Market Structure

1
Chapter 3

• Market Structure
• and
• Market Power

2
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 the industry.

3
Measure of concentration

• Compare two different measures of concentration

Firm Rank Market Share Squared
Market () Share
1 25
25
625
2 25
25
625
3 25
25
625
4 5
5
25
5 5
25
6 5
25
7 5
25
8 5
25
CR4 80
Concentration Index
HHI 2,000
4

• Concentration index is affected by, e.g. merger

Firm Rank Market Share Squared
Market () Share
1 25
Assume that firms 4 and 5 decide to merge
25
Market shares change
625
2 25
25
625
3 25
25
625
4 5
5
25



100
10
5 5
25
6 5
The Concentration Index changes
25
7 5
25
8 5
25
HHI 2,000
CR4 80
Concentration Index
85
2,050
5
3.1.1 What is a market?

• No clear consensusTo use CR4 or HHI as an
  overall measure of a markets 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?

6
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 collection)

7
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

8
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?

9
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

10

• 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 monopolists MR P(dp/dQ)Q
• For profit maximization MRMC

11

• 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 MC0.
• 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

P-SsiMCi
LI
P
12
Assume two identical firms each with costs AC1
If they are to produce a given output at lowest
cost, they must operate at the same marginal cost
/unit
MC
Why? Assume firm A is operating at MCA and firm
B is operating at MCB
MCA
AC1
Transferring one unit of output from A to B
lowers total cost
MCB
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
Quantity
QA
QB
Transferring one unit of output from A to B
lowers total cost
13
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 one
firm.
Now assume that output is produced by two firms.
If total output is 2Q1 then we know that each
firm has to produce Q1 and average cost is AC1
/unit
This market is a natural monopoly up to output QM
even though this is greater than MES Q it is
less costly for output to be produced by one
rather than two firms subadditivity
If total output is 2Q2 then we know that each
firm has to produce Q2 and average cost is AC2
AC1
AC2
AC1
If total output is 2Q then we know that each
firm has to produce Q and average cost is AC
AC2
AC
Quantity
Q
2Q
QM
14
Chapter 4Technology and Cost
15
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
? wixi
subject to F(x1, x2, x3,,xn) Q1
i1
16
Now assume that input 1 becomes cheaper

• Review input choice one output and two inputs

This makes the isocost lines less steep
The production function can be illustrated
as a set of isoquants, one for each level of
output
Cost of producing output Q1 is minimized by
finding the point where an isocost line is
tangent to the Q1 isoquant
x2
The input choice is x11 of input 1 and x12 of
input 2
The cost-minimizing input combination changes
The new cost- minimizing point
x12
Production cost can be illustrated as a set
of isocost lines, with slope w1/w2. The lower
the isocost line, the lower the cost.
x22
Q2
More of input 1 is used and less of input 2
Q1
Q0
x1
x11
x21
17

• 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)

18
Cost curves an illustration
Typical average and marginal cost curves
/unit
Relationship between AC and MC
MC
If MC lt AC then AC is falling
AC
If MC gt AC then AC is rising
MC AC at the minimum of the AC curve
Quantity
19
Economies of scale

• Definition average costs fall with an increase
  in output
• Represented by the scale economy index

AC(Q)
S
MC(Q)

• S gt 1 economies of scale
• S lt 1 diseconomies of scale
• S is the inverse of the elasticity of cost with
  respect to output

dC(Q)
dQ
dC(Q)
C(Q)
MC(Q)
1
hC



C(Q)
Q
dQ
Q
AC(Q)
S
20
An example
Average cost is taken as the mean of 145 and 136

• Take a simple example

Output Total Cost Average Cost Marginal
Cost Scale Economy
() () () Index
5 725
145

91
140.5
140.5/91 1.54
6 816
136
11 1331
121

157
122.5/157 0.78
122.5
12 1488
124
816 - 725
Percentage increase in cost of increasing output
from 5 to 6
11.8
(816725)/2
6-5
Percentage increase in output
18.2
Check the relationship to the elasticity of
the cost curve
(65)/2
hC 11.8/18.2 0.65 and 1/ hC 1/0.65 1.54
21

• Minimum efficient scale
• output at which economies of scale are first
  exhausted

/unit
With average cost curve AC1 minimum efficient
scale is MES1
AC1
With average cost curve AC2 minimum efficient
scale is MES2
AC2
Quantity
MES1
MES2
22
Natural monopoly

• If the extent of the market is less than MES then
  the market is a natural monopoly S gt 1 in such a
  market.
• But a natural monopoly can exist even if S lt 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
• indivisibilities

23
Indivisibilities

• Some inputs can be employed only in indivisible
  units
• transport routes
• major items of capital equipment

VC

• 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

FC
F1
Quantity
Q1

ATC
AVC

• Other inputs vary with output variable costs
• Average total costs exhibit economies of scale
  over some range

AFC
Quantity
Q1
24

• 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 than Q it is
cheaper to install higher capacity even though
there is spare capacity
AC1
AC2
Consistent with evidence on excess capacity see
Federal Statistics
Q1
Q2
Q
Quantity
25
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 affecting entry

26
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

27
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 21.
• 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

C(?1Q, ?2Q)
RAC(Q)
Q
28
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

3Q2
?C(Q1,Q2)
MC1
25 -
2
?Q1
3Q1
?C(Q1,Q2)
MC2
30 -
2
?Q2
29

• Ray average costs assume ?1 ?2 0.5

C(Q1, Q2) 10 25Q1 30Q2 - 3Q1Q2/2
Q1 0.5Q Q2 0.5Q
C(0.5Q, 0.5Q)
RAC(Q)
Q
10 25Q/2 30Q/2 - 3Q2/8
10
55
3Q
-



Q
2
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
10
105
9Q
-



Q
4
32
Q
30
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 definition

31
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 gt 1
This cost function exhibits global economies of
scale
32
Economies of Scope

• Formal definition

C(Q1, 0)
C(0 ,Q2) -
C(Q1, Q2)
SC
C(Q1, Q2)

• The critical value in this case is SC 0
• SC lt 0 no economies of scope SC gt 0
  economies of scope.
• Take the example

10 25Q1
10 30Q2 -
(10 25Q1 30Q2 - 3Q1Q2/2)
gt 0
SC
10 25Q1 30Q2 - 3Q1Q2/2
33
Economies of Scope (cont.)

• Sources of economies of scope
• shared inputs
• same equipment for various products
• shared advertising creating a brand name
• marketing and RD 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

34
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
• Levis
• Mitsubishi
• Production units can be switched easily with
  little if any cost penalty
• requires close contact between design and
  manufacturing

35
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

36
Flexible Manufacturing (cont.)

• An illustration soft drinks that vary in sugar
  content

(Diet)
(LX)
(Super)
0
1
0.5
Low
High
Each product is located on the line in terms of
the amount of the characteristic it has
This is the characteristics line
37
The example (cont.)
(Diet)
(LX)
(Super)
0
1
0.5
Low
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.
38
The example (cont.)

• In the absence of shared costs there would be
  specialized firms.
• Shared costs introduce economies of scope.

m
S
Total costs are
C(zj, qj)
F (m - 1)s
(c r?zj - z1?)qj
j1
If production is 100 units of each product
C3 3F 300c
one product per firm with three firms
one firm with all three products
C1 F 2s 300c 100r
C1 lt C3 if
2s 100r lt 2F
? F gt 50r s
This implies a constraint on set-up costs,
switching costs and marginal costs for
multi-product production to be preferred.
39
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

40
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

41
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