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-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

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.

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

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

p f p d Depicting the solution

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.

Executive summary I n Only a cost leader can do without horizontal product differentiation. With similar costs, it is worthwhile to differentiate. n Horizontal product differentiation has two opposite effects on the demand and profits. If prices are fixed, “moving towards” the other firm pays in terms of sales and profits (direct effect). However, prices go down because of diminished differentiation (strategic effect). n However: geographical nearness may enhance business (furniture shops clustered together).

Executive summary II n The more firms in the market more the more entrants into the market, the lower the prices, outputs and profits. Therefore, incumbent firms should try to drive competitors out of business and deter entry (e.g. product proliferation). n If a firm intends to drive a competitor out of business, then it should move toward the other. Both the direct effect and the strategic effect diminish the competitor‘s profit.

Executive summary III n If the price competition is limited by law, then the firms only compete for the consumers “between“ them in case of a duopoly. There is no differentiation in the equilibrium. n From the social welfare point of view, competition on locations and variants can lead to an excess of product differentiation. This will happen, when the producers‘ surplus increases less than the consumer‘s surplus decreases (because of product differentiation and high prices).