Buyer-seller amount-price equilibrium for prepaid services: Implication for promotional pricing

Prepaid purchase instruments (PPIs; e.g., prepaid transit cards, and mobile phone credit, among others) based prepaid services involve an emerging and innovative mode of transaction. PPI based prepaid buyers make advance deposits in prepaid instruments for making retail payments against multiple purchase. Like prepaid services, advance selling involves advance payment for future consumption. Advance selling models are based on the following two constraints: capacity and consumption timing constraints. However, PPI based prepaid services do not involve above-mentioned constraints. Therefore, to address the problem, this paper proposes time value of money and transaction cost as two underpinning factors to model prepaid services. The paper shows that: (i) it is profitable for a buyer to increase the prepaid purchase amount, but within a limit imposed by the time value of money (ii) it is profitable for a seller to promote higher amounts of prepaid purchases through discounts, but within a limit imposed by the rate of marginal cost of servicing, and (iii) the above two will provide an equilibrium position, which will result in purchase-amount-stickiness behavior of buyers. In sum, the paper distinguishes the concepts of advance selling and prepaid selling of services, presents an approach to model PPI based prepaid selling of services, and provides tool for planning enhanced benefits from prepaid selling of services.