ernando Branco 006-007 all Quarter Sesson 5 Part II The olgopolstc markets There are a few supplers. Outputs are homogenous or dfferentated. Strategc nteractons are very mportant: Supplers react to each other decsons. Olgopoles are dversfed, complex but very relevant. Example: TV broadcasts. Strategc nteractons To fnd the best manageral decson the manager of an olgopolstc suppler needs to thnk about the compettors reactons f: He changes the prce? He changes the producton level? He ntroduces a new product? He changes the advertse budget?... 1
TV broadcasts The competton among RTP, SI and TVI s a good example of an olgopoly n Portugal. The role played by strategc nteractons s clear n the lne-up of programs. Is there one typcal olgopolstc market? The nature of strategc nteractons are very dversfed. Prces vs volume? Smultaneous vs sequental? Homogenous vs dfferentated outputs? The best manageral decsons depend heavly on key elements related to the nature of the strategc nteracton. ompettors follow prce decreases but not the ncreases: The Sweezy olgopoly There are a few supplers; Outputs are dfferentated; Each suppler beleves that compettors wll follow prce decreases, but not prce ncreases. There are barrers to entry. Motvaton: emprcal observaton.
A frm s demand n the Sweezy olgopoly P M P D D Q Q onclusons from the Sweezy olgopoly The prce and output levels are nsenstve to bounded changes on costs; Inerta of the equlbrum However, t s not explaned by the analyss. Rgdtes n prce and output levels n the Sweezy olgopoly P M P D D Q Q 3
ompetton through output/capacty: The ournot olgopoly There are a few supplers; Outputs are substtutes; Each suppler must take hs output decsons wthout knowng the others decsons. There are entry barres. Example: Openng new bank offces. Openng new bank offces The bankng sector was one of the most dynamc n Portugal durng the 1980s. One of the mportant competng dmensons was the openng of new offces. Between 1988 e 199 the number of offces grew by 75%. The development of the network of offces can reasonably be understood havng the ournot olgopoly as a reference. Supplers decsons n a ournot duopoly Each suppler maxmzes proft: Max Π = P ( q, q j q ( q MR q, q = M ( q ( j Reacton functon: q = R q ( j Output of a suppler, gven the other suppler s output. Inverse relatonshp. 4
Supplers decsons n a ournot duopoly: algebrac approach Demand: P ( Q = a b( + q osts: ( q = cq a bq bq j = c a c q j Reacton functon: q = b ( a b( q + q j q cq Max Π = Supplers decsons n a ournot olgopoly: graphcal approach R 1 ( M R ( M Equlbrum n a ournot duopoly What s the output of each suppler? Each frm wll choose accordng wth ts reacton functon; Equlbrum: ntersecton of the reacton functons. Graphcal analyss Algebrac example 5
Equlbrum n a ournot duopoly: graphcal analyss R 1 ( M R ( M Equlbrum n a ournot duopoly: algebrac example a c q j Reacton functons: q = b Equlbrum: a c q q = a c 1 b q1 = 3b a c q 1 q = a c q = b 3b Impact of a change n costs What s the mpact of a reducton n costs of a suppler? hanges the reacton functon. In the equlbrum, that suppler wll ncrease the output, whle the other wll reduce t. 6
A change n costs: graphcal analyss R 1 ( R 1 ( M R ( M The ournot olgopoly n general Each suppler maxmzes proft: Max Π = P( Q q c q P P Q q p + q = c p = c Q 1+ Q p Q p c s = p ε Q, P ournot olgopoly, monopoly and competton If there are n equal supplers: 1 p c s = n p 1 n = ε If n equals 1: Monopoly Q, P As n ncreases: Approaches Perfect ompetton. 7
The tmng of the decsons In the ournot olgopoly, supplers decde wthout knowng the decsons of others. In some market a suppler leads, takng decsons frst. Example: Entry of new countres n EU. What s the equlbrum n an output settng olgopoly wth a leader? Entry of new countres n the EU When new countres are negotatng ther entrance n the European Unon, the exstng members play a leadng role n determnng the condtons that must be met before entry s granted. Durng the negotaton perod, countres play a dynamc game, where the EU countres act as leaders. ompetton through output/capacty: The Stackelberg olgopoly There are a few supplers; Outputs are substtutes; One suppler (the leader takes hs decson frst; The other supplers (the followers take ther decsons after learnng the leader s decson. There are barrers to entry. Example: Entry n a monopoly market. 8
Entry n a new market When a company s consderng to enter n a monopoly market, t should understand that the ncumbent wll have the opportunty to act as leader, settng hs choces n the market just before the entrant comes n. Analysng dynamc problems The Stackelberg olgopoly rases a dynamc problem: not all supplers decde at the same tme. The analyss of dynamc problems should be done backwards: In the Stackelberg olgopoly ths means analyzng the follower s decson frst and the leader s decson afterwards. The follower s decson n a Stackelberg duopoly The follower sets ts output to maxmze ts profts: Max Π = P ( q, q q ( q MR ( q, q = M ( q Reacton functon: q = R q ollower s optmal output level, gven the leader s output level. It s the same as n the ournot olgopoly. ( 9
The leader s decson n a Stackelberg duopoly The leader sets ts output to maxmze ts proft, takng nto consderaton the follower s reacton: Max Π = P ( q, R ( q q ( q MR ( q = M ( q The follower s decson n a Stackelberg duopoly: An algebrac example Demand: P ( Q = a b( q + q osts: ollower s problem: ( q = cq Reacton functon: a bq bq = c q ( a b( q + q q cq Max Π = a c q = b The leader s decson n a Stackelberg duopoly: An algebrac example eader s problem: a c q Max Π = a b q + q b a + c bq = c Optmal producton: a c q = b cq 10
The supplers decsons n a Stackelberg duopoly: A graphcal descrpton q R ( q q Equlbrum n a Stackelberg duopoly How much wll each suppler provde? The follower wll be on ts reacton curve; The leader wll choose the pont from the follower s reacton curve that yelds hm the hghest proft. A graphcal descrpton An algebrac example Equlbrum n a Stackelberg duopoly: A graphcal descrpton q q R ( q q q 11
Equlbrum n a Stackelberg duopoly: An algebrac example a c eader s producton: q = b ollower s producton: q a c 1 a c a c = = b b 4 b Stackelberg versus ournot How do the equlbrum outputs n the Stackelberg duopoly compare wth those on the ournot duopoly? The leader supples more whle the follower supples less; The leader makes more proft and the follower makes less proft than they would make n a ournot duopoly. Stackelberg versus ournot: A graphcal comparson q R ( q q q R ( q q q q 1