Bertrand Paradox and Pricing Decisions: Price Competition
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Chapter 4: Pricing Decisions
Bertrand Paradox
Assumptions
Supply
Market: two firms, A and B, that offer a homogeneous product. There are no limits to firm capacity. Cost: fixed cost = 0, marginal cost = c. Pricing and profits: free setting of prices and the profit for firm A is: πa = (Pa - c) Da(Pa, Pb).
Demand
Free consumer choice, fully homogeneous product, and consumers know all prices. The firm that offers the lower price gets all demand.
Nash Equilibrium
The Nash equilibrium under these assumptions is: Pa = Pb = c and πa = πb = 0.
Solution of the Bertrand Paradox
The central assumptions of the Bertrand paradox are not always valid. Each deviation from these assumptions can allow firms to realize positive profits. Key deviations include:
- Product is not homogeneous — product differentiation allows price dispersion and positive markups.
- Repeated pricing process — repeated interaction can sustain prices above marginal cost.
- Consumers do not know all prices — imperfect information reduces intensity of price competition.
- Consumers react sluggishly to price differences — search costs or switching costs slow down price-driven switching.
- Firms have capacity restrictions — limited capacity prevents serving entire market at low price.
- Prices are partly determined externally — regulations, posted contracts, or third-party pricing can limit undercutting.
Product Differentiation: Consumer Preferences
Product differentiation makes sense when consumer preferences are heterogeneous. Heterogeneity can be related to various dimensions. Examples of differentiation include:
- Technical features
- Durability
- Resale value
- Location
- Timing and delivery time
Vertical vs Horizontal Product Differentiation
Vertical differentiation: most consumers would choose product A over product B because A is objectively higher quality; consumers decide based on their willingness to pay for differences in quality.
Horizontal differentiation: some consumers prefer A, others prefer B based on different tastes or characteristics; with price differences, consumers choose according to their specific willingness to pay for particular characteristics.