Lecture 5

• Product differentiation


  A key element of non-price competition
• If product differentiation is effective


  It increases the monopoly power of a firm
• Cross price elasticity


  Reduced by product differentiation
• Products perceived to be unique


  Become price inelastic
• For some products, reducing price


  Reduces sales
• Horizontal product differentiation


  For some characteristics of a product the optimal choice at a particular price depends on a particular consumer
• There are no goods or 'bads', and therefore similarly priced products can always find a particular niche in the market
• Differentiated products


  Two different reaction functions
• Firm 1 observes p2


  Assumes p2 will remain unchanged
• Firm 2 observes p1


  Assumes p1 will remain unchanged
• Reaction functions


  • Positively sloped
• Positively sloped reaction functions

  • Intercept for RF1 occurs when P2 = 0 (but costs >0); likewise, RF2 occurs when P2 = 0 (but costs >0)
  • P>MC in Bertrand model with differentiated products
  • Equilibrium yields P1* and P2*
  • No requirement that P1 = P2 (brand loyalty)
  • Strategic complements (positive cross price elasticity of demand);

  
• Consumers have finite budgets


  Only purchase a finite bundle of characteristics;

  analysis is farmed in terms of an efficiency frontier (‘budget constraint’), and product space
• Two characteristics:

  • a1 and a2 (e.g. if dealing with breakfast cereals, first characteristic is calories and the second characteristic is vitamin content), each brand varies according to proportion of these two characteristics
  • If have £1 to spend on brand 1: a1 = 100(1/10) = 10, a2 = 20(1/10) = 2
  • For brand 2, a1 = 56 (1/8) = 7, a2 = 56 (1/8) = 7
  • For brand 3, a1 = 12(1/6) = 2, a2 = 60(1/6) = 0

  
• Efficiency frontier

  • Any point inside this frontier are inefficient
  • Frontier is horizontal to axis at x3 as no other brands more than a2
  • Brands 1 & 2 are ‘neighbours’ as are brands 2 & 3 but brands 1 & 3 are not ‘neighbours’

  
• Brand

  • Assume ’brand n’ is introduced to market, either by new or existing firm
  • Brand N is comprised of different ratios of a1 and a2 compared to existing brands (slope ray is different)
  • If brand N is supplied at too high price it will be uncompetitive because inefficient as;
  • As price N is reduced, we expand long the vector to N1, where N becomes efficient
  • As price declines further, expand on vector to N2
  • N2 offers same amount of a1 compared to brand 1, and more of a2, therefore dominates brand 1 (leaves market)
  • N captures all of Brand 1’s market share and half between N and Brand 2

  
• Further price fall of Brand N

  • As price falls further to N3 (dotted line), brand 2 becomes inefficient, and brands N and 3 become neighbours
  • At even lower prices (beyond dotted line through x3), brand 3 becomes inefficient and brand N monopolises the market;
  • also suggests discontinuities in the demand curve for a particular brand as the process of rival brands change;
  • Also consider whether we allow consumers to mix existing combinations of characteristics to achieve their ‘optimal’ ratio
• Models of horizontal product differentiation - spatial interpretation:

  • Hosteling ‘Linear City’
  • Geographical location is the characteristics that differentiates suppliers;
  • The city is a straight line, bounded at each end
  • Customers are uniformly distributed along the city
  • Vendors charge the same price for an identical product
  • Px = Pc + Tx
  • Pc = production cost
  • Tx = transport cost (function of consumer distance from vendor)
• • Locations A & B minimisation average travel distance (Tx), for all consumers
  • Locations A & B are not optimal for either vendor
  • Optimal location for both vendors is not optimal for consumers
  • Competition determines geographical location

  
• Salop and circular city

  Consumers uniformly distributed in this city, unlike hotel long there are no ‘end points’ in this city (circle). Firms aims to locate as far away as possible from rivals

  • If circumference is standardised to 1, and the number of firms is N, optimal distance between each firm is 1/N
  • 4 identical restaurants in thus city
  • 1/4 miles between each, if consumers evenly distributed then max one-way trip is 1/8 mile (1/4 for round trip)

  
• Numerical example:
• Semivity


  L consumers uniformly distributed
• Cost of travel


  £t per mile (say £24)
• If a consumer lived a distance (d) of 1/16 mile to the nearest restaurant, cost of travel £t per mile (e.g. £24)

  Cost of a round trip = 2(1/16 mile) * (£24 per mile) = £3
• Vertical product differentiation


  One product is superior to another
• If a low-quality product was offered for sale at the same price as a high-quality product, all consumers would always choose the latter
• Vertical product differentiation does not mean that all firms have the same market share
• Consumers have identical tastes

  They derive utility according to: u.(t-p) where a consumer with income t, derives utility from consuming one unit of a product of quality level u, at a price, t
• Consumers partition themselves by income, such that brands of successively higher quality are purchased by consumers in successively higher income brackets
• This implies fragmentation of markets
• High-quality products are not mass-produced or mass-marketed products
• Producers of high-quality products prefer to benefit from economic rent, rather than to expand market share
• Ostentatious consumption


  Consumers derive utility from high-quality products
• Lemons


  Second-hand cars
• Asymmetric information


  The vendor knows more about the true quality of the car, than the potential buyer
• con


  Aa LA
• 田


  Convert to Picture
• ACC 2002 Lecture 5
• If uncontrolled, misuse of asymmetric information generates negative externalities:
• Negative externalities


  • Consumers pay a high price for a 'lemon'
  • The price of all second hand cars, irrespective of their true quality, falls to the lowest possible price
  • Vendors of high-quality second hand cars are unable to sell their cars at a remunerative price
  • Buyers who want to pay a premium for good-quality second hand cars are unable to do so (risk of being duped, and the supply of such cars diminishes)
  • Complete market failure (cg Gresham's Law)