Chapter 3
Market Structure
and
Market Power
1
Introduction
• Industries have very different structures
– numbers and size distributions of firms
• ready-to-eat breakfast cereals: high concentration
Top 4 firms account for about 80% of sales
• Games and toys (not including video games):
The largest 4 firms accounts for 35% to 45%
• How best to measure market structure
– summary measure (Figure 3-1)
– concentration curve is possible
– preference is for a single number
– concentration ratio or
– Herfindahl-Hirschman index (HHI)= the sum of the
squares of the market shares of all of the firms in the2
industry.
Measure of concentration
• Compare two different measures of concentration:
Firm Rank
Market Share
(%)
Squared Market
Share
1
25
625
2
25
625
3
25
625
4
5
25
5
5
25
6
5
25
7
5
25
8
5
25
Concentration Index
CR4 = 80
HHI = 2,000
3
• Concentration index is affected by, e.g. merger
Firm Rank
Market Share
(%)
1 Assume that firms
2 4 and 5 decide
to merge
3
25
4
5
5
6
7
}
25
625
Market shares
625
change
25
625
5
The Concentration
Index changes
8
Concentration Index
Squared Market
Share
}
10
25
25
5
25
5
25
5
25
CR4 = 80
85
}
HHI = 2,000
100
2,050
4
3.1.1 What is a market?
• No clear consensus:To use CR4 or HHI as an
overall measure of a market’s structure, we need
to be able to identify a well-defined market first.
Example 1, the market for automobiles
• should we include light trucks; pick-ups SUVs?
Example 2, the market for soft drinks
• what are the competitors for Coca Cola and Pepsi?
– With whom do McDonalds and Burger King
compete?
• Presumably define a market by closeness in
substitutability of the commodities involved
– how close is close?
5
Market definition (cont.)
– how homogeneous do commodities have to be?
• Does wood compete with plastic? Rayon with
wool?
• Definition is important
– without consistency concept of a market is meaningless
– need indication of competitiveness of a market: affected by
definition
– public policy: decisions on mergers can turn on market
definition
• Staples/Office Depot merger rejected on market definition
• Coca Cola expansion turned on market definition
• Standard approach has some consistency
– based upon industrial data
– substitutability is production not consumption (ease of data
6
collection)
Market definition (cont.)
• Government statistical sources
Census Bureau:
Standard Industrial Classification (SIC)
North American Industry Classification System
(NAICS)
• The measure of concentration varies across countries
• Use of production-based statistics has limitations:
– can put in different industries products that are in the
same market
• The international dimension is important
– Boeing/McDonnell-Douglas merger
– relevant market for automobiles, oil, hairdressing 7
Market definition (cont.)
• Geography is important
– barrier to entry if the product is expensive to
transport
– but customers can move
• what is the relevant market for a beach resort or
ski-slope?
• Vertical relations between firms are important
– most firms make intermediate rather than final goods
– firm has to make a series of make-or-buy choices
– upstream and downstream production
– measures of concentration may assign firms at
different stages to the same industry
• do vertical relations affect underlying structure?
8
Market definition (cont.)
– Firms at different stages may also be assigned
to different industries
• bottlers of soft drinks: low concentration
• suppliers of sift drinks: high concentration
• the bottling sector is probably not
competitive.
• In sum: market definition poses real problems
– existing methods represent a reasonable
compromise
9
• Measuring Market Power
• The Lerner Index (LI) is one way to measure how well a
market performs from an efficiency point of view. The LI
measures how far the outcome is from the competitive ideal
in the following way:
• LI= (P-MC)/P
• Because LI directly reflects the discrepancy between price
and marginal cost it captures much of what we are interested
in when it comes to the exercise of market power.
• For a competitive firm, LI is zero since such a firm prices at
marginal cost.
• For a pure monopolist, on the other hand, the LI can be
shown to be the inverse of the elasticity of demand-the less
elastic the demand the greater is the price-marginal cost
distortion. To see this, a monopolist’s MR = P+(dp/dQ)*Q
10
• For profit maximization: MR=MC
• So, P + (dP/dQ)*Q = MC.
• Rearranging and dividing by price P, we obtain
(P-MC)/P = - (dP/dQ)*(Q/P) = 1/ elasticity of the demand.
• Note that the LI can never exceed 1 and that it can
only achieve this maximum value if MC=0.
• With more than one but not “many” firms, the
Lerner Index is more complicated: need to average.
– suppose the goods are homogeneous so all firms sell at
the same price
LI =
P-SsiMCi
P
11
Assume two identical firms each with costs AC1
$/unit
MC
MCA
AC1
MC´A
If they are to produce a given output at lowest
cost, they must operate at the same marginal cost
Why? Assume firm A is operating at MCA and
firm B is operating at MCB
Transferring one unit of output from A to B
lowers total cost
MC´B
MCB
QB
QA
Quantity
If the two firms operate at the same
marginal cost they must produce identical
outputs
Suppose not: firm A has output QA and firm
B has output QB
Transferring one unit of output from A to B
lowers total cost
12
It follows that AC2 represents the lowest possible average
cost if output is produced by two firms: AC2 is obtained by
adding AC1 to itself horizontally
AC1 is average cost if
output is produced by
Now assume that
one firm.
output is produced by
If total output is 2Q1 then
two firms.
$/unit we know that each firm has
This market is a
to produce Q1 and average
natural
cost is AC1 If total output is 2Q2 then
monopoly up to
AC1 we know that each AC
firm
has
2
output QM even
to produce Q2 and average
AC1
though this is
cost is AC2
greater than
If total output is 2Q* then
AC2
MES Q*: it is
we know that each firm has
AC*
less costly for
to produce Q* and average
output to be
cost is AC*
produced by
one rather than
Q1 2Q1 Q* QM
2Q*
Quantity
two firms:
Q2 2Q
2
subadditivity
13
Chapter 4
Technology and Cost
14
The Single-Product Firm
• Profit-maximizing firm must solve a related problem
– minimize the cost of producing a given level of output
– combines two features of the firm
• production function: how inputs are transformed into output
Assume that there are n inputs at levels x1 for the first, x2 for the second,…, xn
for the nth. The production function, assuming a single output, is written:
Q = F(x1, x2, x3,…,xn)
• cost function: relationship between output choice and
production costs. Derived by finding input combination
that minimizes cost
n
Minimize
S wixi
subject to F(x1, x2, x3,…,xn) = Q1
i=1
15
Now assume that input 1 becomes
cheaper
• Review input choice: one
This makes the isocost
output and two inputs
lines less steep
The production function
Cost of producing
can be illustrated as a set of
output Q1 is minimized
isoquants, one for
x2
by finding the point
each level of output
The input choice
where an isocost line
is x11 of input 1
is tangent to the
The cost-minimizing input
and x12 of
Q1 isoquant
combination changes
input 2
x12
More of
input 1 is
used and less
of input 2
x2
The new costminimizing point
2
x11
x21
Production cost can be
Q2 illustrated as a set of
isocost lines, with slope
Q1
w1/w2. The lower the
Q0
isocost line, the lower
the cost.
x1
16
• This analysis has interesting implications
– different input mix across
• time: as capital becomes relatively cheaper
• space: difference in factor costs across countries
• Analysis gives formal definition of the cost
function
– denoted C(Q): total cost of producing output Q
– average cost = AC(Q) = C(Q)/Q
– marginal cost:
• additional cost of producing one more unit of output.
• Slope of the total cost function
• formally: MC(Q) = dC(Q)/d(Q)
17
Cost curves: an illustration
Typical average and marginal cost curves
$/unit
Relationship between AC and MC
MC
If MC < AC then AC is falling
AC
If MC > AC then AC is rising
MC = AC at the minimum of the
AC curve
Quantity
18
Economies of scale
• Definition: average costs fall with an increase in
output
• Represented by the scale economy index
AC(Q)
S=
MC(Q)
• S > 1: economies of scale
• S < 1: diseconomies of scale
• S is the inverse of the elasticity of cost with respect to
outputdC(Q) dQ
dC(Q) C(Q)
MC(Q)
1
hC =
C(Q)
Q
=
dQ
Q
=
AC(Q)
=
S
19
An example
Average cost is
taken as the mean
of 145 and 136
• Take a simple example
Output
5
6
11
12
Total Cost Average Cost Marginal Cost Scale Economy
($)
($)
($)
Index
725
145
140.5
91
140.5/91 = 1.54
816
136
1331
121
122.5
157
122.5/157 = 0.78
1488
124
}
}
Percentage increase in cost of
increasing output from 5 to 6
Percentage increase in output
Check the
relationship to
the elasticity of
the cost curve
816 - 725
= 11.8%
(816+725)/2
6-5
= 18.2%
(6+5)/2
hC = 11.8/18.2 = 0.65 and 1/ hC = 1/0.65 = 1.54
20
• Minimum efficient scale:
– output at which economies of scale are first exhausted
$/unit
AC1
AC2
MES1
MES2
With average cost curve
AC1 minimum efficient
scale is MES1
With average cost curve
AC2 minimum efficient
scale is MES2
Quantity
21
Natural monopoly
• If the extent of the market is less than MES then the
market is a natural monopoly: S > 1 in such a market.
• But a natural monopoly can exist even if S < 1.
Economies of scale
• Sources of economies of scale
– “the 60% rule”: capacity related to volume while
cost is related to surface area
– product specialization and the division of labor
– “economies of mass reserves”: economize on
inventory, maintenance, repair
22
– indivisibilities
Indivisibilities
• Some inputs can be employed
only in indivisible units
VC
$
– transport routes
– major items of capital equipment
• Three implications:
– cost is “lumpy” or fixed at F1
– maximum rated capacity Q1
– average fixed cost F1/Q falls with
output up to rated capacity
• Other inputs vary with output: variable
costs
• Average total costs exhibit economies
of scale over some range
F1
FC
Quantity
Q1
$
ATC
AVC
AFC
Quantity
Q1
23
• If projected output is greater than current capacity
install higher-rated capacity equipment or add
additional capacity
• It may be cheaper to have spare capacity than
operate up to capacity
$/unit
If projected output is greater
AC1
AC2
than Q* it is cheaper to
install higher capacity even
though there is spare
capacity
Consistent with evidence
on excess capacity: see
Federal Statistics
Q*
Q1
Q2
Quantity
24
Fixed costs, indivisibilities and sunk costs
• Indivisibilities make scale of entry an important strategic
decision:
– enter large with large-scale indivisibilities: heavy overhead
– enter small with smaller-scale cheaper equipment: low overhead
• Some indivisible inputs can be redeployed
– aircraft
• Other indivisibilities are highly specialized with little
value in other uses
– market research expenditures
– rail track between two destinations
• The latter are sunk costs: nonrecoverable if production
stops
• Fixed costs and sunk costs affect market structure by 25
affecting entry
Multi-Product Firms
• Many firms make multiple products
– Ford, General Motors, 3M etc.
• What do we mean by costs and output in these cases?
• How do we define average costs for these firms?
–
–
–
–
total cost for a two-product firm is C(Q1, Q2)
marginal cost for product 1 is MC1 = C(Q1,Q2)/Q1
but average cost cannot be defined fully generally
need a more restricted definition: ray average cost
26
Ray average cost
• Assume that a firm makes two products, 1 and 2 with the
quantities Q1 and Q2 produced in a constant ratio of 2:1.
• Then total output Q can be defined implicitly from the
equations Q1 = 2Q/3 and Q2 = Q/3
• More generally: assume that the two products are
produced in the ratio 1/2 (with 1 + 2 = 1).
• Then total output is defined implicitly from the equations
Q1 = 1Q and Q2 = 2Q
• Ray average cost is then defined as:
RAC(Q) =
C(1Q, 2Q)
Q
27
An example of ray average costs
• Assume that the cost function is:
C(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2
• Marginal costs for each product are:
MC1 =
MC2 =
C(Q1,Q2)
Q1
C(Q1,Q2)
Q2
= 25 -
= 30 -
3Q2
2
3Q1
2
28
• Ray average costs: assume 1 = 2 = 0.5
C(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2
Q1 = 0.5Q; Q2 = 0.5Q
RAC(Q) =
=
C(0.5Q, 0.5Q)
Q
10 + 25Q/2+ 30Q/2 - 3Q2/8
Q
Now assume 1 = 0.75; 2 = 0.25
C(0.75Q, 0.25Q)
RAC(Q) =
Q
10 + 75Q/4+ 30Q/4 - 9Q2/32
=
Q
10
55
+
=
Q
2
3Q
8
10
105
+
=
Q
4
9Q
32
29
Economies of scale and multiple
products
• Definition of economies of scale with a single
product
C(Q)
AC(Q)
S=
MC(Q)
=
Q.MC(Q)
• Definition of economies of scale with multiple
products
C(Q1,Q2,…,Qn)
S=
MC1Q1 + MC2Q2 + … + MCnQn
• This is by analogy to the single product case
– relies on the implicit assumption that output proportions
are fixed
– so we are looking at ray average costs in using this
30
definition
The example once again
C(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2
MC1 = 25 - 3Q2/2 ; MC2 = 30 - 3Q1/2
Substitute into the definition of S:
C(Q1,Q2,…,Qn)
S=
MC1Q1 + MC2Q2 + … + MCnQn
=
10 + 25Q1 + 30Q2 - 3Q1Q2/2
25Q1 - 3Q1Q2/2 + 30Q2 - 3Q1Q2/2
It should be obvious in this case that S > 1
This cost function exhibits global economies of scale
31
Economies of Scope
• Formal definition
SC =
C(Q1, 0) + C(0 ,Q2) - C(Q1, Q2)
C(Q1, Q2)
• The critical value in this case is SC = 0
– SC < 0 : no economies of scope; SC > 0 : economies of scope.
• Take the example:
10 + 25Q1 + 10 + 30Q2 - (10 + 25Q1 + 30Q2 - 3Q1Q2/2)
SC =
>0
10 + 25Q1 + 30Q2 - 3Q1Q2/2
32
Economies of Scope (cont.)
• Sources of economies of scope
• shared inputs
– same equipment for various products
– shared advertising creating a brand name
– marketing and R&D expenditures that are generic
• cost complementarities
–
–
–
–
–
producing one good reduces the cost of producing another
oil and natural gas
oil and benzene
computer software and computer support
retailing and product promotion
33
Flexible Manufacturing
• Extreme version of economies of scope
• Changing the face of manufacturing
• “Production units capable of producing a range of
discrete products with a minimum of manual
intervention”
–
–
–
–
Benetton
Custom Shoe
Levi’s
Mitsubishi
• Production units can be switched easily with little if
any cost penalty
– requires close contact between design and manufacturing
34
Flexible Manufacturing (cont.)
• Take a simple model based on a spatial analogue.
– There is some characteristic that distinguishes
different varieties of a product
• sweetness or sugar content
• color
• texture
– This can be measured and represented as a line
– Individual products can be located on this line in
terms of the quantity of the characteristic that they
possess
– One product is chosen by the firm as its base product
– All other products are variants on the base product
35
Flexible Manufacturing (cont.)
• An illustration: soft drinks that vary in sugar
content
(Diet)
0
Low
(LX)
(Super)
0.5
1
High
Each product is located
on the line in terms
of the amount of the
characteristic it has
This is the
characteristics
line
36
The example (cont.)
(Diet)
0
Low
(LX)
(Super)
0.5
1
High
• Assume that the process is centered on LX as base product.
A switching cost s is incurred in changing the process to
either of the other products.
There are additional marginal costs of making Diet or Super - from
adding or removing sugar. These are r per unit of “distance”
between LX and the other product.
There are shared costs F: design, packaging, equipment.
37
The example (cont.)
• In the absence of shared costs there would be
specialized firms.
• Shared costs introduce economies of scope.
m
Total costs are: C(zj, qj) = F + (m - 1)s +
S
[(c + rzj - z1)qj]
j=1
If production is 100 units of each product:
one product per firm with three firms C3 = 3F + 300c
one firm with all three products
C1 = F + 2s + 300c + 100r
C1 < C3 if 2s + 100r < 2F  F > 50r + s
This implies a constraint on set-up costs, switching costs and
marginal costs for multi-product production to be preferred.
38
Economies of scale and scope
• Economies of scale and scope affect market
structure but cannot be looked at in isolation.
• They must be considered relative to market size.
• Should see concentration decline as market size
increases
• For example, entry to the medical profession is
going to be more extensive in Chicago than in
Oxford, Miss
39
Network Externalities
• Market structure is also affected by the presence
of network externalities
– willingness to pay by a consumer increases as the
number of current consumers increase
• telephones, fax, Internet, Windows software
• utility from consumption increases when there are more
current consumers
• These markets are likely to contain a small
number of firms
– even if there are limited economies of scale and scope
40
The Role of Policy
• Government can directly affect market structure
– by limiting entry
• taxi medallions in Boston and New York
• airline regulation
– through the patent system
– by protecting competition e.g. through the
Robinson-Patman Act
41