Final answer:
The residual elasticity of demand faced by a firm generally increases as the number of firms increases due to a dilution of market power, but the precise effect depends on specific market conditions and cannot be quantified without additional information.
Step-by-step explanation:
The effect of an increase in the number of firms on the residual elasticity of demand that a firm faces can be analyzed using economic theory and the concept of market demand elasticity. Supposing the market faces a certain elasticity of demand and there are several firms, the residual demand facing each firm (the demand that remains after accounting for the supply of other firms) can be influenced by how many firms participate in the market. This influence relates to the concept that each additional firm shares a portion of the market demand, thereby decreasing the demand faced by individual firms.
In other words, assuming we hold the market elasticity of demand (e) and the supply elasticity of other firms (η₀) constant, an increase in the number of firms (n) typically dilutes the market power of each firm, thereby increasing the residual elasticity of demand each one faces. However, quantifying this effect requires an in-depth analysis based on specific market conditions and cannot be precisely determined without further information.
Economic models that deal with these concepts can be used to approximate the changes in residual elasticity of demand, which often depends on factors like the nature of the product, the degree of substitutability between firm's products, and other market dynamics.