Download - Lecture 9 costs
Chapter 7
The Cost of Production
©2005 Pearson Education, Inc. Chapter 7 2
Expansion Path
Expansion Path
The expansion path illustratesthe least-cost combinations oflabor and capital that can be used to produce each level of
output in the long-run.
Capitalper
year
25
50
75
100
150
50Labor per year
100 150 300200
A
$2000
200 Units
B
$3000
300 Units
C
©2005 Pearson Education, Inc. Chapter 7 3
Optimal Inputs
The minimum cost combination can then be written as:
Increase in output for every dollar spent on an input is same for all inputs.
rwKL MPMP
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Expansion Path
It shows optimal input combinations to minimize cost to produce different levels of output
It shows the minimum cost to produce different levels of output
It shows the maximum amount of output that can be produced for different levels of expenditure.
©2005 Pearson Education, Inc. Chapter 7 5
A Firm’s Long Run Total Cost Curve
Long Run Total Cost
Output, Units/yr100 300200
Cost/ Year
1000
2000
3000
D
E
F
©2005 Pearson Education, Inc.
©2005 Pearson Education, Inc.
LONG RUN AND SHORT RUN COSTS
Chapter 7 7
©2005 Pearson Education, Inc. Chapter 7 8
Long Run Versus Short Run Cost Curves
In the short run, some costs are fixedIn the long run, firm can change anything
including plant sizeCan produce at a lower average cost in long
run than in short runCapital and labor are both flexible
We can show this by holding capital fixed in the short run and flexible in long run
©2005 Pearson Education, Inc. Chapter 7 9
Capital is fixed at K1.To produce q1, min cost at K1,L1.If increase output to Q2, min cost
is K1 and L3 in short run.
The Inflexibility of Short Run Production
Long-RunExpansion Path
Labor per year
Capitalper
year
L2
Q2
K2
D
C
F
E
Q1
A
BL1
K1
L3
PShort-RunExpansion Path
In LR, can change capital and min costs falls to K2 and L2.
©2005 Pearson Education, Inc. Chapter 7 10
Production technology measures the relationship between input and output
Production technology, together with prices of factor inputs, determine the firm’s cost of production
©2005 Pearson Education, Inc. Chapter 7 11
Introduction
The optimal, cost minimizing, level of inputs can be determined
A firm’s costs depend on the rate of output
The characteristics of the firm’s production technology affect costs in the long run and short run
©2005 Pearson Education, Inc. Chapter 7 12
Measuring Cost:Which Costs Matter?
For a firm to minimize costs, we must clarify what is meant by costs and how to measure them
It is clear that if a firm has to rent equipment or buildings, the rent they pay is a cost
What if a firm owns its own equipment or building?
How are costs calculated here?
©2005 Pearson Education, Inc. Chapter 7 13
Measuring Cost:Which Costs Matter?
Accounting CostActual expenses plus depreciation charges
for capital equipment
Economic CostCost to a firm of utilizing economic resources
in production, including opportunity cost
©2005 Pearson Education, Inc. Chapter 7 14
Opportunity Cost
An ExampleA firm owns its own building and pays no rent
for office spaceDoes this mean the cost of office space is
zero?The building could have been rented insteadForegone rent is the opportunity cost of
using the building for production and should be included in the economic costs of doing business
©2005 Pearson Education, Inc. Chapter 7 15
Opportunity Cost
A person starting their own business must take into account the opportunity cost of their timeCould have worked elsewhere making a
competitive salary
©2005 Pearson Education, Inc. Chapter 7 16
Measuring Cost:Which Costs Matter?
Some costs vary with output, while some remain the same no matter the amount of output
Total cost can be divided into:
1. Fixed Cost Does not vary with the level of output
2. Variable Cost Cost that varies as output varies
©2005 Pearson Education, Inc. Chapter 7 17
Fixed and Variable Costs
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), or…
VC FC TC
©2005 Pearson Education, Inc. Chapter 7 18
Fixed and Variable Costs
Which costs are variable and which are fixed depends on the time horizon
Short time horizon – most costs are fixedLong time horizon – many costs become
variable
©2005 Pearson Education, Inc. Chapter 7 19
Measuring Cost:Which Costs Matter?
Personal ComputersMost costs are variable Largest component: labor
SoftwareMost costs are sunkInitial cost of developing the software
©2005 Pearson Education, Inc.
Narayan Hridalaya
Providing health care
involves high costs and low accessibilityWhat does a hospital produce?What does a hospital use to produce this?Narayan Hridalaya founded on the principle
of providing low cost and accessible health care to all
20
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Daily Bread
Multiple outlets in and
around Bangalore
What are the outputs they produce?
What are the inputs?
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AVERAGE AND MARGINAL COST
Chapter 7 22
©2005 Pearson Education, Inc. Chapter 7 23
Marginal and Average Cost
In completing a discussion of costs, must also distinguish between
Average CostMarginal Cost
©2005 Pearson Education, Inc. Chapter 7 24
Measuring Costs
Marginal Cost (MC):The cost of expanding output by one unitFixed costs have no impact on marginal cost,
so it can be written as:
Δq
ΔTC
Δq
ΔVC MC
©2005 Pearson Education, Inc. Chapter 7 25
Measuring Costs
Average Total Cost (ATC)Cost per unit of outputAlso equals average fixed cost (AFC) plus
average variable cost (AVC)
q
TVC
q
TFC
q
TC ATC
AVCAFC q
TC ATC
©2005 Pearson Education, Inc. Chapter 7 26
A Firm’s Short Run Costs
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MC AND AC CURVES
Chapter 7 27
©2005 Pearson Education, Inc. Chapter 7 28
Determinants of Short Run Costs – An Example
Assume the wage rate (w) is fixed relative to the number of workers hired
Variable costs is the per unit cost of extra labor times the amount of extra labor: wL
q
Lw
q
VC MC
©2005 Pearson Education, Inc. Chapter 7 29
Determinants of Short Run Costs – An Example
Remembering that
L MPL
Q
LMP
1
Q
L Qunit 1 afor L
And rearranging
©2005 Pearson Education, Inc. Chapter 7 30
Determinants of Short Run Costs – An Example
We can conclude:
LMP MC
w
…and a low marginal product (MPL) leads to a high marginal cost (MC) and vice versa
©2005 Pearson Education, Inc. Chapter 7 31
Determinants of Short Run Costs
The rate at which these costs increase depends on the amount of input changes with change in output
i.e. Costs depend upon the nature of production process..
©2005 Pearson Education, Inc. Chapter 7 32
Determinants of Short Run Costs
If marginal product of labor decreases significantly as more labor is hired
Costs of production increase rapidly
Greater and greater expenditures must be made to produce more output
©2005 Pearson Education, Inc. Chapter 7 33
Determinants of Short Run Costs
Consequently (from the table):
MC decreases initially with increasing returns 0 through 4 units of output
MC increases with decreasing returns5 through 11 units of output
©2005 Pearson Education, Inc. Chapter 7 34
Cost Curves for a Firm
Output
Cost($ peryear)
100
200
300
400
0 1 2 3 4 5 6 7 8 9 10 11 12 13
VC
Variable costincreases with production and
the rate varies withincreasing and
decreasing returns.
TC
Total costis the vertical
sum of FC and VC.
FC50
Fixed cost does notvary with output
©2005 Pearson Education, Inc. Chapter 7 35
Cost Curves
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Output (units/yr)
Co
st (
$/u
nit
)
MC
ATC
AVC
AFC
©2005 Pearson Education, Inc.
©2005 Pearson Education, Inc. Chapter 7 37
Cost Curves
When MC is below AVC, AVC is fallingWhen MC is above AVC, AVC is risingWhen MC is below ATC, ATC is fallingWhen MC is above ATC, ATC is risingTherefore, MC crosses AVC and ATC at
the minimumsThe Average – Marginal relationship
©2005 Pearson Education, Inc. Chapter 7 38
Cost Curves for a FirmThe line drawn from
the origin to the variable cost curve: Its slope equals AVCThe slope of a point
on VC or TC equals MC
Therefore, MC = AVC at 7 units of output (point A)
1 2 3 4 5 6 7 8 9 10 11 12 13
Output
P
100
200
300
400
FC
VC
TC
A
©2005 Pearson Education, Inc.
LONG RUN COSTS
Chapter 7 39
©2005 Pearson Education, Inc.
©2005 Pearson Education, Inc.
©2005 Pearson Education, Inc. Chapter 7 42
Long Run Cost with Economiesand Diseconomies of Scale
©2005 Pearson Education, Inc. Chapter 7 43
Long Run Cost withConstant Returns to Scale
The optimal plant size will depend on the anticipated outputIf expect to produce q0, then should build
smallest plant: AC = $8If produce more, like q1, AC rises
If expect to produce q2, middle plant is least cost
If expect to produce q3, largest plant is best
©2005 Pearson Education, Inc. Chapter 7 44
Long Run Cost with Economiesand Diseconomies of Scale
©2005 Pearson Education, Inc. Chapter 7 45
Long Run Cost withConstant Returns to Scale
What is the firm’s long run cost curve?Firms can change scale to change output in
the long runThe long run cost curve is the dark blue
portion of the SAC curve which represents the minimum cost for any level of output
Firm will always choose plant that minimizes the average cost of production
©2005 Pearson Education, Inc. Chapter 7 46
Long Run Cost withConstant Returns to Scale
The long-run average cost curve envelops the short-run average cost curves
The LAC curve exhibits economies of scale initially but exhibits diseconomies at higher output levels
©2005 Pearson Education, Inc.
RETURNS TO SCALE
Chapter 7 47
©2005 Pearson Education, Inc.
BIG CITIES
Metropolis twice the size of one, number of gas stations, length of pipelines, infrastructure decreases by 15%
Why?
48
©2005 Pearson Education, Inc.
Narayan Hridalaya
Provide health care at full price
To patients from well to do background
These patients subsidize `poor’ patientsRun at a profit of 7.7%Why is Narayan Hridalaya able to do this?
49
©2005 Pearson Education, Inc.
Narayan Hridalaya
Number of Beds, 2001: 225
Current No. of Beds across India: 30,000
How does number of beds play a role in profits?
50
©2005 Pearson Education, Inc. 51
Returns to Scale
Rate at which output increases as inputs are increased proportionately
Increasing returns to scaleConstant returns to scaleDecreasing returns to scale
©2005 Pearson Education, Inc. 52
Returns to Scale
Increasing returns to scale: output more than doubles when all inputs are doubled
What happens to the isoquants?
©2005 Pearson Education, Inc. 53
Increasing Returns to Scale
10
20
30
The isoquants move closer together
Labor (hours)5 10
Capital(machine
hours)
2
4
A
©2005 Pearson Education, Inc. Chapter 7 54
Long Run Versus Short Run Cost Curves
Increasing Returns to Scale
If input is doubled, output will more than double
To double output input is less than doubled AC decreases at all levels of output
©2005 Pearson Education, Inc. Chapter 7 55
Long Run Costs
As output increases, firm’s AC of producing is likely to decline to a point
1. On a larger scale, workers can better specialize
2. Scale can provide flexibility – managers can organize production more effectively
3. Firm may be able to get inputs at lower cost if can get quantity discounts. Lower prices might lead to different input mix.
©2005 Pearson Education, Inc. 56
Returns to Scale
Constant returns to scale: output doubles when all inputs are doubled
Isoquants are equidistant apart
©2005 Pearson Education, Inc. 57
Returns to Scale
Constant Returns:
Isoquants are
equally spaced
20
30
Labor (hours)155 10
A
10
Capital(machine
hours)
2
4
6
©2005 Pearson Education, Inc. Chapter 7 58
Long Run VersusShort Run Cost Curves
Constant Returns to Scale
If input is doubled, output will double To double output, input has to less than
double AC cost is constant at all levels of output
©2005 Pearson Education, Inc. 59
Returns to Scale
Decreasing returns to scale: output less than doubles when all inputs are doubled
Isoquants become farther apart
©2005 Pearson Education, Inc. Chapter 7 60
Long Run Versus Short Run Cost Curves
Decreasing Returns to Scale
If input is doubled, output will less than double
To double output has to more than double
AC increases at all levels of output
©2005 Pearson Education, Inc. Chapter 7 61
Long Run Costs
At some point, AC will begin to increase1. Factory space and machinery may make it
more difficult for workers to do their jobs efficiently
2. Managing a larger firm may become more complex and inefficient as the number of tasks increase
3. Bulk discounts can no longer be utilized. Limited availability of inputs may cause price to rise.
©2005 Pearson Education, Inc.
©2005 Pearson Education, Inc. Chapter 7 63
Long Run Versus Short Run Cost Curves
In the long run:Firms experience increasing and decreasing
returns to scale and therefore long-run average cost is “U” shaped.
Long-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit
©2005 Pearson Education, Inc. Chapter 7 64
Long Run Versus Short Run Cost Curves
Long-run marginal cost leads long-run average cost:If LMC < LAC, LAC will fallIf LMC > LAC, LAC will riseTherefore, LMC = LAC at the minimum of
LAC
In special case where LAC is constant, LAC and LMC are equal
©2005 Pearson Education, Inc. Chapter 7 65
Long Run Average and Marginal Cost
Output
Cost($ per unitof output
LAC
LMC
A
©2005 Pearson Education, Inc. Chapter 7 66
Economies and Diseconomies of Scale
Economies of ScaleIncrease in output is greater than the
increase in inputsDiseconomies of Scale
Increase in output is less than the increase in inputs
U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels
©2005 Pearson Education, Inc. Chapter 7 67
Long Run Costs
Increasing Returns to ScaleOutput more than doubles when the
quantities of all inputs are doubled
Economies of ScaleDoubling of output requires less than a
doubling of cost
©2005 Pearson Education, Inc.
COST OUTPUT ELASTICITY
Chapter 7 68
©2005 Pearson Education, Inc. Chapter 7 69
Long Run Costs
Economies of scale are measured in terms of cost-output elasticity, EC
EC is the percentage change in the cost of production resulting from a 1-percent increase in output
ACMC
QQCCEC
©2005 Pearson Education, Inc. Chapter 7 70
Long Run Costs
EC is equal to 1, MC = ACCosts increase proportionately with outputNeither economies nor diseconomies of scale
EC < 1 when MC < ACEconomies of scaleBoth MC and AC are declining
EC > 1 when MC > ACDiseconomies of scaleBoth MC and AC are rising
©2005 Pearson Education, Inc.
ECONOMIES OF SCOPE
Chapter 7 71
©2005 Pearson Education, Inc.
Economies of Scope
P&G produces different types of anti aging creams
Would it benefit P&G to
Produce them separately?
Chapter 7 72
©2005 Pearson Education, Inc. Chapter 7 73
Production with Two Outputs – Economies of Scope
Many firms produce more than one product and those products are closely linked
Examples:Chicken farm--poultry and eggsAutomobile company--cars and trucksUniversity--teaching and research
©2005 Pearson Education, Inc. Chapter 7 74
Production with Two Outputs – Economies of Scope
Advantages
1. Both use capital and labor
2. The firms share management resources
3. Both use the same labor skills and types of machinery
©2005 Pearson Education, Inc. Chapter 7 75
Production with Two Outputs – Economies of Scope
The degree of economies of scope (SC) can be measured by percentage of cost saved producing two or more products jointly:
C(q1) is the cost of producing q1
C(q2) is the cost of producing q2
C(q1,q2) is the joint cost of producing both products
)qC(q
)qC(q)C(q)C(q SC
,
,
21
2121
©2005 Pearson Education, Inc. Chapter 7 76
Production with Two Outputs – Economies of Scope
With economies of scope, the joint cost is less than the sum of the individual costs
Interpretation:If SC > 0 Economies of scopeIf SC < 0 Diseconomies of scopeThe greater the value of SC, the greater the
economies of scope
©2005 Pearson Education, Inc. Chapter 7 77
Production with Two Outputs – Economies of Scope
There is no direct relationship between economies of scope and economies of scaleMay experience economies of scope and
diseconomies of scaleMay have economies of scale and not have
economies of scope