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Differentiating products in order to overcome Bertrand paradox n With homogeneous goods, competition can be quite intense: Even in a market with only two competitors, firms may face a no-profit situation in a Bertrand-Nash equilibrium. n Differentiation products may help to achieve positive profits.

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Preferences (Example: drinks) Homogeneous preferencesDiffuse preferences Clustered preferences calorie content sweetness calorie content sweetness

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

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

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

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Heterogeneous competition Types of differentiation: Competiton on variants Competiton on location Competition on advertising Competition on compatibility Competition on qualities

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

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

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Locations or range of variants Demand in the case of identical prices hinterland 1 0

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

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Proportionate demand with uniform distribution 01 1 h The consumers are supposed to be equally distributed over the interval (constant density of consumers). The consumer in h is indifferent between good 1 and good 2.

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The demand function n Firm 1s demand function: intensity of competition consumers in case of equal prices firm 1s price advantage

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A two-stage game a1a2a1a2 p1p2p1p2

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Solving the pricing game I n Profit functions n Reaction functions

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

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Equilibrium in the simultaneous competition p 1 p 2

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Exercises (elasticity, sequential price competition) n Find the price elasticity of demand in the case of n Assume maximal differentiation ( ). Find the Bertrand equilibrium in the case of sequential price competition. Calculate the profits.

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

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Equilibrium locations n Reduced profit functions: n Influence of location on profit functions: n Nash equilibrium:

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Firm 1s reduced profit function 10.80.60.40.2 0 11 influence of firm 1s choice of location on its profit (with several locations of firm 2 given) In contrast, why do firms cluster in reality?

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Summarizing the equilibrium n Prices n Output levels and profits n Which locations would you expect in the case of sequential choice of location? a 1 p 1 p 2 a 2

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Direct and strategic effects for accommodation n Firm 1s reduced profit function: >0 >0

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Exception: negative direct effect 10a 1 hh a 2 x1x1 x2x2 10a 1 hh a 2 x1x1 x2x2

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Direct and strategic effects for deterrence 0