑀𝐶=$40+$0.02𝑄=$40+$0.02 5,000 =$140
𝑀𝑅=$140=𝑀𝐶
$940−$0.04𝑄=$140
$0.04𝑄=$800
𝑄=20,000

23. Firm Size and Plant Size
𝑂𝑝𝑖𝑚𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑙𝑎𝑛𝑡𝑠= 𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑀𝑢𝑙𝑡𝑖𝑝𝑙𝑎𝑛𝑡 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝐿𝑒𝑣𝑒𝑙 𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑃𝑒𝑟 𝑃𝑙𝑎𝑛𝑡
𝑂𝑝𝑖𝑚𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑃𝑙𝑎𝑛𝑡𝑠= 20,000 5,000 =4
𝑃=$940−$0.02𝑄=$940−$ ,000 =$540
𝜋=𝑇𝑅−𝑇𝐶
𝜋=𝑃∙𝑄−4∙𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 𝑝𝑒𝑟 𝑃𝑙𝑎𝑛𝑡
𝜋=$540 20,000 −4($250,000+$40 5,000 +$ )
𝜋=$8,000,000

24. Economies of Scope Economies of Scope Concept
Scope economies are cost advantages that stem from producing multiple outputs.
Big scope economies explain the popularity of multi-product firms.
Without scope economies, firms specialize.
Exploiting Scope Economies
Scope economics often shape competitive strategy for new products.