Economics 101A(Lecture 19)Stefano DellaVignaNovember 9, 2004Outline1. Monopoly2. Price Discrimination3. Oligopoly?4. Game Theory1Profit Maximization: Monopoly• Monopoly. Firm maximizes profits, that is, revenueminus costs:maxyp (y) y − c (y)• Notice p (y)=D−1(y)• First order condition:p0(y) y + p (y) − c0y(y)=0orp (y) − c0y(y)p= −p0(y)yp= −1εy,p• Compare with f.o.c. in perfect competition• Check s.o.c.• Elasticity of demand determines markup:— very elastic demand → low mark-up— relatively inelastic demand → higher mark-up• Graphically, y∗is where marginal revenue¡p0(y) y + p (y)¢equals marginal cost (c0y(y))• Find p on demand function• Example.• Linear inverse demand function p = a − by• Linear costs: C (y)=cy, with c>0• Maximization:maxy(a − by) y − cy• Solution:y∗(a, b, c)=a − c2bandp∗(a, b, c)=a − ba − c2b=a + c2• s.o.c.• Figure• Comparative statics:— Change in marginal cost c— Shiftindemandcurvea• Monopoly p rofits• Case 1. High profits• Case 2. No profits• Welfare consequences of monopoly— Too little production— Too high prices• Graphical analysis2 Price Discrimination• Nicholson, Ch. 13, pp. 397—404 [OLD: Ch. 18, pp.508—515].• 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 pur-chased, equal across people (second degree pricediscrimination).— Segmented markets: equal per-unit prices acrossunits (third degree price discrimination).2.1 Perfect price discimination• Monopolist decides price and quantity consumer-by-consumer• What does it charge? Graphically,• Welfare:— gain in efficiency;— all the surplus goes to firm2.2 Self-selection• Perfect price discrimination not legal• Cannot charge different prices for same quantity toAandB• Partial Solution:— offer different quantities of goods at differentprices;— allow consumers to choose quantity desired• Examples (very important!):— bundling of goods (xeroxing machines and toner);— quantity discounts— two-part tariffs (cell phones)• Example:• Consumer A has value $1 for up to 100 photocopiesper month• Consumer B has value $.50 for up to 1,000 photo-copies per month• Firm maximizes profits by selling (for ε small):— 100-photocopies for $100-ε— 1,000 photocopies for $500-ε• Problem if resale!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 pA(y) or— Market B: inverse dunction pB(y)• Profit maximization problem:maxyA,yBpA(yA) yA+ pB(yB) yB− c (yA+ yB)• First order conditions:• Elasticity interpretation• Firm charges more to markets with lower elasticity• 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 dothe latter.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• Firm i maximizes:maxyip (yi+ y−i) yi− c (yi)where y−i=Pj6=iyj.• First order condition with respect to yi:p0Y(yi+ y−i) yi+ p − c0y(yi)=0.• Problem: what is the value of y−i?— simultaneous determination?— can firms −i observe yi?• Need to study strategic interaction4GameTheory• Nicholson, Ch. 15, pp. 440—449 [OLD: Ch. 10, pp.246—255].• Unfortunate name• Game theory: study of decisions when payoff of playeri depends on actions of player j.• Brief history:— von Neuman and Morgenstern, Theory of Gamesand Economic Behavior (1944)— Nash, Non-cooperative Games (1951)— ...— Nobel Prize to Nash, Harsanyi (Berkeley), Selten(1994)• Definitions:— Players: 1,...,I— Strategy si∈ Si— Payoffs: Ui(si,s−i)• Example: Prisoner’s Dilemma— I =2— si= {D, ND}— Payoffs matrix:1 \ 2 DNDD −4, −4 −1, −5ND −5, −1 −2, −2• What prediction?• Maximize sum of payoffs? No• Choose dominant strategies!• Battle of the Sexes game:He \ She Ballet FootballBallet 2, 10, 0Football 0, 01, 2• Choose dominant strategies? Not possible• Nash Equilibrium.• Strategies s∗=³s∗i,s∗−i´are a Nash Equilibrium ifUi³s∗i,s∗−i´≥ Ui³si,s∗−i´for all si∈ Siand i =1,...,I5 Next lecture• More game theory• Back to oligopoly:— Cournot—