Post on 18-Dec-2015
transcript
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Chapter 2
Technology, Costs
and
Market Structure
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Introduction• Industries have very different structures
– numbers and size distributions of firms• ready-to-eat breakfast cereals: high concentrationTop 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 (p55, Figure 2-1)– concentration curve is possible– preference is for a single number– concentration ratio or Herfindahl-Hirschman
index (HHI)
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Measure of concentration• Compare two different measures of concentration:
Firm Rank Market Share Squared Market (%) Share
1 25
2 25
3 25
4 5
5 5
6 5
7 5
8 5
625
625
625
25
25
25
25
25
CR4 = 80Concentration Index HHI = 2,000
25
25
25
5
4
• Concentration index is affected by, e.g. merger
Firm Rank Market Share Squared Market (%) Share
1 25
2 25
3 25
4 5
5 5
6 5
7 5
8 5
625
625
625
25
25
25
25
25
CR4 = 80Concentration Index HHI = 2,000
25
25
25
5} } }10
85
100
2,050
Assume that firms4 and 5 decide
to merge
The ConcentrationIndex changes
Market shareschange
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2.1.2 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?
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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)
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• Government statistical sourcesCensus 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
Market definition (cont.)
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• 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?
Market definition (cont.)
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– 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
Market definition (cont.)
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2.2.1 The Neoclassical View of the Firm
• Concentrate upon a neoclassical view of the firm– the firm transforms inputs into outputs
Inputs Outputs
The Firm
• There is an alternative approach (Coase)– What happens inside firms?– How are firms structured? What determines size?– How are individuals organized/motivated?
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2.2.2 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
Minimize subject to F(x1, x2, x3,…,xn) = Q1 wixii=1
n
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• Review input choice: one output and two inputs
x2
x1
Q0
Q1
Q2
The production functioncan be illustrated as a set of
isoquants, one foreach level of output
The production functioncan be illustrated as a set of
isoquants, one foreach level of output
Production cost can beillustrated as a set of
isocost lines, with slopew1/w2. The lower theisocost line, the lower
the cost.
Production cost can beillustrated as a set of
isocost lines, with slopew1/w2. The lower theisocost line, the lower
the cost.
Cost of producing output Q1 is minimized
by finding the pointwhere an isocost line
is tangent to theQ1 isoquant
Cost of producing output Q1 is minimized
by finding the pointwhere an isocost line
is tangent to theQ1 isoquant
x11
x12
The input choiceis x1
1 of input 1and x1
2 of input 2
The input choiceis x1
1 of input 1and x1
2 of input 2
Now assume that input 1 becomes cheaper
This makes the isocost lines less steep
The new cost-minimizing point
The new cost-minimizing point
More ofinput 1 is
used and lessof input 2
More ofinput 1 is
used and lessof input 2 x2
1
x22
The cost-minimizing input combination changes
The cost-minimizing input combination changes
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• 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)
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Cost curves: an illustration
$/unit
Quantity
AC
MC
Typical average and marginal cost curvesTypical average and marginal cost curves
Relationship between AC and MC
If MC < AC then AC is falling
If MC > AC then AC is rising
MC = AC at the minimum of the AC curve
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Economies of scale• Definition: average costs fall with an increase in output• Represented by the scale economy index
S =AC(Q)
MC(Q)• S > 1: economies of scale• S < 1: diseconomies of scale• S is the inverse of the elasticity of cost with respect to output
C =dC(Q)
C(Q)
dQ
Q=
dC(Q)
dQ
C(Q)
Q=
MC(Q)
AC(Q)=
1
S
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An example
• Take a simple example
Output Total Cost Average Cost Marginal Cost Scale Economy ($) ($) ($) Index5 725 145
6 816 13691}
11 1331 121
12 1488 124} 157
140.5 140.5/91 = 1.54
122.5/157 = 0.78Average cost is
taken as the mean of 145 and 136
Average cost istaken as the mean
of 145 and 136122.5
Check the relationship to the elasticity of the cost curve
Check the relationship to the elasticity of the cost curve
816 - 725Percentage increase in cost of increasing output from 5 to 6 (816+725)/2
= 11.8%
Percentage increase in output6-5
(6+5)/2= 18.2%
C = 11.8/18.2 = 0.65 and 1/ C = 1/0.65 = 1.54
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• Minimum efficient scale: – output at which economies of scale are first exhausted
$/unit
Quantity
AC1
MES1
AC2
MES2
With average cost curve AC1 minimum efficient
scale is MES1
With average cost curve AC2 minimum efficient
scale is MES2
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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– indivisibilities
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Indivisibilities• Some inputs can be employed
only in indivisible units– transport routes
– major items of capital equipment
$
$
Quantity
Quantity
Q1
Q1
FC
VC
AFC
AVCATC
• 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
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• 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
AC1 AC2
QuantityQ1 Q2
If projected output is greater than Q* it is cheaper to
install higher capacity even though there is spare
capacity
Q*
Consistent with evidence on excess capacity: see
Federal Statistics
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• 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
Fixed costs, indivisibilities and sunk costs
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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
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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
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An example of ray average costs
• Marginal costs for each product are:
C(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2• Assume that the cost function is:
MC1 =C(Q1,Q2)
Q1
= 25 -3Q2
2
MC2 =C(Q1,Q2)
Q2
= 30 -3Q1
2
25
• 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=
10
Q+
55
2-
3Q
8
Now assume 1 = 0.75; 2 = 0.25
RAC(Q) =C(0.75Q, 0.25Q)
Q
=10 + 75Q/4+ 30Q/4 - 9Q2/32
Q=
10
Q+
105
4-
9Q
32
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Economies of scale and multiple products
• Definition of economies of scale with a single product
S =AC(Q)
MC(Q)=
C(Q)
Q.MC(Q)
• Definition of economies of scale with multiple products
S =C(Q1,Q2,…,Qn)
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
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The example once againC(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2
MC1 = 25 - 3Q2/2 ; MC2 = 30 - 3Q1/2
Substitute into the definition of S:
S =C(Q1,Q2,…,Qn)
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
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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:
SC =10 + 25Q1 + 10 + 30Q2 - (10 + 25Q1 + 30Q2 - 3Q1Q2/2)
10 + 25Q1 + 30Q2 - 3Q1Q2/2 > 0
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• 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
Economies of Scope (cont.)
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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
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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
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Flexible Manufacturing (cont.)
• An illustration: soft drinks that vary in sugar content
0 10.5
This is the characteristics
line
Each product is locatedon the line in termsof the amount of thecharacteristic it has
Low High
(Diet) (LX) (Super)
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The example (cont.)
• Assume that the process is centered on LX as base product.
0 10.5Low High
(Diet) (LX) (Super)
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.
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The example (cont.)
• In the absence of shared costs there would be specialized firms.
• Shared costs introduce economies of scope.
Total costs are: C(zj, qj) = F + (m - 1)s + j=1
m[(c + rzj - z1)qj]
If production is 100 units of each product:
C3 = 3F + 300cone product per firm with three firms
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.
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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
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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
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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
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Market Performance• Market structure is often a guide to market
performance• But this is not a perfect measure
– can have near competitive prices even with “few” firms
• Measure market performance using the Lerner Index
LI =P-MC
P
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Market Performance (cont.)• Perfect competition: LI = 0 since P = MC• Monopoly: LI = 1/– inverse of elasticity of
demand• 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-siMCi
P
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$/unit
Quantity
AC1
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
costMC Why? Assume firm A is operating at MCA and firm B is operating at MCBMCA
MCB
Transferring one unit of output from A to B lowers total costMC´A
MC´B
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
QAQB
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$/unit
Quantity
AC1 AC2
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
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
Q* 2Q*QM
AC1 is average cost ifoutput is produced by
one firm.
Now assume thatoutput is produced by
two firms.If total output is 2Q1 thenwe know that each firm has to produce Q1 and average
cost is AC1
If total output is 2Q1 thenwe know that each firm has to produce Q1 and average
cost is AC1
AC1
2Q1Q1
2Q2Q2
If total output is 2Q2 thenwe know that each firm has to produce Q2 and average
cost is AC2
If total output is 2Q2 thenwe know that each firm has to produce Q2 and average
cost is AC2
If total output is 2Q* thenwe know that each firm has to produce Q* and average
cost is AC*
If total output is 2Q* thenwe know that each firm has to produce Q* and average
cost is AC*AC2
AC*
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0 4 8
12 16 20
0
8
16
0100200
300
400
500
600
700
800
Total Cost
Output 1
Output 2
Illustration of ray average costs