Monopoly. E. Glen Weyl. Lecture 8 Price Theory and Market Design Fall University of Chicago

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1 and Pricing Basics E. Glen Weyl University of Chicago Lecture 8 Price Theory and Market Design Fall 2013

2 Introduction and Pricing Basics Definition and sources of monopoly power Basic monopolistic incentive Lerner s mark-up pricing rule Today we ll introduce the idea of market power: monopoly 1 What is monopoly and why does it arise? Natural v. unnatural monopoly 2 pricing Quantity reduction Lerner s Mark-up rule Subtleties of pricing Ironing and empirical applications to ebay pricing 3 distortion and incidence Basic distortion Contrast to incidence under competition Pass-through under monopoly and demand curvature Applications of incidence logic Taxing foreign trade and creating new markets

3 and Pricing Basics When does monopoly apply? Definition and sources of monopoly power Basic monopolistic incentive Lerner s mark-up pricing rule sounds like this is the only company But basic mechanism applies to any non-price-taker Includes when company can affect purchase price More or less severe depending on size of distortion So when do we use monopoly v. oligopoly? 1 focuses on direct effects of interventions Effects through changes in other eq. behavior ignored takes these as fixed, changes small 2 ignores welfare effects on other firms Value to them ignored or pecuniary Cannot be used to think about cross-firm externalities 3 model cannot study changes in structure Useless for topics like merger analysis, effect of competition = Focus on incentives of one firm, input to other analysis

4 and Pricing Basics Unnatural monopoly Definition and sources of monopoly power Basic monopolistic incentive Lerner s mark-up pricing rule What causes firm to have market power? Unnatural v. natural 1 Intellectual property Either private trade secrets or government protection Focus of our Tuesday s lecture 2 Lobbying and protection Very harmful, both from static and dynamic perspective Try to stop by restrictions on lobbying 3 Private/illegal violence Mafia has gained monopoly through intimidation Gambling, other sin industries, etc. Should be solved through law enforcement 4 Advantage/first-to-market/talent Resolves itself in time, but how long? Transparency, low bureaucracy helps aid entry

5 Natural monopoly and Pricing Basics Definition and sources of monopoly power Basic monopolistic incentive Lerner s mark-up pricing rule Things are tricker when monopoly inevitable or natural? 1 Economies of scale through full range sufficient If large firms always more efficient... Then it never makes sense to have more than one Most common case for natural monopoly 2 But not necessary: sub-additivity is requirement Any two operations more efficient when combined Can occur without global economies Crucial: size of market relative range of economies If economies only when small, natural only in small market Some examples of natural monopolies? 1 Electrical utilities 2 Social or telephone networks (absent interconnection) 3 Monitoring income (government supply of public goods) 4 Public transportation in many settings

6 and Pricing Basics Definition and sources of monopoly power Basic monopolistic incentive Lerner s mark-up pricing rule Quantity reduction and marginal revenue Basic idea: monopolies reduce quantity to raise price To sell more, price must fall on all infra-marginal units = Trade-off between selling more and higher price Maximize π(q) = P(q)q C(q); but don t set P = MC Instead set MR = MC: MR formula? MR(q) = P(q) } {{ } + P (q)q } {{ } good, competitive market power/cournot distortion Distortion is proportional to: 1 The number of units you sell If you are small part of industry, small impact 2 The amount you move the price If industry impact on price is small, distortion small Distortion proportional to bigness, elasticity (soon)

7 and Pricing Basics Definition and sources of monopoly power Basic monopolistic incentive Lerner s mark-up pricing rule Graphical examples of marginal revenue

8 and Pricing Basics Lerner s mark-up pricing rule Another way to write MR is P(q) Definition and sources of monopoly power Basic monopolistic incentive Lerner s mark-up pricing rule ( ) 1 1 ɛ(q) ; why? ɛ = dq p dp q so 1 ɛ = dp q dq p So P ɛ = P q = MR P = Marginal revenue is negative if ɛ < 1 = Elasticity of demand determines level of prices Summarizes bigness in market, substitution to other goods Rearranging yields canonical formula: Lerner s elasticity pricing rule p MC p = 1 ɛ Can be problematic measure when price negative Credit cards have market power, but negative cost = Subsidies consumers to profit from merchants Better to use absolute mark-up P q in this case

9 and Pricing Basics Wrinkles on monopoly pricing Ironing The monopoly distortion Uncertainty and learning about demand Simple story, but applies even with several wrinkles: 1 What if demand is not known We have assumed simple price-quantity relationship When demand uncertain, choose both price and quantity Still, Lerner rule based on costs and elasticity: Average quantity sold, not average quantity produced Uncertainty just raises cost of sales, demand function 2 Learning about demand To avoid this, choose right price, learn about demand Try charging various prices, see what happens Base price on past experience Even more creative idea (Segal 2003): current experience Everyone reports values, used to form demand curve Gets object if value above monopoly optimal price v. others

10 and Pricing Basics Wrinkles on monopoly pricing Ironing The monopoly distortion Einav et al. (2013) analysis of seller experiments One place where learning is very easy is the internet Einav et al. collect data from seller experiments on EBay Many seller try identical items at different prices Trying to figure out what price to charge, terms to use Just like they should do to learn Use to construct demand curve in auctions? Higher reserve price set = higher price if sale If higher than bid of second highest, raises price Also reduces probability of sale If no one bids above, no sale occurs = Just like a demand curve Draw out average price, probability of sale relationship Marginal cost always constant (probability of sale) Basic shape very similar across products

11 Einav et al. data and Pricing Basics Wrinkles on monopoly pricing Ironing The monopoly distortion Measured demand curves Fit marginal revenue Ironing line Fit demand curve

12 and Pricing Basics Wrinkles on monopoly pricing Ironing The monopoly distortion The ironing procedure and other applications However, marginal revenue curve not decreasing! = Multiple intersections with constant marginal cost How to find a solution? Which one is right one? Profit is area between MR and MC We lose are above MR and below MC So if we draw line, choose based on larger area This suggests procedure for getting rid of non-montonicity 1 Take point where equal area above and below, draw line 2 Below this ironing line choose right; above choose left 3 Monopolist behaves exactly as if this was MR Notice that this means small MC = q, p jump Never sell quantities in ironed-over region This ironing can be applied much more broadly Anytime concavity (or stability?) fails, iron out Makes problem simpler to analyze

13 and Pricing Basics The monopoly wedge Wrinkles on monopoly pricing Ironing The monopoly distortion raises prices above costs; two effects: 1 Transfers wealth from consumer to monopoly Distributive problems, but no net social loss 2 Reduces quantity of goods consumed Some individuals would be willing to buy at cost But don t because price is higher = Deadweight loss from monopoly Monopolist raises prices on all to charge infra-marginal If could tell who is who, price discriminate, no distortion = Consumer purchases create externality, firm profits Internalize with Pigouvian subsidy? Problems in Lecture 12 Mandate higher quantity, lower price? More on Tuesday Anything that makes consumers value more good here For example, deceptive advertising...

14 and Pricing Basics The deadweight loss triangle Wrinkles on monopoly pricing Ironing The monopoly distortion To measure these losses we consider standard welfare triangle Like distortions from tax: externality loss same as tax loss Only difference is size determined by monopoly s optimum = Particular size, relationship to monopoly profits We ll explore this in a bit Two different expressions, as usual: 1 2 q q M P(qM ) MC(q M ) P(q) MC(q)dq min {S(p), D(p)} dp Similarly profits can be area above MC plus: 1 Square of price above MC 2 Or area between MR and MC Also CS is between P and MR, or above price

15 and Pricing Basics under monopoly Basic principles of monopoly incidence Pass-through Applications of monopoly incidence This makes monopoly incidence fundamentally different 1 Still, physical and economic incidence independent p final to consumers, ρ pass-through 2 But now, tax not just split; excess burden Firm chooses q to maximize profits [P(q) t] q C(q)? By envelope theorem, hold fixed q in dπ dt = Firm bears full burden q But consumer still loses ρq; ρq is excess burden 3 I = ρ 1 = ρ This can be integrated just as before = I = CS PS = ρ

16 and Pricing Basics Basic principles of monopoly incidence Pass-through Applications of monopoly incidence Graphical representation of monopoly incidence

17 and Pricing Basics Basic principles of monopoly incidence Pass-through Applications of monopoly incidence Exogenous competition and social incidence Tax moves CS, PS both down, but raises DWL What about something that moves DWL and PS down? This is useful for measuring relative size of these Let s focus on simple case of constant marginal cost c Suppose a firm comes in to compete Exogenously produces quantity q, total q Profits are P(q) (q q) C(q), FOC P + P (q q) = MC? = q equivalent to tax of P, so dp d q = P ρ Equivalently dq d q = ρ Again by envelope hold q fixed in dps d q Marginal DWL is M(q) so ddwl d q We can define social incidence ddwl d q = ρm(q) = M(q) P(q) c dps d q = ρ To integrate up for DWL PS weight by mark-ups, ρ

18 and Pricing Basics Pass-through under monopoly Basic principles of monopoly incidence Pass-through Applications of monopoly incidence Under monopoly, logic of incidence differs in two ways 1 Now MR not D, so pass-through depends on curvature 2 Deadweight loss = incidence not just split (excess) Let s first consider pass-through MR(q) = MC(q) + t so MR (q) dq dt = MC (q) dq dt + 1 P (q) MR (q) MC (q) = dq 1 dp dt = MR (q) MC (q) so ρ = dt = Recall MR(q) = P(q) + P (q)q and let MS(q) P (q)q Identify MC with supply then MC (q) = P qɛ S, P (q) = P This gives ρ = P qɛ ( D ) MS (q) P + MC qɛ D P P qɛ S 1 1+ ɛ D 1 ɛ S + 1 ɛ MS, ɛ MS is elasticity of inverse MS qɛ D

19 and Pricing Basics Basic principles of monopoly incidence Pass-through Applications of monopoly incidence Interpreting pass-through and curvature 1 How should we interpret ɛ MS? Measures demand curvature > 1 for concave, 1 linear, 0 negative exponential Log-convex (constant elasticity) makes If negative enough, ρ can be infinite, as in Einav et al. So in addition to elasticities, now care about curvature Intuitively, how should we think about this? Measures how much valuation out in the tails Inelasticity variance of valuations Curvature kurtosis Related to power laws: fat tail = 1 ɛ MS very negative More of a power law among very rich (ɛ MS α) Income generates values = 1 ɛ MS more for luxuries Similarly products with niche appeal More mass-market is +

20 and Pricing Basics Basic principles of monopoly incidence Pass-through Applications of monopoly incidence Graphical representation of pass-through

21 and Pricing Basics Applications of incidence Basic principles of monopoly incidence Pass-through Applications of monopoly incidence Let s go back to a few applications of incidence logic 1 Optimal taxation of foreign trade? Government gains D, domestic loses ρ (D + td ) Optimum is t p = 1 ρ ρɛ D 1 ɛ S if foreign monopolist = Logic based on incidence robust (also for oligopoly) 2 Creating a new market Again, suppose project to create market? Common example with monopoly: auction off concession What are biases of private profit only? Again incidence; now 1 + ρ v. 1 rather than 1 v. 1 ρ Favor/subsidize projects with niche markets, high income When competitive instead about elasticities Same basic logic as before, just difference ρ Lesson: much added by market power summarized in incidence

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