# PAUL.S.CALEM DANIEL.F.SPULBER.   This paper examines two part pricing by a multiproduct monopoly and a differentiated oligopoly.  Two part pricing.

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PAUL.S.CALEM DANIEL.F.SPULBER

  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. INTRODUCTION

  We see that although competition lowers unit prices, it doesn’t have a tendency to reduce entry fee.  Start with single representative consumer, model 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)

  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) TWO PART TARIFF MODEL

  (1b) can be written as  (1c) can be written as

  Let, i=1,2 solve (1a) 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)

  The gains from trade from purchasing good j along 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 from purchasing j, will exceed his demand for good i when he is not excluded from purchasing good j, qi(p1,p2) iff goods are substitutes.

  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)  MULTIPRODUCT MONOPOLY

  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.

  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) OLIGOPOLY

  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.

  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 TWO PART TARIFFS WITH HETEROGENEOUS CONSUMERS

  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:  (16) FOC: (17)

  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.

  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. CONCLUSION

  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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