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Course outline II

Course outline II. Product differentiation Advertising competition Compatibility competition. Heterogeneous goods. Competition on variants, locations, and qualities. Basic idea of product differentiation The Hotelling Model The Schmalensee-Salop model

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Course outline II

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  1. Course outline II • Product differentiation • Advertising competition • Compatibility competition Heterogeneous goods

  2. Competition on variants, locations, and qualities • Basic idea of product differentiation • The Hotelling Model • The Schmalensee-Salop model • Competition on qualities and variations • Executive summary

  3. Differentiating products in order to overcome the Bertrand paradox • With homogeneous goods, competition can be quite intense: Even in a market with only two competitors, firms may face a zero-profit situation in a Bertrand-Nash equilibrium. • Differentiating products may help to achieve positive profits.

  4. Preferences (Example: drinks) Homogeneous preferences Diffuse preferences sweetness sweetness calorie content calorie content Clustered preferences sweetness calorie content

  5. Example: product differentiation of drinks Sweetness Cola light Coca-Cola (nonalcoholic) beer Mineral water Calorie content

  6. Product differentiation • Horizontal product differentiation:Some consumers prefer a good (or rather a feature), while others prefer a different good (or its feature). • Vertical product differentiation (quality):A good is regarded as better than the other by all consumers (unanimous ranking).

  7. Horizontal vs. vertical differentiation price horizontal product differentiation within a quality class A Audi A8 Mercedes S-Class BMW 7 Series line of Competition vertical product differentiation (different qualities) Audi A6 BMW 5 Series Mercedes E-Class Mercedes C-Class BMW 3 Series Audi A4 B BMW 1 Series Audi A3 Mercedes A-Class quality

  8. Long-term and short-term action parameters • Variants and locations (horizontal differentiation) • Qualities (vertical differentiation) • Recognition, image (image differentiation) • Compatibility (compatibility differentiation) Prices Quantities

  9. The Hotelling Model • Linear city of length 1 • Interpretation • Competition on location: Two firms offer the same product in different places. • Competition on variants: Two firms offer differentiated products in one place. 1 0 a 1 a 2 h

  10. Demand in the case of identical prices home turf home turf Locations or range of variants 1 0

  11. Costs of transport 1 0 a 1 a 2 h The consumer at h prefers producer 1’s good if:

  12. Proportionate demand with uniform distribution • The consumers are supposed to be equally distributed over the interval (constant density of consumers). 1 h 0 1 • The consumer in h is indifferent between good 1 and good 2.

  13. The demand function • Firm 1’s demand function: firm 1’s price advantage consumers in case of equal prices intensity of competition

  14. Exercise (Hotelling) • Deduce ! • Calculate all equilibria in the simultaneous location competition, if prices are given by

  15. The two-stage differentiation game p1 p2 a1 a2

  16. Solving the pricing game I • Profit functions • Reaction functions

  17. Solving the pricing game II • Bertrand-Nash equilibrium • Output levels • Profits • When do the firms earn the same profits and why?

  18. Equilibrium in the simultaneous competition p 2 p 1

  19. Exercises (elasticity, sequential price competition) • Find the price elasticity of demand in the case of • Assume maximal differentiation ( ).Find the Bertrand equilibrium in the case of sequential price competition. Calculate the profits. a 1 a 2 P 1 P 2 p 1 p 2

  20. Depicting the equilibria p 2 Prices in sequential price competition Prices in simultaneous price competition p 1

  21. Exercise (Strategic trade policy) • Two firms, one domestic (d), the other foreign (f), engage in simultaneous price competition on a market in a third country. Assume . • The domestic government subsidizes its firm’s exports using a unit subsidy s. • Which subsidy s maximizes domestic welfare

  22. Depicting the solution p f p d

  23. Exercise (linear costs of transport) Find the demand functions and the Bertrand equilibrium in the case of and linear cost of transport, i.e. t(h-0) for buying x1and t(1-h) for buying x2.

  24. Equilibrium locations (1st stage) • Reduced profit functions: • Influence of location on profit functions: • Nash equilibrium:

  25. Firm 1’s reduced profit function (1st stage) influence of firm 1’s choice of location on its profit(with several locations of firm 2 given) 1 0 0.2 0.4 0.6 0.8 1

  26. Equilibrium outcomes • Maximal differentiation: • Prices • Output levels and profits

  27. Lerner index (Hotelling) • Lerner index for one firm = Lerner index for the industry (equal costs):

  28. Exercises (sequential choice of location, clusters) • Which locations would you expect in the case of sequential choice of location? • Why do firms often form clusters in reality? p 1 p 2 a 2 a 1

  29. Direct and strategic effects for accommodation • Firm 1’s reduced profit function: • ? =0 >0 <0 • direct or profit maximizing strategic effect • demand effect prices in equilibrium of positioning • of 2nd stage • (Envelopetheorem) *in most cases >0

  30. Exception: negative direct effect 0 h a 1 a 2 1 x1 x2 0 h a 1 a 2 1 x1 x2

  31. Direct and strategic effects for deterrence • ?* ?* =0 >0 <0 • direct strategic effects effect *in most cases <0

  32. Welfare analysis • Equilibrium locations are a1=0 and a2=1 • Total quantity is exogenous, at 1. •  costs of transport should be minimized. • Locations a1=0.25 and a2=0.75 minimize transportation costs (too much differentiation).

  33. The circular city 2 3 1 4 5

  34. The Schmalensee-Salop model • Model for the analysis of blockade, deterrence (limit number of variants) • Circular city of length 1 • Firms are uniformly distributed  • The circular city can be considered to be made out of n linear cities.

  35. The demand function I • Indifferent consumer between firm 1 and 2

  36. The demand function II • Indifferent consumer between firm 2 and firm 3: • Firm 2’s demand function:

  37. Entry and pricing decisions • The firms decide whether to enter the market: • all firms simultaneously and equidistantly • potential competitors midway between two established firms. • Firms incur location costs of CF. • Game structure (note ): Entry firm 1 : : Entry firm k p 1 : : pn P 1 : : P k

  38. Solving the pricing game • Firm 2’s profit function: • Firm 2’s reaction function: • Symmetric Nash equilibrium:

  39. Equilibrium number of firms with free entry • Profit function depending on number of firms: • Entry:

  40. Lerner index (Schmalensee) • Lerner index for one firm = Lerner index for the industry (equal costs):

  41. Market equilibrium • While the price is above marginal costs, entry costs prevent firms from realizing profits. • An equilibrium with zero profits prevails. • The lower the costs of entry the higher the number of entering firms. • The higher the costs of transport the higher the price and the number of entering firms.

  42. Entry deterrence • 1st stage: The established firms choose the number of variants/locations. • 2nd stage: Potential competitors decide whether to enter the market. • 3rd stage: All firms compete in prices.

  43. Entry by a potential competitor 1 2 E 3

  44. Product proliferation • If there are n established firms, the potential entrant‘s profit expectation is determined by 2n. • Limit variants or limit locations: • The established firms are able to realize positive profits while deterring entry.

  45. Linear costs of transport • Consider linear cost of transport and keep all other assumptions of our models. • Firm 2‘s demand functions (located between firms 1 and 3):

  46. Exercise (linear costs of transport) • Calculate the price reaction function for firm 2 and the symmetric Bertrand equilibrium (p1=p2=...=pn). • Find the maximal number of firms and the limit locations.

  47. Executive summary I • Differentiation of products gives some monopolistic power to firms. • Direct effect: If prices are fixed, “moving towards” the other firm pays in terms of sales and profits (direct effect). However: geographical nearness may enhance business (furniture shops clustered together). • Strategic effect: Prices go down because of diminished differentiation (strategic effect). • Both effects work towards deterrence.

  48. Executive summary II • The more firms are in the market, the lower prices, outputs and profits. Therefore, incumbent firms may try to drive competitors out of business and deter entry by product proliferation. • From the social welfare point of view, competition on locations and variants need not lead to optimal product differentiation.

  49. Competition on qualities and variants • Maximal horizontal product differen-tiation: h position of consumer in hori-zontal product space. • Quality differentia-tion, v consumers’ • willingness to pay for quality. 1 quality (vertical) 0 1 variation (horizontal)

  50. Competition on qualities and variations - demand function • Linear costs of transport: t(h-0) for firm 1 and t(1-h) for firm 2 • Consumer buys product 1 if • Derivation of demand curve: http://www.uni-leipzig.de/~micro/wopap.html where

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