#### Transcript MULTIPRODUCT TWO PART TARIFFS

```PAUL.S.CALEM
DANIEL .F.SPULBER
INTRODUCTION

 This paper examines two part pricing by a
multiproduct monopoly and a differentiated
oligopoly.
 Two part pricing policies depend on whether
products are complements or substitutes and on
whether market is segmented.
 Unit pricing markups shown proportional to
demand elasticities as in Ramsey pricing rule.

 We see that although competition lowers unit prices,
it doesn’t have a tendency to reduce entry fee.
extended to two consumer types.
 Oligopoly equilibrium unit prices equal marginal
cost when there is one consumer type, whether
products are complements or substitutes
 Complements: multiproduct monopolist who can’t
bundle sets unit price>Marginal cost

Multiple consumer types: given normality condition
 Unit prices exceed marginal costs at oligopoly
equilibrium.
 Monopolist producing substitutes sets unit price
above marginal cost.
 Single product monopolist sets unit price above
marginal cost given two consumer types if
consumer’s demand curves do not intersect.(Oi 1971)
TWO PART TARIFF
MODEL

 U(q1, q2) + q0 ;
q1, q2= qty of goods,
q0=numeraire good ,
 The two part tariff for good i=1,2 is (pi,Ei) where
pi is the unit price and Ei is the lump sum charge.
 Consumer’s net surplus exclusive of lumpsum charges for
purchase of one or both goods:
(1a)
 (1b) can be written as
 (1c) can be written as


, i=1,2 solve (1a)
 Let
solve (1b) and
solve (1c).
 If consumer purchases both goods, there must be
positive consumer surplus and gains from trade.
 Both goods purchased iff (2a), (2b) and (2c) hold.
f(p1,p2)-E1-E2 ≥ 0;
(2a)
f(p1,p2)-E1-E2 ≥ f1(p1)-E1
(2b)
f(p1,p2)-E1-E2 ≥ f2(p2)-E2
(2c)

with good i, f(p1,p2)-fi(pi) will exceed surplus from
purchasing only j, fj(pj) iff products are complements
 The consumer’s demand for good i when excluded
will exceed his demand
for good i when he is not excluded from purchasing
good j, qi(p1,p2) iff goods are substitutes.
MULTIPRODUCT
MONOPOLY

 Two part pricing by multiproduct monopolist not
allowed to bundle, i.e must price and sell products
separately.
 Monopolist needs to set separate two part tariffs for
each product.
 One type of customer, multiproduct monopolist
chooses (pi,Ei),i=1,2 to max profit ∏ subject to (2a)(2c): (3)


 Where ci(qi),i=1,2 is production cost.
 Suppose q1,q2 are complements: acc to lemma 1
Hence ,monopolist’s pricing problem given by (4)

 Using Roy’s identity and consumer’s problem (1a)(1c), FOC for the monopolist: (5)
Also,
Hence if the products are complements ,the monopolist
sets price =MC and extracts all of the consumer surplus.

 Suppose q1,q2 are substitutes: by lemma 1
(6)
Thus given
monopolist maximizes profit sub
to (2a)-(2c) by setting
i.e monopolist doesn’t extract all of the consumer
surplus.
 Bundling helps extract all of the consumer surplus
and increases profits if goods are substitutes.

 From (6) ,monopolist’s pricing problem:
(7)
Where
Using Roy’s identity and consumer problem, FOC for 6
(8)

 Solving for relative markup yields:
(9)
Where:
is the own or cross elasticity of dd.
and
Hence, when products = substitutes, price above MC.
OLIGOPOLY

 Consider a Nash equilibrium
with two
part pricing firms each producing a differentiated
product.
maximizes
(10)
subject to
and (2a)-(2c); similarly for firm2
 The profit maximizing choices of
given
and
can be shown to satisfy:
(11)


 q1 and q2 are complements:
(12)
Thus the two firms divide the entire consumer surplus
between them.
Prices
solve
and
(13)

 Goods are substitutes:
(14)
 The Nash equilibrium unit prices differ from
multiproduct monopoly when goods are substitutes.
 Hence unit prices < monopoly prices

 However Nash equilibrium entry fees may be
greater than under monopoly since
is increasing in and decreasing in ,similarly for E2
 For a two part pricing oligopolist, when goods are
substitutes and consumers are identical ,unit price is
only strategic variable and equilibrium unit prices
determined by equation 13.
TWO PART TARIFFS WITH
HETEROGENEOUS
CONSUMERS

 MULTIPRODUCT MONOPOLY:
Let
and we define
as before. There are two types of consumers,
A>B.
 Goods are complements and increasing and normal
in α.Also assume
that is relative benefits from consuming both goods
increase with α.
 Total demand

 Given non exclusion to maximize profit,monopolist
chooses
subject to(2a)-(2c) for each type
of α.
(15)
The entry fees =relative benefits of consuming both
goods for group of consumers with lowest α.

 Monopolist’s profit max problem:

FOC: (17)
(16)

 Hence monopoly prices>MC when products are
substitutes.
 OLIGOPOLY:
consider Nash equilibrium where no consumers are
excluded. Entry fee at Nash equilibrium equals
hence Nash equilibrium
unit prices satisfy:
(18)

 or
(19)
Where
Since
by normality ,Nash
equilibrium unit prices exceed marginal costs when
there are two types of consumers.
 Firms recognize different returns from two part
pricing from two consumer types.
 with one type of consumer, reduced returns from an
increase in price over marginal cost cancels out
returns from increase in entry fee.

 Given strong substitutability:
(20)
Nash equilibrium unit prices lower under two part
pricing than uniform pricing.Multiproduct monopoly
prices can be higher under two part pricing, hence,
multiproduct monopoly two part pricing results in
higher unit prices than Nash equilibrium.
Competitor ignores cross price effects on demand and
entry fees,this lowers Marginal revenue of competitor
w.r.t monopolist.
CONCLUSION

 Identical consumers: Nash equilibrium unit prices equal
marginal cost whether complement or substitute.
 Two part pricing multiproduct monopoly: sets unit price
above marginal cost when substitutes.
 identical consumers: Nash equilibrium entry
fees=consumers gains from trade when product are
substitutes.
 When goods are complements: firm captures consumer’s
entire surplus net of expenditures on rival’s profit.

 Non identical consumers:multiproduct normality
condition ensures that nash equilibrium unit prices
exceed marginal costs.When products are
substitutes,nash equilibrium also guarantees that
multi product monopolies sets unit prices above
marginal costs.
 Hence market structure is really important in a
firm’s pricing behaviour.
THANK YOU

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