Cost Theory & Analysis
Lecture 5
Econ 340H
Managerial Economics
Christopher Michael
Trent University
Department of Economics
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Topics
• Meaning and Measurement of
Cost
• Short-Run Cost Functions
• Long-Run Cost Functions
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Overview
The Importance of Cost Analysis
» Managers seek to produce the highest quality
products at the lowest possible cost.
» Firms that are satisfied with the status quo find
that competitors arise that produce at lower
costs and drive them out of business.
» The advantages once assigned to being a large
firm (economies of scale and scope) have NOT
provided the advantages of flexibility and agility
found in some smaller companies.
» Cost analysis is helpful in the task of finding
lower cost methods to produce goods and
services.
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Meaning and
Measurement of Costs
There a number of cost concepts in business.
• Opportunity Cost – value of next
best alternative use.
• Explicit vs. Implicit Cost – actual
prices paid vs. opportunity cost of
owner-supplied resources.
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Accounting vs.
Economic Cost
• Accounting costs involve explicit historical costs.
They attempt to use the same rules for different firms,
so we can compare firm performance.
• Economic costs are based on making decisions.
These costs can be both implicit and explicit.
» A chief example is that economic costs include the
opportunity costs of owner-supplied resources such as
time and money, which are implicit costs.
» Economic Profit =
Total Revenues - Explicit Costs - Implicit Costs
» Both explicit and implicit costs make economic profit
lower than accounting profit
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• Depreciation Cost Measurement. Accounting
depreciation (e.g., straight-line depreciation) tends to
have little relationship to the actual loss of value
» To an economist, the actual loss of value is the true
cost of using machinery.
• Inventory Valuation. Accounting valuation depends on
its acquisition cost
» Economists view the cost of inventory as the cost of
replacement.
• Unutilized Facilities. Empty space may appear to have
"no cost”
» Economists view its alternative use (e.g., rental value)
as its opportunity cost.
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• Sunk Costs -- already paid for, or
•
•
there already exists a contractual obligation to
pay
Incremental Cost - - extra cost of
implementing a decision =  TC of a
decision
Marginal Cost -- cost of last unit
produced =  TC/Q
SHORT-RUN COST FUNCTIONS
1.
TC = FC + VC fixed & variable costs
2.
ATC = AFC + AVC = FC/Q + VC/Q
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Short-Run Cost Graphs
MC
ATC
3.
1.
AFC
Q
2.
AVC
AFC
Q
MC intersects lowest point
AVC
of AVC and lowest point of
ATC.
When MC < AVC, AVC declines
Q When MC > AVC, AVC rises
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Relationships Among Cost & Production Functions
When Factor Markets Are Perfectly Competitive
• AP & AVC are inversely
related. (ex: one input)
• AVC = WL /Q = W/ (Q/L) =
W/ APL
Q
prod. functions
AP
» As APL rises, AVC falls
• MP and MC are inversely
related
• MC = dTC/dQ = W dL/dQ =
W / (dQ/dL) = W / MPL
» As MPL declines, MC rises
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MPL
cost
AVC
L
MC
cost functions
Q
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Problem
Let there be a cubic VC function:
VC = 0.5 Q3 - 10 Q2 + 150 Q
1. find AVC from the VC function above.
2. find minimum variable cost output from AVC.
3. and find MC from the VC function
A1: AVC = 0.5 Q 2 -10 Q + 150 (divide by Q)
A2: Minimum AVC is where dAVC/dQ = 0
dAVC / dQ = Q - 10 = 0
Q = 10, so AVC = 100 @ Q = 10
A3: MC= dVC/dQ= 1.5 Q2 - 20 Q + 150
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Long-Run Cost Functions
• All inputs are variable in the
long run
• LAC is long-run average cost
SMC2
» ENVELOPE of SAC curves
SAC2 LMC
• LMC is FLATTER than
SMC curves
• The optimal plant size for a
given output Q2 is plant size
2. (A SR concept.)
• However, the optimal plant
size occurs at Q3, which is the
lowest cost point overall. (A
LR concept.)
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LAC
Q2
Q3
Q
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Long-Run Cost Function (LAC)
Envelope of SAC curves
Avg Cost
SAC-small capital
SAC-med. capital
SAC-big capital
LAC--Envelope
of SRAC curves
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Economists think that the
LAC is U-shaped
• Downward section due to:
» Product-level economies which include specialization
and learning curve effects.
» Plant-level economies, such as economies in
overhead, required reserves, investment, or interactions
among products (economies of scope).
» Firm-level economies which are economies in
distribution and transportation of a geographically
dispersed firm, or economies in marketing, sales
promotion, or R&D of multi-product firms.
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LAC
• Flat section of the LAC
CRS region
DRS
» Displaces constant returns to scale
MES
Max ES
» The minimum efficient scale (MES) is the smallest scale at which
minimum per unit costs are attained.
• Upward rising section of LAC is due to:
» diseconomies of scale. These include transportation costs,
imperfections in the labour market, and problems of coordination and
control by management.
» The maximum efficient scale (Max ES) is the largest scale before
which unit costs begin to rise.
» Modern business management offers techniques to avoid
diseconomies of scale through profit centers, transfer pricing, and
tying incentives to performance.
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Problem
Q Suppose we have the following info:
TC = 200 + 5Q - 0.4Q2 + 0.001Q3
MC =
5 - 0.8Q + 0.003Q2
1.
2.
3.
4.
FIND fixed cost
FIND AVC function
FIND AVC at Q = 10
If FC rises $500, what happens to
the average variable cost function?
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TC = 200 + 5Q - 0.4Q2 + 0.001Q3
MC =
5 - 0.8Q + 0.003Q2
1. FIND fixed cost
Answer: FC = 200, the intercept in the TC curve.
2. FIND AVC function
Answer: VC = 5Q - 0.4Q2 + 0.001Q3
So AVC = 5 - 0.4Q + 0.001Q2 (Divide VC by Q)
3. FIND AVC at Q = 10.
Answer: Substitute Q = 10 into the AV C function.
AVC = 5 - 0.4(10) + 0.001(102) = 5 – 4 + .1 = 1.1
4. If FC rises $500, what happens to the average variable
cost function?
Answer: No change, since AVC does NOT include
fixed cost.
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