Industrial Organization I

Industrial Organization I Product Differentiation (I)

Logistics • Homework 3 is posted (2 problems), due tomorrow. • Read Nevo 2000 (posted) for tomorrow • Project 3 coming up, due next week, we will start working on project 3 tomorrow @ lab.

Differentiated Products: Introduction • Until now: • One firm, or • All firms produce the exact same product • Examples of homogeneous goods (?): • Gas/electricity • Agricultural products • Gasoline • Phone

Differentiated Products: Introduction • Differentiation dimensions: • Geographic • Product characteristics • Service • Subjective differentiation (advertising) • Most markets exhibit differentiation: • Gasoline: location, services (snacks, ATM, car wash), brand • Cell phone service: distributors’ locations, coverage, customer service, advertising, phones.

Types of Demand • Representative consumer: population demand has a “representative” consumer • Traditional demand curve with negative slope (multiple-unit demand) • Consumers heterogeneous but there is a way to represent all of them with a single demand curve • Discrete choice demand: Consumers have different tastes (heterogeneity is important) • Consumers purchase 1 unit of the good that provides the highest utility (eg.: car, cell phone, computer)

Types of Differentiation: Horizontal • Consumers have different product rankings: • Consumer A prefers a light-colored car: UA=1-|A-x| • Consumer B prefers a dark car: UB=1-|B-x| UB=1-|B-x1| 0 A x1 UB=1-|B-x2| x2 1 (black) 0 (white) B UA=1- |A-x1| UA=1-|A-x2|

Horizontal Differentiation • Consumer A prefers car X1, B prefers X2 • Geographic differentiation is a type of horizontal differentiation • Most common type of product differentiation

Vertical Differentiation • Consumers agree on product ranking (more is better): 1 (max) UA= UB=x1 UA= UB=x2 x1 x2 0 (min)

Vertical Differentiation • Both (and all) consumers prefer X1 (given same price) • Quantity is an example of vertical differentiation • Examples: • Computer processors • “Homogeneous” goods: rice, gold, iron

Representative Consumer Product Differentiation

Representative Consumer • Every firm can now charge a different price • There is some “market power” because increasing price does not mean you lose all the demand • Each firm faces a different market demand, but demands are inter-related (rival’s price influences q) Substitutability Parameter

Representative Consumer p1 p2 Product 1 Product 2 100+ αp2 100+ αp1 Π1>0 Π2>0 p*1 p*2 D1 D2 MC MC q1 q2 q*1 100+ αp2 q*2 MR1 MR2 100+ αp1

Representative Consumer Product 2 “More differentiated” Product 1 “Less Differentiated” p1 p2 • Greater differentiation=greater profit (all else equal) • Price elasticity decreases (absolute value) • Cross-price elasticity decreases (less substitutability) Π1<Π2 Π2>0 p*1 p*2 D2 D1 MC MC q1 q2 q*1 q*2 MR1 MR1

Price Competition • Assuming constant mc: • Under Bertrand-Nash (price competition) conjecture=0 • BUT: equilibrium price is no longer equal to MC Conjecture

Price Competition • Mark-up depends on price elasticity (as with Cournot competition) • Reaction functions can be derived p1(p2) and p2(p1) • From i’s FOC solve for pi as a function of pj

Bertrand-Nash Equilibrium p2 r2 (p1) NE: both choices are simultaneously optimal p2*(p1*) r1 (p2) p1 p1*(p2*) Upward sloping reaction functions: “strategic complements”

Quantity Competition • Invert demand system so that p is a function of q • Under Cournot and differentiated products: conjecture=0 • Again we have: Conjecture

Cournot Equilibrium q2 r1 (q2) NE: both choices are simultaneously optimal qM r2 (q1) q2*(q1*) qM q1 q1*(q2*) • Reaction functions q1(q2) and q2(q1) can be derived in a similar fashion: • From i’s FOC solve for qi as a function of qj

Theoretical Models ofDiscrete Choice Differentiation (aka “Location” Approach)

Hotelling: Fixed price X1=0.3 X=0.45 X2=0.6 • “Location” or Hotelling model • Consumers are uniformly distributed (Ui(j)=G-t|yi-xj|-pj): • Each consumer has a “favorite” color and purchases from the closest firm • Transportation costs: less utility the farther away • Fixed price = 1 • Firms choose differentiation (location) 0 (white) 1 (black) Π1=X1+(X2-X1)/2=0.45 Π2=(1-X2)+(X2-X1)/2=0.55

Hotelling: Fixed Price X2=0.6 X1=0.6-e • Equilibrium? • Strategies: [0,1] • Profit: Π1(X1,X2), Π2(X1,X2) • X1 has an incentive to relocate to 0.6-e. Is this an equilibrium? • X2 has an incentive to relocate to the left of x1 • Rival relocates to the left if x>0.5 and to the right if x<0.5 0 (white) 1 (black) Π1=0.6-e Π2=0.4

Hotelling: Fixed Price X1=X2=0.5 0 (white) • Equilibrim is the middle location • “Principle of minimum differentiation” • When does it hold? • Why does it not hold? Variable price. 1 (black) Π1=0.5 Π2=0.5

Hotelling: Fixed location p1+|yi-X1| p + |y-x| = 2.5 p2+|yi-X2| • Firms choose p1, p2 • Consumers minimize cost: t|yi-xj|+pj (t=1 to illustrate): • Example: X1=0, X2=1; p1=p2=2 • Π1= Π2=p10.5=1 p1=2 p2=2 X1=0 X2=1 y=0.5 Π1=1 Π2=1

Hotelling: Fixed location p1+|yi-X1| p2+|yi-X2| p=2.25 • Firm 1 captures larger share and larger profit by offering a lower price: • p1=p2=2 is not an equilibrium • Firm 2 can also improve profits p2=2 p1=1.5 X1=0 X2=1 y=0.75 Π1=1.13 Π2=0.5

Hotelling: Fixed location p1+|yi-X1| p=1.5 p2+|yi-X2| • In this example, there is an equilibrium: • If p1=p2=1, changing p does not improve either firms’ profits p1=1 p2=1 X1=0 X2=1 y=0.5 Π1=0.5 Π2=0.5

Hotelling: Fixed location π1 • In general, there are 2 types of equilibria: • If X1=X2, p1=p2=0 is an equilibrium • If X1 and X2 are not too close: p1=[3+X1-(1-X2)]/3; p2=[3+(1-X2)- X1]/3 • If X1 y X2 are too close: no equilibrium (in pure strategies), there is always incentive to change price Firm 1’s profit when p2=1 p1 p1=0 p1=1 p1=2

Hotelling: Variations and Important Points • With variable price and location there is no equilibrium • Advantages: • With fixed price: it predicts geographic location of vendors • With fixed location: many markets exhibit large degree of differentiation (Ej.. clothing, arts, etc.) • Limitations: • Unidimensional (geographic distance, 1 product dimension) • Equilibria with more than two players are difficult/impossible to calculate • Consumers have linear transportation costs • With quadratic transportation costs there is an equilibrium: maximum differentiation

Hotelling: Variations and Important Points • Circular Model: • All firms face competition on both sides

Hotelling: Variations and Important Points • Examples: • Price per minute depends on time of day • Circular highway (around cities) • Trains, planes, buses that provide 24 hour service • Equilibrium (look at Shy’s book chapter, if interested): • Several firms enter the market (differentiation) • Firms locate at equally spaced intervals • Number of firms depends on fixed costs

Industrial Organization I