Deriving the Long Run Cost Curve

1
Deriving the Long Run Cost Curve

• In the Long run, all inputs variable
• Can choose capital
• LRAVC LRATC LRAC
• LRAC in long-run

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Deriving the Long Run Cost Curve

SRAC1K1
LRAC
Output
3
Deriving the Long Run Cost Curve

Suppose there is another possible technology
using capital K2 that lowers costs at higher
output
SRAC1K1
SRAC2K2
LRAC
Output
Q0
4
Deriving the Long Run Cost Curve

There is another possible technology using
capital K3 that lowers costs at yet higher output
SRAC1
SRAC2
SRAC3
LRAC
Q0
Q1
Output
5
Deriving the Long Run Cost Curve

Eventually as we add output, opportunities to
further lower average cost disappear
SRAC1
SRAC2
SRAC4
SRAC3
LRAC
Output
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Deriving the Long Run Cost Curve

What does the shape of the LRAC tell us?
SRAC5
SRAC1
LRAC
SRAC2
SRAC4
SRAC3
Output
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Deriving the Long Run Cost Curve

What does the shape of the LRAC tell us? W 3 r
2
AC1, K10, L20, TC 320210 80
AC2, K20, L40, TC 340220 160
LRAC
2
1.6
40
100
Output
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Deriving the Long Run Cost Curve

What does the shape of the LRAC tell us? W 3 r
2
Average Costs Fall if Double All Inputs,
Costs Output More Than Doubles
AC1, K10, L20, TC 320210 80
AC2, K20, L40, TC 340220 160
LRAC
2
1.6
40
100
Output
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Example of Increasing Returns to Scale

• W 3
• r 2
• K 10
• L 20
• Q 40
• TC (320) (210)
• 80

• W 3
• r 2
• K 20
• L 40
• Q 100
• TC (340) (220)
• 160

Costs Rise 2X Output rises 2.5X
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Deriving the Long Run Cost Curve

What does the shape of the LRAC tell us?
Average Costs Fall if Double All Inputs,
Costs Output More Than Doubles
ATC TC/Q 80/40 2
ATC 160/100 1.6
LRAC
2
1.6
40
100
Output
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Returns to Scale

• Increasing Returns to Scale (IRS)
• Output rises faster than cost
• ATC (TC/Q) falling
• Constant Returns to Scale (CRS)
• Output rises at the same pace as cost
• ATC (TC/Q) constant
• Decreasing Returns to Scale (DRS)
• Output rises more slowly than Cost
• ATC (TC/Q) rising

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Shape of Long-run Average Cost Curve and Returns
to Scale

LRAC
CRS
IRS
DRS
Q
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Shape of Long-run Average Cost Curve and Returns
to Scale

LRAC
CRS
IRS
DRS
Argument that you will never see the upward
sloping portion of LRAC curve in practice----WHY?
Q
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Source of Increasing Returns to Scale

• 1. Specialization according to comparative
  advantage
• Larger firms can more easily take advantage
• 2. Physical dimensions
• Warehouse
• Length Circumference Area
• 1 ft 4 ft 1 sq ft

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Source of Increasing Returns to Scale

• 1. Specialization according to comparative
  advantage
• Larger firms can more easily take advantage
• 2. Physical dimensions
• Warehouse
• Length Circumference Area
• 1 ft 4 ft 1 sq ft
• 2 ft 8 ft 4 sq ft

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Source of Increasing Returns to Scale

• 1. Specialization according to comparative
  advantage
• Larger firms can more easily take advantage
• 2. Physical dimensions
• Warehouse
• Length Circumference Area
• 1 ft 4 ft 1 sq ft
• 2 ft 8 ft 4 sq ft
• 3 ft 12 ft 9 sq ft
• Triple size of wall, raise capacity by 9

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Source of Increasing Returns to Scale

• Physical dimensions of a pipe
• radius Circumference Area
• 1 in 2 sq in cu in
• 2 in 4 sq in 4 cu in
• 3 in 6 sq in 9 cu in
• Triple size of pipe, raise capacity by 9

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Source of Increasing Returns to Scale

• 3. Lumpy inputs
• Gains from fully using capacity
• Buying in bulk
• Joint Marketing
• Limits to returns to scale
• information
• managerial ability
• Example Ford River Rouge Plant

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Ford River Rouge Plant

• In early 1920s, Ford decides to bring all aspects
  of car production into one place

Rubber Iron Ore Coal Glass
CAR
93 miles of railroad, 27 miles of conveyors, 330
acres of windows, 75000 employees,...
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Ford River Rouge PlantBuilding begins in 1917

• Never fully operational
• Vulnerable to strikes
• Henry Ford ultimately favored decentralized
  manufacturing. He established nineteen village
  industries by the 1940s, all within sixty-miles
  of Ford world headquarters in Dearborn.
• By 1938, "Ford was buying parts from 6,000
  independent plants throughout the nation. Life
  Magazine
• The plant now employs 6,000 workersFords
  largest plant

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Minimum Efficient Scale Smallest output that
yields minimum long-run average cost

LRAC
Q
minimum efficient scale
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Minimum Efficient Scale Smallest output that
yields minimum long-run average cost

LRAC
If competition forces efficiency, firms will
produce here in the long run
Q
Number of firms in market depends on size of
demand, minimum efficient scale
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Suppose that market demand is 1000 units

LRAC
Pmin
Q
Minimum efficient scale 10 implies there could
be as many as 100 firms
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Suppose that demand is 1000 units

LRAC
Pmin
Q
Minimum efficient scale 1500 implies there
would be only 1 firm
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Implications

• Small minimum efficient scale implies easy entry
• Fast food, other franchise operations
• Every McDonalds looks the same for a reason
• Large minimum efficient scale implies substantial
  barriers to entry
• Cable, Phone, Electric Utilities, Steel, Autos

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Returns to scale in retailing

• Wal-Mart 265 billion
• Home Depot 65 billion
• Sears-K-Mart merged 55 billion

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• Wal-Mart has huge size advantage
• Returns due to mass purchases (3 of the Chinese
  economy)
• Inventory Management (4 billion information
  system)
• Lower prices (avg U.S. household saves 450/yr)

Sears cannot match Wal-Mart scale, options?
LRAC
55 billion
Output
265 billion
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• Wal-Mart has huge size advantage
• Returns due to mass purchases (3 of the Chinese
  economy)
• Inventory Management (4 billion information
  system)

Costco largest warehouse retailer (50) vs Sams
(40) Mechanism only 4K items vs 100K at Sams
LRAC, Costco
LRAC, Wal-Mart
55 billion
Output
265 billion
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Average Sierra Nevada Brewing (2 craft) 600000
bls capacity
Average size of 18 Anheuser-Busch and Miller
breweries is 8.5 million bls
Tremblay, Victor J. and Carol H. Tremblay (2005)
The U.S. Brewing Industry Cambridge, MA The MIT
Press.
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MES has a 33 cost advantage
Average Sierra Nevada Brewing (2 craft) 600000
bls capacity
Average size of 18 Anheuser-Busch and Miller
breweries is 8.5 million
Tremblay, Victor J. and Carol H. Tremblay (2005)
The U.S. Brewing Industry Cambridge, MA The MIT
Press.
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Brewery plants by Capacity, 1950-2000
Tremblay, Victor J. and Carol H. Tremblay (2005)
The U.S. Brewing Industry Cambridge, MA The MIT
Press.
32
Note Beer consumption doubled over this period
Elzinga, K. G. (2001) in Adams and Brock eds. The
Structure of American Industry 10th ed.
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Beer Industry Returns to scale with a high
quality small scale fringe

• Big five produce low cost, mass produced beer
• Craft beers are made in small batches, high
  costs, high prices, better quality

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Constant Cost Industries

• Agriculture
• Allows broad range of farm sizes, but incomes
  differ by acreage

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300 acres
A. Hallam (1993) Size, Structure and the Changing
Face of American Agriculture
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Relative costs of different Electricity
generation modes, by capacity, no CO2 cost
Solar
Anaerobic Digestion
Biomass
Wind
CoalBiomass
Coal
Landfill Gas
Natalie Rolph. 2009. Planning for Future
Electric Generation Demands. Black Veatch
37
Relative costs of different Electricity
generation modes, by capacity, CO2 cost 60/ton
Solar
Anaerobic Digestion
Biomass
Coal
Wind
CoalBiomass
Landfill Gas
Natalie Rolph. 2009. Planning for Future
Electric Generation Demands. Black Veatch
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Cable Television large minimum efficient scale,
high entry costs
LRAC, cable
Output
10 million
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Satellite Television smaller minimum efficient
scale and entry costs
LRAC, satellite
LRAC, cable
3 million
Output
10 million
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Current Market Share of Pay Television

• Satellite Television (24 of households)
• DirectTV 15 million
• Dish Network 12 million
• Growth since 1995 700
• Basic Cable 66 million (59 of households)
• Growth since 1995 1

Because of Direct Satellite television, basic
cable cost s 15 less
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Added Conditions for Long-Run Equilibrium

• Profit Maximization P MC
• No incentive to enter or exit
• Zero Economic Profit, P SRATC
• No incentive to change scale of operation
• Produce at efficient scale, P LRAC
• P MC SRATC LRAC