Abstract
In this paper, the risk sharing structure between the firm providing transportation services and the customers of the pre- and post paid systems are theoretically investigated. The pre-paid systems refer to the complete contracts, which have to be established before service transactions, while the post-paid systems do the incomplete contracts where the application of the pre-specified fee structure is described in the contract, and the actual payments are conditional upon the actual consumption by the consumers. The three period contract model is formulated to investigate the impacts of the pre- and post paid systems upon the firm's profit and the consumers' welfare. The paper concludes that social welfare can be always improved by introducing the post-paid system in addition to the conventional price systems.