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.

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

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

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.

Audi A3 Mercedes A-Klasse BMW 3er comp Audi A4 Mercedes C-Klasse BMW 3er Audi A8 BMW 7er Mercedes S-Klasse 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-Klasse BMW 5er

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

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

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

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

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

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.

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

A two-stage game a1a2a1a2 p1p2p1p2

Solving the pricing game I n Profit functions n Reaction functions

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?

Equilibrium in the simultaneous competition p 1 p 2

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.

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

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

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

Direct and strategic effects for accommodation n Firm 1‘s reduced profit function: >0  >0 <0 =0 direct or strategic effectprofit maximizing prices in demand effectof positioningequilibrium of second stage (Envelope theorem) *in most cases

Exception: negative direct effect 10a 1 hh a 2 x1x1 x2x2 10a 1 hh a 2 x1x1 x2x2

Direct and strategic effects for deterrence 0<0 direct strategic effects effect

Crowding-out Firm 1 with a sufficiently high cost advantage drives firm 2 out of business. h p 1

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

The Schmalensee-Salop model n Circular city of length 1 n A two-stage game: – At first potential competitors decide whether they enter the market (each entering firms locates midway between two established firms). Firms incur location costs of F. – Then the firms compete in prices. n The circular city can be considered to be made of n linear cities.

The circular city !!

p 1 : p n 1::n1::n Entry Entry Firm 1 : Entry Firm n

The demand function n Firm 2‘s demand functions (located between firms 1 and 3): n Two linear cities :

Solving the pricing game n Firm 2‘s profit function: n Firm 2‘s reaction function: n Symmetric Nash equlibrium:

Equilibrium number of firms with free entry n Profit function depending on number of firms: n Entry:

Market equilibrium n Despite positive contribution margins, entry costs prevent firms from realizing profits. n If there are no further entry barriers, an equilibrium without profits is realized. n The lower the costs of entry F the higher the number of firms to enter in equilibrium. n The higher the costs of transport the higher the contribution margins and the number of entering firms.

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

Entry by a potential competitor E

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

Exercise (linear costs of transport) n Find the demand functions in a circular city with n firms. Consider linear cost of transport and keep all other assumptions of our models. n Which market shares and profits are realized? n Find the maximal number of firms and the limit locations.