In an oligopolistic setting, firms have two possible strategies in response to any price change by their rivals--they may either match the price change or they may ignore it. Let P = f(Q) be the demand curve corresponding to a "match-price strategy" and P = g(Q) be the demand curve corresponding to an "ignore-price strategy." Both demand curves are downward sloping, however f(Q) is steeper than g(Q): f ’(Q) > g’(Q). (P = f(Q) is shown by demand curve "D₁" in your text while P = g(Q) is shown by demand curve "D₂.") The "kinked" demand curve model assumes a combined strategy by firms in an oligopoly: match a price decrease but ignore a price increase by one’s rivals. If all firms follow such a strategy, then the demand curve facing each firm will have a "kink" in it at the going price. That is, demand is given by P = f(Q) for prices below the going price, by P = g(Q) for prices above the going price.

The firm’s revenue after a price decrease is R₁(Q₁) = Qf(Q₁) and marginal revenue is R₁’(Q₁) = f(Q₁) + Q₁f ’(Q₁) = P(1 - 1/E₁) where E₁ is the elasticity of demand along the demand curve P = f(Q) at Q₁. (This correspondence between marginal revenue and the elasticity of demand was illustrated in the previous math note.) However, the firm’s revenue after a price increase is R₂(Q₂) = Q₂g(Q₂) and marginal revenue is R₂’(Q₂) = g(Q₂) + Q₂g’(Q₂) = P(1 - 1/E₂) where E₂ is the elasticity of demand along the demand curve P = g(Q) at Q₂. At the going price, Q₁ = Q₂ and E₁ < E₂. Substituting these relationships into the corresponding relationships for marginal revenue, it is clear that MR₁ = P(1 - 1/E₁) < P(1 - 1/E₂) = MR₂. That is, the firm’s marginal revenue for a price decrease is less than the marginal revenue for a price increase; the marginal revenue function must have a "gap" at the going price.