Chapter 25: Monopoly Behavior - PDF Free Download

Econ 401 Price Theory Chapter 25: Monopoly Behavior Instructor: Hiroki Watanabe Summer 2009 1 / 46 1 Introduction 2 First-degree Price Discrimination Optimal Pricing Welfare Property 3 Third-Degree Price Discrimination Optimal Pricing: Equate Marginal Revenue 4 Two-Part Tariffs Definition Implication 5 Monopolistic Competition Monopolistically Competitive Environment Monopolistic Competition Is Not Efficient 6 Summary 2 / 46

So far a monopoly has been thought of as a firm which has to sell its product at the same price to every customer. Uniform pricing. Q: Does a monopolist really charge the same price for anyone at anytime in anywhere? 3 / 46 4 / 46

Three Types of Price Discrimination 1 1st-degree: Each output unit is sold at a different price. Prices may differ across buyers. 2 2nd-degree: The price paid by a buyer can vary with the quantity demanded by the buyer. But all customers face the same price schedule. E.g., bulk-buying discounts. 3 3rd-degree: Price paid by buyers in a given group is the same for all units purchased. But price may differ across buyer groups. E.g., senior citizen and student discounts vs. no discounts for middle-aged persons. 5 / 46 group-wise PD no group-wise PD PD w/ quantity 1st degree PD 2nd degree PD no PD w/ quantity 3rd degree PD Ch24 6 / 46

1 Introduction 2 First-degree Price Discrimination Optimal Pricing Welfare Property 3 Third-Degree Price Discrimination Optimal Pricing: Equate Marginal Revenue 4 Two-Part Tariffs Definition Implication 5 Monopolistic Competition Monopolistically Competitive Environment Monopolistic Competition Is Not Efficient 6 Summary 7 / 46 Optimal Pricing Each output unit is sold at a different price. Price may differ across buyers. The monopolist should be able to discover 1 the buyer with the highest valuation of its product, 2 the buyer with the next highest valuation, 3 and so on to engage in 1st-degree price discrimination. 8 / 46

Optimal Pricing 9 / 46 Optimal Pricing Figure: 10 / 46

Optimal Pricing 11 / 46 Welfare Property Figure: First-degree price discrimination gives a monopolist all of the possible gains-to-trade, leaves the buyers with zero surplus. Is the outcome efficient? (more on this in Ch16) It is. It just doesn t seem fair (more on equity in Ch31). 12 / 46

1 Introduction 2 First-degree Price Discrimination Optimal Pricing Welfare Property 3 Third-Degree Price Discrimination Optimal Pricing: Equate Marginal Revenue 4 Two-Part Tariffs Definition Implication 5 Monopolistic Competition Monopolistically Competitive Environment Monopolistic Competition Is Not Efficient 6 Summary 13 / 46 Optimal Pricing: Equate Marginal Revenue Price paid by buyers in a given group is the same for all units purchased. But price may differ across buyer groups. A monopolist manipulates market price by altering the quantity of product supplied to that market. Note unlike 1st-degree price discrimination, firm cannot set the price respectively for each quantity. A monopolist can set the desired price by adjusting local quantity supplied for each group. Assume marginal cost is constant for the following. 14 / 46

Optimal Pricing: Equate Marginal Revenue Suppose there are two markets for Metrolink: students and adults. Let y S and y A denote the transaction volume in each market. Aggregate transaction volume: Y = y S + y A. Metrolink s profit maximization problem w/ 3rd degree price discrimination: max π(y S, y A ) = MWTP S (y S )y S +MWTP A (y A )y A TC(y S +y A ). y S,y A 15 / 46 Optimal Pricing: Equate Marginal Revenue First order condition is the same as before: MR S (y S ) = TC(y S + y A ) y S MR A (y A ) = TC(y S + y A ) y A Note additional cost of serving one more student is same as additional cost of serving one more adult. MR S (y S ) = TC(y S + y A ) y S = MR A (y A ) = TC(y S + y A ) y A. In addition to first order condition, Metrolink engaged in 3 PD satisfies MR S (y S ) = MR A (y A ). 16 / 46

Optimal Pricing: Equate Marginal Revenue What if MR S (y S ) > MR A (y A )? Metrolink transfer some y A to y S. The total cost is the same (MC(y S ) is cancelled by the equal amount of MC(y A )) but they will have larger revenue (MR S (y S ) > MR A (y A )). (In effect, instead of segmenting the seats for students and adults, they charge different price in the beginning. Metrolink slightly leans toward 1st-degree price discrimination, but still they can t charge different price among students). 17 / 46 Optimal Pricing: Equate Marginal Revenue 18 / 46

Recall from Ch24: MR(y ) = p 1 1, ε(y ) (called Ramsey rule). Since MR S and MR A are equated at the optimal amount, 1 1 p 1 S ε S (y S ) = p 1 A ε A (y A ). 19 / 46 Suppose that p S > p A, then p A 1 1 ε A 1 1 ε S > p A 1 1 ε A > 1 1 ε S 1 ε A < 1 ε S ε A > ε S. Metrolink charges higher price for a group with inelastic demand. 20 / 46

Discussion: Ramsey Rule and Equity While the theory implies that Ramsey rule maximizes monopolistic profit, it is often criticized by politicians. Why? 21 / 46 Example Suppose Metrolink faces MWTP S (y S ) = 5y S + 12, MR S (y S ) = 10y S + 12, MWTP A (y A ) = y A + 8, MR A (y A ) = 2y A + 8, MC(y) = 2. How service do they provide for each (y S, y )? What is A the elasticity at y S and y A? 22 / 46

Price ($) 12 11 10 9 8 7 6 5 4 3 2 1 Metrolink s Supply MWTP S (y)= 5y+12 MR S (y)= 10y+12 MWTP A (y)= y+8 MR A (y)= 2y+8 MC(y)=2 0 0 1 2 3 4 5 6 Passenger (y) 23 / 46 Elasticity: ( 5y ε S (y S ) = S + 12)/y S ( y 5 and ε A (y A ) = A + 8)/y A 1. Metrolink charges students more while ε S (y S = 1) = 1.4 > ε A (y A = 3) 1.66. 24 / 46

1 Introduction 2 First-degree Price Discrimination Optimal Pricing Welfare Property 3 Third-Degree Price Discrimination Optimal Pricing: Equate Marginal Revenue 4 Two-Part Tariffs Definition Implication 5 Monopolistic Competition Monopolistically Competitive Environment Monopolistic Competition Is Not Efficient 6 Summary 25 / 46 Definition Recall how Sprint charge the for minutes exceeding anytime minute. Even if you do not make a single phone call, you have to pay the monthly charge. Why does t Sprint engage in 1st degree price discrimination? The way Sprint constructs its price schedule is called two-part tariffs. Two-Part Tariffs A two-part tariff is a lump-sum fee, p 1, plus a price p 2 for each unit of product purchased. Greg, in effect, has to pay p 1 + p 2 y dollars to consume y. 26 / 46

What is the optimal lump-sum fee p 1 and unit price p 2? The maximum gains from trade greg can enjoy are CS. So if Sprint sets p 1 = CS, then Greg becomes indifferent between making a contract and not making a contract. If Sprint charges more than CS, then Greg won t make a contract and Sprint gets nothing. Think of p 1 as the market entrance fee. 27 / 46 Where should Sprint set the unit price p 2? MR(y ) = MC(y ) and p = MWTP(y )? 28 / 46

29 / 46 Figure: Note Greg is indifferent between consuming y = y or y = 0. He will get no consumer s surplus in either case. How about p = MC(y) instead? 30 / 46

31 / 46 Figure: 32 / 46

Implication The optimal pricing strategy for two-part tariffs: 1 Set lump-sum fee (or entrance fee) at p 1 = CS(y ). 2 Set unit price at p 2 = MC(y ) There is no consumer s surplus and Sprint takes 100% of total surplus. Compared to uniform pricing (Ch24), two-part tariffs make: 1 consumer s surplus smaller (down to zero) 2 producer s surplus larger 3 total surplus larger (completely eliminates the deadweight loss) Two-part tariffs are efficient but probably not fair (more on this in Ch31). 33 / 46 Implication Example 2 (Increasing MC, cont d from Ch24) For Sprint MWTP(y) = y + 12, MR(y) = 2y + 12 and MC(y) = 2y, compute producer s surplus they introduce two-part tariffs and compare it to PS when they charge their customers uniformly. Steps: 1 Find the target production level y by MWTP(y ) = MC(y ) and obtain p 2 = MWTP(y ). 2 Compute CS(ish) above and set p 1 = CS(ish). 3 Compute regular PS and add it to CS(ish) to find true PS. 34 / 46

Implication 1 (y, p ) = (4, 8). 2 CS(ish) = 8 so that p 1 = 8 as well. 3 True PS = 8 + 16 = 24 (w/ TS = 24). PS = 18 when Sprint charges uniform price (w/ TS = 22.5) 35 / 46 Implication Price ($) 12 11 10 9 8 7 6 5 4 3 2 1 Metrolink s Supply Demand MWTP(y)= y+12 MR(y)= 2y+12 MC(y)=2y 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Passenger (y) 36 / 46

1 Introduction 2 First-degree Price Discrimination Optimal Pricing Welfare Property 3 Third-Degree Price Discrimination Optimal Pricing: Equate Marginal Revenue 4 Two-Part Tariffs Definition Implication 5 Monopolistic Competition Monopolistically Competitive Environment Monopolistic Competition Is Not Efficient 6 Summary 37 / 46 Monopolistically Competitive Environment What do we really mean by monopoly? Metrolink the exclusive provider of public transportation. But then cars are its substitutes. In many markets the commodities traded are very close, but not perfect, substitutes. Each individual supplier thus has some slight monopoly power. What does an equilibrium look like for such a market? 38 / 46

Monopolistically Competitive Environment Monopolistic Competition In a monopolistically competitive market, 1 Free entry. 2 Monopolistic pricing (Ramsey condition). 3 Less than perfect substitutes between commodities. Implications: 1 Zero profit (like perfect competition in the long run). 2 MR(y) = MC(y) (like monopoly). 3 Elastic (slightly downward-sloping) demand. 39 / 46 Monopolistically Competitive Environment 40 / 46

Monopolistic Competition Is Not Efficient Is a monopolistically competitive market efficient? No, because p > MC(y). 41 / 46 Monopolistic Competition Is Not Efficient 42 / 46

Monopolistic Competition Is Not Efficient Also, a firm is not producing at the level where unit production cost is minimized. 43 / 46 Monopolistic Competition Is Not Efficient 44 / 46