Download - Cost Analysis
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Ch 5 COST
The theory of cost is important to a manager because it provides the foundation for two important production decisions:
1) whether or not to shut down2) how much to produce
Also, this chapter supports the theory of supply.
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“Buy low and sell high”
Increasing competitive pressures,changing technology, and customer demand have made it harder for firms to achieve high profit margins by raising their prices
– cost management, restructuring, downsizing etc.
– outsourcing and relocation of manufacturing facilities to low-wage countries
– mergers, consolidations, and then reduced headcount
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Choosing Output:
COSTS REVENUES
Technology & costs of
hiring factors of production
TC curves(short & long run)
AC(short &long run)
MC
Demandcurve
AR
MR
CHECK: produce in SR?close down in LR?
Choose output level
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Which Costs Matter?
• Opportunity vs. accounting cost• Opportunity cost is the cost associated with
opportunities that are foregone by not putting resources in their highest valued use
• Accounting cost considers only explicit cost, the out of pocket cost for such items as wages, salaries, materials, and property rentals
• Sunk vs. incremental cost• A sunk cost is an expenditure that has been
made and cannot be recovered--they should not influence a firm’s decisions
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Costs in the Short Run
• Total output is a function of variable inputs and fixed inputs
• Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs)
• Fixed costs– costs that do not vary with output levels
• Variable costs– costs that do vary with output levels
• TC = FC + VC
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Costs in the Short Run continued
Q
TC
Q
VC MC
Marginal Cost (MC) is the cost of expanding output by one unit. Since fixed cost have no impact on marginal cost, it can be written as:
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Costs in the Short Run continued
• Average Total Cost (ATC) is the cost per unit of output, or average fixed cost (AFC) plus average variable cost (AVC)
• This can be written:
Q
TC
Q
TVC
Q
TFC ATC
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The Determinants of Short-Run Cost
• The relationship between the production function and cost can be detected by looking at the relationship between either increasing returns (to a factor) and cost, or decreasing returns (i.e. when the law of diminishing returns takes effect) and cost:
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The relationship between the production function and cost
– Increasing returns and cost
• With increasing returns, output is increasing relative to input and variable cost and total cost will fall relative to output
– Decreasing returns and cost
• With decreasing returns, output is decreasing relative to input and variable cost and total cost will rise relative to output
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SR Cost Curves for a Firm• Unit Costs
– AFC falls continuously and – MC equals AVC and ATC at their minimum – Minimum AVC occurs at a lower output
than minimum ATC due to FC
Output
P
25
50
75
100
0 1 2 3 4 5 6 7 8 9 10 11
AFC
AVCATC
MC
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The Firm’s Short-Run Output Decision
• Firm sets output at Q1, where SRMC=MR• subject to checking the average condition:
– if price is above SRATC1 firm produces Q1 at a profit– if price is between SRATC1 and SRAVC1 firm
produces Q1 at a loss– if price is below SRAVC1, firm produces zero output
SRAVC1
£
Output
MR
SRAVC
SRMC
Q1
SRATCSRATC1
SMC = MR
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The firm’s long-run output decision
• The decision:– If the price is at or above LAC1, the firm
produces Q1.– If the price is below LAC1 the firm goes out
of business
AC1
£
Output(goods per week)
MR
LAC
LMC
Q1
LMC = MR
LMC always passes through the minimum point of LAC.
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The firm’s output decisions – a summary
Marginal condition Check whether to produce
Short-run decision Long-run decision
Choose the output level at which MR = SRMC Choose the output level at which MR = LRMC
Produce this output unless price lower than SRAVC. If it is, produce zero. Produce this output unless price is lower than LRAC. If it is, produce zero.
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Long-Run Cost Function
The long-run total cost curve describes the minimum cost of producing each output level when the firm is free to vary all input levels.
One of the first decisions to be made by the owner/manager of a firm is to decide the scale of operation (size of the firm).
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Long-Run Average CostThe LAC is a graph that shows the different scales on which a firm can choose to operate in the long run. Long-run average cost (LRAC) is often assumed to be U-shaped:
LRAC
Ave
rag
e co
st
Output
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Economies of ScaleHowever, economies of scale occur when long-run average costs decline as output rises:
LRAC
Ave
rag
e co
st
Output
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Economies of Scale continued
• A cost related concept1
• When a company is experiencing economies of scale its LRAC declines as output is increasing
• Diseconomies of scale:
LRAC increasing as output increasing
1 Compare with returns to scale which is a production concept!
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Long-Run Cost Function: Displaying
Economies/Diseconomies of Scale
LRAC
$
Economies of scale Diseconomies of scaleQ
MC increasing
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Economies of scale can be classified as
a) External economies of scaleadvantages that a firm gains from the expansion and size of the industry as whole industrial clusters
b) Internal economies of scaleadvantages that a firm gains from increasing the scale of its own operation
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Why can a firm become more efficient as the scale of
production rises?• Technical economies
• Marketing economies
• Financial economies
• Managerial economies
• Risk-bearing economies
• Administrative economies
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Why can a firm become more inefficient as the scale of
production rises?
Diseconomies of scale:• Large enough operation may
increase input prices• Disproportionate rise in
transportation costs• Red tape• Management coordination problems• Labor specialization and repetitive
work too little stimulation, productivity suffers
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• Primary reason for long-run scale economies (diseconomies) is the underlying pattern of returns to scale in the firm’s long-run production function
– Increasing returns to scale lead to economies of scale and decreasing returns to scale leads to diseconomies of scale
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Using LRAC as Decision-Making Tool
• Which plant size to choose?
• Both production cost information and accurate demand forecasts are necessary
• The cost structure of the industry will determine the competitive structure of the industry
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The long-run average cost curve LRAC: an envelope of short-run
cost curves
Output
Ave
rag
e co
st
SRATC1
Each plant sizeis designed fora given outputlevel
SRATC2
SRATC3
SRATC4
So there is a sequence of SRATCcurves, eachcorresponding toa different optimal output level.
LRAC
In the long-run, plant size itself is variable, and the long-run average cost curve LRAC is found to be the ‘envelope’ of the SRATCs
TU-91.113 Managerial Economics / Hannele Wallenius
The existence of economies of scale means that in the long run, as the
firms increases its scale of operation, the LRAC of production
falls.
SRMC
SRMC
SRMC
SRAC
SRAC
SRAC
Units of output
Cos
ts p
er u
nit (
$)
LRAC
Each individual scale of the firm will still be subject to diminishing returns and have a U-shaped SRAC curve.
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Minimum Efficient Scale• A firm can not expect always to
achieve economies of scale when it expands: at some point it is likely that the further increase in size does not produce any reduction in the average cost per unit
– minimum efficient scale (MES)
LRAC
MES Scale of firm
$
TU-91.113 Managerial Economics / Hannele Wallenius
Increasing LRAC: Diseconomies of Scale
SRMCSRAC
SRMCSRAC
SRMCSRAC
Units of output
Cos
ts p
er u
nit (
$)
LRAC
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Constant Returns to Scale
• Constant RTS refers to when an increase in scale of operation leads to no change in average costs per unit produced LRAC is horizontal
– when the firm doubles the use of inputs, it will double output as well as its costs
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Production with Two (or more) Outputs--Economies
of Scope
• Economies of scope exist when the unit cost of producing two or more products/services jointly is lower than producing them separately
– producing related products, products that are complementary
• the average total cost of production decreases as a result of increasing the number of different goods produced
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Why Advantages May Exist
For example:
1) Both products use same inputs (capital and labor)
2) The firms share management resources
3) Both products use the same labor skills and type of machinery
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Economies of Scope continued
• Examples:– Chicken farm--poultry and eggs– Automobile company--cars and
trucks– University--teaching and research
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Economies of Scope continued
• Another example is a company like Proctor & Gamble, which produces hundreds of products from soap to toothpaste. They can afford to hire expensive graphic designers and marketing experts who can use their skills across the product lines. Because the costs are spread out, this lowers the average total cost of production for each product
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P&G acquires The Gillette
Company (29.1.2005) • Both companies have complementary
expertise in health and personal care• The companies also share
complementary technology platforms in skin care and particularly in oral care
• Same distribution channels (Wal-Mart etc.)
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Degree of Economies of Scope
• The degree of economies of scope measures the savings in cost:
– C(Q1) is the cost of producing product Q1
– C(Q2) is the cost of producing product Q2
– C(Q1Q2) is the joint cost of producing both products
– If SC > 0 -- Economies of scope– If SC < 0 -- Diseconomies of scope
)QC(Q
)QC(Q)C(Q)C(Q SC
21,
21,21
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Dynamic Changes in Costs--
The Learning Curve
• The learning curve measures the impact of worker’s experience on the costs of production
• It describes the relationship between a firm’s cumulative output and amount of inputs needed to produce a unit of output
• The learning curve implies:
1) The labor requirement per unit falls
2) Costs will be high at first and then will fall with learning
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The Learning Curve
Cumulative number of machine lots produced
Hours of laborper machine lot
10 20 30 40 500
2
4
6
8
10
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The Learning Curve
Cumulative number of machine lots produced
Hours of laborper machine lot
10 20 30 40 500
2
4
6
8
10
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The Learning Curve
Cumulative # of machine lots produced
Hours of laborper machine lot
10 20 30 40 500
2
4
6
8
10
• The horizontal axis measures the cumulative number of hours of machine lots the firm has produced
• The vertical axis measures the number of hours of labor needed to produce each lot
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Economies of Scale Versus Learning continued
Output
Cost($ per unitof output)
AC1
AB
Economies of Scale