L5 - Product Differentiation

Question 1

Why is it important to study product differentiation?

Answer 1

Only topic in the course than is indirectly related to competition policy

• Very difficult to think of any product/markets that fits Bertrand’s assumptions…
  
  • Products are identical (so a small change in price, could lead to everyone buying from the cheaper seller
    
    • ● How does product differentiation affect price competition?
    • ● How does price competition affect product differentiation?
      
      • Why we are using the hotelling framwork
• Important for policy: (covered in next two weeks)
  
  • i) Predicting Cartels (OFT, 2005)
    
    • “Cartels are far more likely if the product is fairly homogeneous betweencompanies in the market. Considerable product differentiation has the opposite effect.”
  • ii) Merger assessment guidelines: (CC & OFT, 2010)
    
    • “Where products are differentiated, for example by branding or quality, unilateral effects are more likely where the merging firms’ products compete closely.”

Question 2

Maximum differentiation with endoengous prices: Assumptions?

Answer 2

• located at the exogenous points 0,1 –> furthest place apart
• Utility of consumer is based off their location on the line and the firm’s price
  
  • Also looking at quadratic transportation costs
  • k –> degree of product differentiation in the market
    
    • So as k increases, product differentiation increases which creates disutility for the consumer –> more likely to travel to a closer firm
• Profit it based on what the other competitor price is set at

Question 3

Maximum differentiation with endogenous prices: graph of the utilities, finding the marginal consumer and deriving demand?

Answer 3

• Two lines represent the Utility of the consumer if they brought from each of the firm’s
  
  • Obviously utility is greater the closer they are to that firm
• Based on the first differential of the utility equation
  
  • Each step away from the chosen firm we take, the greater the increase in disutility we feel (more costly it becomes)–> negative gradient is increasing
• at the point of intersection –> marginal consumer
  
  • So those to the left of the marginal consumer receive greater utility from A and the same applies for those to the right of the marginal consumer and B

Question 4

MDEP: The marginal consumer?

Answer 4

• Last week we saw that consumers would only visit the firms that were the closest to them
  
  • But this week thats not the case:
    
    • If firms set the same price –> all that matters is the transportation costs (same as last week)
    • this week, a consumer located at the midpoint, may have a strict preference for A if the difference in prices of A and B (where b is more expensive) is greater than the tranportation cost differential
      
      • In the maximum differential case –> transportation costs are the same and disappears to 0 –> so its purely based on prices
      • Consumer will go to a store that is far away as long as the price is sufficiently cheaper tha the closer store

Question 5

MDEP: How does the Marginal Consumer change when Firm A lowers its price?

Answer 5

• As firm A lowers its prices
  
  • The Utility of the consumer buying from A shift up –> leading to the marginal consumer shifting right and increasing their demand

Question 6

MDEP: Firm’s demand functions?

Answer 6

• If Firm A prices is much lower than B’s –> they will get all the demand
  
  • Equally if it is much larger Firm B will get all the demand

Question 7

MDEP: Properties of the Firm’s demand functions?

Answer 7

• Demand for Firm B is the reflection of the Demand for Firm A
• Own price differential
  
  • As P increases Q decreases
• Rival’s price differential;
  
  • AS their P increases, your Q increases
• Cross Price Elasticity of Demand –> how responsive is firm A demand given a change in firm B prices
• Demand is less responsive when a there is more differentiation
  
  • they are less concerned about being undercut so can charge a higher price

Question 8

MDEP: How changes in Product differentiation affect demand?

Answer 8

• More k (product differentiation) causes the curve of the utility function to become more defined –~> where the firm i’s utility curve cross firm j’s axis is now lower
  
  • Thus the negative differntial increases –> the cost of each step away from the firm creates even more disutility than before
  • Hence a fall in the price of A increases demand for their goods less in the second case when product differentiation is higher
    
    • They gain less for doing so (less incentive to undercut) and Firm B loses less by being undercut they are less bothered by it –> so higher prices are charged

Question 9

MDEP: Equilibrium Prices and Nash Equilibrium?

Answer 9

Question 10

MDEP: Properties of the Nash Equilibrium?

Answer 10

• k = 0 model collapses to Bertrand’s where p=MC
• To ensure the marginal consumer purchases at these prices the value of the good much be sufficiently large

Question 11

How does the hotelling model change when we have a multi-product monopolist?

Answer 11

• Stylised Merger
• As we want consumers to be indifferent between buying and not we set utility equal to zero and rearrange for price
• price is higher than the NE price under the assumption that all consumers will be participating in the market

“Where products are differentiated, for example by branding or quality, unilateral effects (the extent to which prices increase when the firms merge) are more likely where the merging firms’ products compete closely.”

Question 12

Multi-Product Monopoly equilibrium compared to MDEP graphically?

Answer 12

Question 13

Principle of Minimum Differentiation: Where would two firms locate if prices are endogenous?

Answer 13

• Need to use backwards induction to solve the two staged game
• What we saw in Topic 2 is the Demand effect –> the closer firms get to each other the more their profits increase –> provide incentives for firms to locate near each other
• Now we also have to consider the Price Effect
  
  • The closer the firms get to each other the less product differentiation there is –> increases price competition which harms their profits –> provide incentives for firms to locate further away from each other
• In this settling d’Asprement et al (1979) found that maximum differentation was the equilibrium location

Question 14

Symmetric Differentiation: What happens to prices and profits if firms locate closer together?

Answer 14

• Assumptions from slide 3:
  
  • 1. Suppose there are only 2 firms, A & B, that compete in prices
  • 2. Normalise marginal costs c= 0 and fixed costs F = 0
  • 3. Locations are exogenous & there is maximum differentiation: θA & θ_B = 1 –> different
  • 4. All consumers purchase in equilibrium
  • 5. NOT SURE WHAT THIS IS