Market Friction and Product Diversity

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Market Friction and Product Diversity
August 2004 Sung Hyun Kim Ewha Womans University
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Summary

• Ingredients
• Horizontal differentiation (Hotellings linear
  city model)
• Welfare effects of introducing a new product
• Market structure monopoly versus duopoly
• Friction positive cost of purchasing a new
  product
• Results
• - Frictionless Too much diversity both for
  monopoly and duopoly
• Friction Optimum diversity with duopoly
• Some implications
• - Online versus offline commerce

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2.1 Basic setup

• Consumers populated on 0, 1, unit demand,
  transportation cost t per distance, gross surplus
  of s from consumption
• Assumption 1. s gt 2t
• Seller located at point 0, MC 0
• Profit-maximization of monopolist p s t
• (extraction of surplus of marginal consumer)

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Consumer 0 (if p p) s p s s/2 s/2
s/2
t
Assumption 1. s gt 2t
Consumer y s p ty 0
By monopolists actual choice p s - t
y
1
0
marginal
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2.2 A second product by monopolist

• New product at point 1 (identical s)
• Fixed cost of developing the new product f
• Profit-max of 2-product monopolist
• p s t/2 (extraction of surplus of marginal
  consumer at point 1/2)
• Can charge a higher price than before
• (Better fit with consumers tastes)

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Surplus for consumers
t
1-product monopoly
(-)
t/2
t/2
2-product monopoly
()
1/2
1
0
marginal
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2.2 (continued)

• Assumption 2. t/4 lt f lt t/2
• Profit change t/2 f gt 0
• Welfare change t/4 f lt 0
• Consumers lose more than monopolists gain
• (Less travel, higher price fixed cost)
• Diversity offered, socially not desirable

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2.3 A second product by entrant

• Back to basic setup, an entrant at point 1
• After entry, Cournot competition in price
• Cournot-Nash equilibrium
• prices (incumbent, entrant) (t , t)
• Two firms divide the market equally

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s t
Surplus for consumers
t
duopoly
s t/2
t/2
t/2
1-product monopoly
2-product monopoly
1/2
1
0
marginal
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2.3 A second product by entrant

• Proposition 1. Under Assumptions 1 2
• overprovision Socially optimal number of
  product is 1, but 2 products are offered, either
  by monopolist or an entrant
• consumers prefer duopoly Consumer surplus is
  ordered
• Duopoly gt one-product monopoly gt two-product
  monopoly

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2.4 Digression incumbents reaction
Proposition 2. If allowed, the incumbent will buy
out the entrant, and become a two product
monopoly buyout price is between (t/2 f) and
t/2 hence, consumers are probably worse off
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3 Market friction

• Nature of friction
• Search cost? (Kim 01, Bakos 97, Harrington 02)
• Switching cost?
• Inertia?
• Any cost that a buyer faces in purchasing a newly
  introduced product
• Buyers surplus
• existing product s p ty
• new product s p ty c

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3.1 Friction and 2-product monopoly

• Location of marginal consumer
• s p0 tym s p1 t(1 ym) c
• Profit function p0ym p1(1 ym)
• Profit-max prices
• p0 s t/2 c/4 p1 s t/2 3c/4
• subsidy for
  friction cost
• Consumer price including friction
• p0 s t/2 c/4 p1 s t/2 c/4

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3.2 Friction and entry

• Cournot-Nash equilibrium prices
• (incumbent, entrant) (t c/3, t c/3)
• Location of marginal consumer (lt 1)
• (entry game) ½ c/6t
• (2-product monopoly) ½ c/4t
• diversity offer depends on c
• condition on c differs between monopoly and
  duopoly

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• Proposition 3. With friction,
• diversity offered when costs are low If c and f
  are sufficiently low, second product is offered
  either by monopolist or entrant
• with friction, f has to be lower the upper
  bound on f for which second product offered is
  lower than t/2 with friction
• entrant is more aggressive entrant may enter
  when monopolist would not offer a second product

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• Proposition 4. When a second product is offered
  with friction
• overprovision by incumbent When the incumbent
  offers it, welfare always decreases
• optimal provision by entrant When the entrant
  offers it, welfare increases
• Remark Friction improves situation even with
  monopoly when f is high, monopoly does not
  offer second product

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Some concluding thoughts

• Elimination of friction may lead to too much
  diversity (over-customization)
• Does e-commerce eliminate friction? (e.g. reduce
  buyers search cost)