# Economics 101A (Lecture 19) Stefano DellaVigna

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1 Economics 101A (Lecture 19) Stefano DellaVigna November 9, 2004

2 Outline 1. Monopoly 2. Price Discrimination 3. Oligopoly? 4. Game Theory

3 1 Profit Maximization: Monopoly Monopoly. Firm maximizes profits, that is, revenue minus costs: max y p (y) y c (y) Notice p (y) =D 1 (y) First order condition: or p 0 (y) y + p (y) c 0 y (y) =0 p (y) c 0 y (y) p = p 0 (y) y p = 1 ε y,p Compare with f.o.c. in perfect competition Check s.o.c.

4 Elasticity of demand determines markup: very elastic demand low mark-up relatively inelastic demand higher mark-up Graphically, y is where marginal revenue p 0 (y) y + p (y) equals marginal cost (c 0 y (y)) Find p on demand function

5 Example. Linear inverse demand function p = a by Linear costs: C (y) =cy, with c>0 Maximization: max y (a by) y cy Solution: and y (a, b, c) = a c 2b p (a, b, c) =a b a c 2b = a + c 2

6 s.o.c. Figure Comparative statics: Change in marginal cost c Shiftindemandcurvea

7 Monopoly profits Case 1. High profits Case 2. No profits

8 Welfare consequences of monopoly Too little production Too high prices Graphical analysis

9 2 Price Discrimination Nicholson, Ch. 13, pp [OLD: Ch. 18, pp ]. Restriction of contract space: So far, one price for all consumers. But: Can sell at different prices to differing consumers (first degree or perfect price discrimination). Self-selection: Prices as function of quantity purchased, equal across people (second degree price discrimination). Segmented markets: equal per-unit prices across units (third degree price discrimination).

10 2.1 Perfect price discimination Monopolist decides price and quantity consumer-byconsumer What does it charge? Graphically, Welfare: gain in efficiency; all the surplus goes to firm

11 2.2 Self-selection Perfect price discrimination not legal Cannot charge different prices for same quantity to AandB Partial Solution: offer different quantities of goods at different prices; allow consumers to choose quantity desired

12 Examples (very important!): bundling of goods (xeroxing machines and toner); quantity discounts two-part tariffs (cell phones)

13 Example: Consumer A has value \$1 for up to 100 photocopies per month Consumer B has value \$.50 for up to 1,000 photocopies per month Firm maximizes profits by selling (for ε small): 100-photocopies for \$100-ε 1,000 photocopies for \$500-ε Problem if resale!

14 2.3 Segmented markets Firm now separates markets Within market, charges constant per-unit price Example: cost function TC(y) =cy. Market A: inverse demand dunction p A (y) or Market B: inverse dunction p B (y)

15 Profit maximization problem: max y A,y B p A (y A ) y A + p B (y B ) y B c (y A + y B ) First order conditions: Elasticity interpretation Firm charges more to markets with lower elasticity

16 Examples: student discounts prices of goods across countries: airlines (US and Europe) books (US and UK) cars (Europe) As markets integrate (Internet), less possible to do the latter.

17 3 Oligopoly? Extremes: Perfect competition Monopoly Oligopoly if there are n (two, five...) firms Examples: soft drinks: Coke, Pepsi; cellular phones: Sprint, AT&T, Cingular,... car dealers

18 Firm i maximizes: max p (y y i + y i ) y i c (y i ) i where y i = P j6=i y j. First order condition with respect to y i : p 0 Y (y i + y i ) y i + p c 0 y (y i )=0. Problem: what is the value of y i? simultaneous determination? can firms i observe y i? Need to study strategic interaction

19 4 Game Theory Nicholson, Ch. 15, pp [OLD: Ch. 10, pp ]. Unfortunate name Game theory: study of decisions when payoff of player i depends on actions of player j. Brief history: von Neuman and Morgenstern, Theory of Games and Economic Behavior (1944) Nash, Non-cooperative Games (1951)... Nobel Prize to Nash, Harsanyi (Berkeley), Selten (1994)

20 Definitions: Players: 1,...,I Strategy s i S i Payoffs: U i (s i,s i )

21 Example: Prisoner s Dilemma I =2 s i = {D, ND} Payoffs matrix: 1 \ 2 D ND D 4, 4 1, 5 ND 5, 1 2, 2

22 What prediction? Maximize sum of payoffs? No Choose dominant strategies!

23 Battle of the Sexes game: He \ She Ballet Football Ballet 2, 1 0, 0 Football 0, 0 1, 2 Choose dominant strategies? Not possible Nash Equilibrium. Strategies s = ³ s i,s i are a Nash Equilibrium if ³ U i s i,s ³ i Ui si,s i for all s i S i and i =1,...,I

24 5 Next lecture More game theory Back to oligopoly: Cournot Bertrand

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