11.14 : Equilibrium in a Differentiated-Products Bertrand Market

In the Bertrand model with differentiated products, firms compete on price while offering similar but not identical goods. Differentiation softens price competition by reducing direct substitutability, but it does not eliminate price sensitivity. Firms still engage in price competition, but differentiation reduces intensity by lowering cross-price elasticity.

Consider two smartphone manufacturers, NovaPhone and SwiftMobile. NovaPhone focuses on high-performance devices with advanced features, while SwiftMobile offers budget-friendly models with long battery life. Each firm’s demand depends on its own-price elasticity, which measures how much its sales change with its own price, and cross-price elasticity, which captures how its sales respond to the competitor’s price.

The number of units each firm sells, represented as QN for NovaPhone and QS for SwiftMobile, reflects the degree of substitutability between the two brands. Consumers may switch brands if price differences become too large, but differentiation reduces this effect by making products less interchangeable. The baseline demand (DN for NovaPhone and DS for SwiftMobile) reflects the number of customers who prefer each brand under normal pricing conditions, though extreme price changes can still lead to brand switching.

If Nova Phone increases its price (PN), its sales (QN) decrease because fewer customers are willing to buy at a higher price due to its own-price elasticity. Similarly, if SwiftMobile raises its price (PS), its sales (QS) decline. However, because the products are substitutes to some degree, an increase in PN raises QS due to cross-price elasticity, and vice versa. The strength of this effect depends on the level of product differentiation.

A simplified demand equation for NovaPhone is QN = DN - 2PN + PS, where DN is its baseline demand. Similarly, SwiftMobile’s demand is QS = DS - 2PS + PN. These equations illustrate how firms adjust their pricing strategies, balancing competition and differentiation to attract customers.