5/2/2016. Intermediate Microeconomics W3211. Lecture 22: Game Theory 4 Not Really Game Theory. The Story So Far. Today. Two Part Tariff.

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1 Intermediate Microeconomics W3 Lecture : Game Theor 4 Not Reall Game Theor Introduction Columbia Universit, Spring 06 Mark Dean: The Stor So Far. 3 Toda 4 Last lecture we compared the behavior of a monopolist to oligopolists who competed on quantit When we thought about the monopolist, we restricted the tpes of thing the could do The were allowed to pick the per unit price at which the sold their product Each unit sold at the same price, regardless of who bought it No additional charges or fees We are going to think about other sneak things that a monopolist could do. Two part tariff. Price discrimination 6 Think of a monopolist who has costs of producing given b And faces a demand curve given b Monopol Behavior : Two part tariff We showed last lecture that if the firm chooses to maximize Then the will set marginal revenue equal to marginal costs 5 4

2 Surplus under Monopol 7 Surplus under Monopol 8 p m p m Consumer surplus Producer surplus Marginal Revenue Demand Marginal Cost Marginal Revenue Demand Marginal Cost m m Monopolies 9 Surplus under Monopol 0 Here is another strateg Charge the consumer a fixed fee F to be allowed to bu stuff from ou at all After the have paid F, the consumer can bu as much as the like at a price equal to our marginal cost c=p e e How much profit does the firm make before charging F? Zero! Revenue = p=c Cost = c Consumer surplus So all profits come from F c=p e What is the largest F the can charge? Well, think back to consumer surplus We said that the consumer surplus of output at price p is the amount that the consumer would be prepared to pa to bu that amount at that price e So that is the maximum amount that the firm could charge

3 3 4 The consumer surplus of selling at price c is equal to What is going on here? The strateg of selling at is inefficient Does not maximize total surplus This is the maximum amount of profit the firm could make Greater than what the would get from selling at and charging no fee! Surplus under Monopol 5 6 p m Consumer surplus Producer surplus Inefficienc What is going on here? The strateg of selling at is inefficient Does not maximize total surplus The strateg of selling at c is efficient It is the outcome we would expect from perfect competition Maximizes total surplus m 7 8 Consumer surplus What is going on here? The strateg of selling at is inefficient Does not maximize total surplus c=p e The strateg of selling at c is efficient It is the outcome we would expect from perfect competition Maximizes total surplus So with a two part tariff the monopol can Maximize total surplus Extract all of it with the up front fee! e Real life examples? Mobile phones? TV bundles? 3

4 How Should a Monopolist Price? 0 So far a monopolist has been thought of as a firm which has to sell its product at the same price to ever customer. This is uniform pricing. Monopol Behavior : Price Discrimination In particular: if monopolist lowers the price for some customers, it must lower it for everone Can price-discrimination earn a monopolist higher profits? 9 Tpes of Price Discrimination st-degree: Each output unit is sold at a different price. Prices ma differ across buers. Perfect, or personalized price discrimination nd-degree: The price paid b a buer can var with the quantit demanded b the buer. All customers face the same price schedule, but per unit price is different depending on how much ou bu Product versioning or menu pricing Each output unit is sold at a different price. Price ma differ across buers. Think of the demand curve as coming from man different individuals with different willingness to pa 3rd-degree: Price paid b buers in a given group is the same for all units purchased. But price ma differ across buer groups. Group pricing /output unit Sell the th unit for p( ) p ( ). MC() 3 /output unit Sell the th unit for p ( ). Later on sell the th unit for p ( ). p( ) p ( ) MC() 4 p() p() 4

5 /output unit Sell the th unit for p ( ). Later on sell the th unit for p ( ). Finall p( ) sell the th unit for marginal p ( ) cost, p ( ). MC() p ( ) 5 The gains to the monopolist on these trades are: p ( ) MC ( ), p ( ) MC ( ) p( ) and zero. /output unit p ( ) p ( ) MC() 6 p() p() The consumers gains are zero. So the sum of the gains to the monopolist on all trades is the maximum possible total gains-to-trade. /output unit 7 The monopolist gets the maximum possible gains from trade. /output unit 8 PS MC() PS MC() p() p() First-degree price discrimination is efficient but bad for consumers! 9 Second-degree Price Discrimination 30 First-degree price discrimination gives a monopolist all of the possible gains-to-trade, leaves the buers with zero surplus, and supplies the efficient amount of output. Real world example? Hard for monopolists to do this. Requires Can identif the willingness to pa of all consumers Can charge different consumers different prices No reselling Second-degree price discrimination is when all customers have access to the same price schedule, but consumers self-select Unlike first example, cannot explicitl charge different prices to different people Idea: Monopolist differentiates b offering to high-willingness-topa customers a high price, and to low-willingness-to-pa customers a lower price but also lower qualit 5

6 Second-degree Price Discrimination 3 3 Example? TV Bundles If ou bu just the sports package, then this is quite expensive If ou bu sports and movies both become cheaper Someone who cares onl about sport pas a higher price Someone who cares about movies (and so has the movie channel) faces a lower price for sports Ke is to make bundles incentive compatible People bu the packages the are supposed to As ou will see for homework Price paid b buers in a given group is the same for all units purchased. But price ma differ across buer groups. Cannot change different prices to everone Can charge different prices to different groups A monopolist manipulates market price b altering the quantit of product supplied to that market. So the question What discriminator prices will the monopolist set, one for each group? is reall the question How man units of product will the monopolist suppl to each group? For given suppl levels and the firm s profit is (, ) p( ) p( ) c( ). What values of and maximize profit? Two markets, and. is the quantit supplied to market. Market s inverse demand function is p ( ). is the quantit supplied to market. Market s inverse demand function is p ( ). (, ) p( ) p( ) c( ). The profit-maximization conditions are 35 p p c ( ) ( ) 36 p ( ) c( ) ( ) and c( ) ( ) p ( ). 6

7 p p c ( ) ( ) 37 p p c ( ) ( ) 38 MR ( ) = MR ( ) sas that the allocation, maximizes the revenue from selling + output units. E.g., if MR ( ) > MR ( ) then an output unit should be moved from market to market to increase total revenue. The marginal revenue common to both markets equals the marginal production cost if profit is to be maximized Market Market Market Market p ( *) p ( ) p ( *) p ( ) p ( *) p ( ) p ( *) p ( ) MC MC MC MC * * MR ( ) MR ( ) MR ( *) = MR ( *) = MC * * MR ( ) MR ( ) MR ( *) = MR ( *) = MC and p ( *) p ( *) 4 4 In which market will the monopolist cause the higher price? In which market will the monopolist cause the higher price? Recall that and MR( ) p( ) MR( ) p( ). 7

8 In which market will the monopolist cause the higher price? 43 So * * p( ) p( ). 44 Recall that But, MR( ) p( ) and MR( ) p( ). * * * * MR( ) MR( ) MC( ) So * * p( ) p( ). 45 So * * p( ) p( ). 46 * * Therefore, p( ) p( ) if and onl if Therefore, * * p ( ) p ( ) if and onl if. So * * p( ) p( ). 47 Examples of 3 rd degree price discrimination? Can we think of examples? 48 Therefore, * * p( ) p( ) if and onl if. The monopolist sets the higher price in the market where demand is least own-price elastic. 8

9 Examples of 3 rd degree price discrimination? Can we think of examples? 49 Think of student discounts! One ma sa, these are nice gus that want to help students But in truth, this is a wa to price discriminate Students usuall have a lower available income, so their demand is more elastic (the won t pa too much) Summar Discrimination allows firm to charge more to non-students So this is not done to lower student s prices, but to increase the price to others!! Coherent with what we have seen: lower price to more pricesensitive group 50 Summar 5 Toda we have Modelled two was for monopolists to extract more profit Two part tariffs Price discrimination 9

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