Linear Market Areas

1
Linear Market Areas

• Chapter 2

2
Shopping models

• Depict the competitive behavior of firms that
  sell directly to consumers
• Retail trade and service industries,
• Manufacturing industries if input costs are
  identical everywhere
• F.O.B. pricing (Free on board) Consumers pay all
  transport costs

3
Delivered price

• Delivered price (full price)
• store price (mill price, gate price)
  transportation costs
• Transport costs cost of gas, oil, insurance,
  etc., (fare or ticket prices) cost of time

4
Pricing categories

• F.O.B. mill price consumers pay store price
  transport costs.
• Uniform delivered pricing (C.I.F. price cost
  insurance freight paid ) firm pays transport
  costs
• Limit price maximum price that consumers are
  willing and able to pay for a good where the
  demand curve intersects the vertical axis.

5
Price-Distance Function and Demand
6
Market areas when the mill (store) price changes
7
Market areas when transport costs change
8
Elasticity of demand

• If gt 1, demand is elastic
• If 1, demand is unit elastic
• If lt 1, demand is inelastic

9
Pricedistance function and elasticity of demand
10
Hotellings Linear Markets

• Excess profits invite entry
• Will firms cluster or disperse?
• Assumptions
• Costless firm movement
• Homogenous product
• Consumers equally spaced along main street (i.e.,
  sales are a function of the market area)
• Perfectly inelastic demand

11
Unstable market areas for a duopoly
12
Market areas for duopoly under perfectly
inelastic demand
13
Principle of minimum differentiation

• Tendency for firms to cluster in the middle of
  the market
• Tendency of politicians to try to appeal to the
  median voter just before election day
• Tendency of retail goods to suffer from
  excessive sameness.

14
Hotellings market areas II

• Assumptions
• Costless firm movement
• Homogenous product
• Consumers equally spaced along main street (i.e.,
  sales are a function of the market area)
• Demand not perfectly inelastic, i.e., there is a
  limit price

15
Market area for monopoly when the firms demand
has a limit price
16
Market areas when duopolists demand curves have
limit prices
17
Break-even location

• Location between duopolists where consumer pays
  the same delivered price at each firm.

18
Demand curves for a duopoly when one has higher
transport costs
19
Three or more firms locate to share the market
20
Threshold size

• Minimum market area needed that will allow a firm
  to earn only a normal profit.
• If excess profits in a market are not enough to
  maintain threshold size for one more firm? Excess
  profits continue until
• Market grows enough to generate sufficient
  profits for newcomer
• New firm benefits from lower costs (agglomeration
  economies)
• Owner is content with less than a normal monetary
  profit.

21
Challenging the principle of minimum
differentiation

• DAsprement, Gabszewicz and Thisse (1979)
• Hotellings model does not provide stable
  equilibrium unless the market prices cannot
  change.
• Price competition too strong in the center
• Firms move to the edge of the market
• Lack of customersfirms move to the center

22
Duopoly when one firm lowers its price
23
Bertrand model of oligopoly behavior

• A firm lowers its price assuming that its rivals
  prices will not change.
• Rival firm lowers its price assuming that the
  original firm will not change its price again.
• Etc.
• Every firm is surprised when the other firm
  retaliates.
• Result Price shading continues until the firms
  price at or (temporarily) below MC

24
Price shading
25
Solution to Hotelling dilema

• Heterogeneous products create stability with
  firms clustered at the market center

26
Travel to shop behavior

• Multi-stop shopping
• Multi-purpose shopping
• Commuter shopping (trip chaining)
• Economies of retail agglomeration

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Mathematical Appendix

• Demand Q  5 - ½ P
• Inverse Demand Solve for P
• P  10 - 2Q
• Mill price 4, transport costs per unit of
  distance 75, Price-distance function is
  P  4  0.75 D

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Figure 2-1

• Inverse Demand P  10 - 2Q
• Mill price 4, transport costs per unit of
  distance 75, the price-distance function
  P  4  0.75 D
• Radius of a market area
• 4  0.75 D  10, and D8

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Figure 2-2

• Mill price 4
• PD1  4  0.75 D
• D 8
• Mill price 6
• PD2   6  0.75 D
• D 5.33
• Mill price 2
• PD3  2  0.75 D
• D 10.67

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Figure 2-3

• Transport costs 0.75/unit of distance
  PD1  4  0.75 D
• Transport costs 1.50/unit of distance
  PD2  4  1.5 D
• Transport costs 0.50/unit of distance
  PD3  4  0.5 D

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Figure 2-7

• Limit Price 10 the market area radius 8
  When demand changes
• Price-distance function P  4  0.75 D
• Limit Price 12, market area radius 10.67
• Limit Price 6, the market area radius 2.67

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Figure 2-9

• Price-distance functions for C and D intersect at
  6.55
• The break-even point is 10.2 units of distance
  right of C (where 4  0.25 D  2.55, or
  D  2.55/0.25  10.2) and 1.7 units to the left
  of D (where 4  1.5D  2.55, or
  D  2.55/1.5  1.7).
• Similarly, the price-distance functions equate to
  the right of D at 7.57, a point 2.38 units to
  the right of D, and 14.28 units right of C.