A general framework for retailer competition under elastic demand and quantity-dependent transport costs

This paper extends the classic Hotelling model by addressing two critical limitations: the assumption of perfectly inelastic demand and the exclusion of quantity-dependent transport costs. Traditional models fail to capture key market dynamics where consumer purchasing behavior depends on both price sensitivity and transport costs that vary with the quantity purchased. While prior studies have incorporated elastic demand into spatial competition, they often rely on specific demand functions and assume quantity-independent transport costs, limiting their applicability to diverse market scenarios. To address these gaps, we propose a general elastic demand framework and a novel transport cost function that depends on both distance and purchase quantity, introducing the elasticity of transport costs with respect to quantity as a key parameter. This dual extension highlights how store differentiation, demand elasticity, and transport cost elasticity jointly influence equilibrium prices and profits. Our findings demonstrate that, consistent with the classic Hotelling model, prices and profits increase with store differentiation. Higher demand elasticity intensifies competition, lowering prices and profits, whereas higher transport cost elasticity reduces competition by discouraging consumers from traveling for larger purchases, particularly for bulky goods. Conversely, for lightweight goods with low transport cost sensitivity, competition is more intense, leading to lower prices and profits. By integrating demand and transport cost elasticities, our model bridges significant gaps in spatial competition literature and provides actionable insights for pricing strategies across diverse product categories. These findings advance theoretical understanding and offer practical guidance for retail pricing and market policy.