A distributed grid computing environment, like the European DataGrid (EDG), that manages enormous numbers of computing resources (in terms of processing power, disk space, memory usage, etc.) and astronomical amounts of scientific data, requires mechanisms for a balanced access of many thousands of simultaneous users. The DataGrid Accounting System (DGAS), that we present in this paper, is designed to support an economy-based approach to regulating the distribution of the resources among the authorized Grid users. We describe two possible models for resource pricing and a utility function for economic brokering.