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This paper presents a utility-based market mechanism for dynamic resource allocation in computational grid. The proposed competitive market economy is described. It consists of three different types of agents: grid request agent, grid resource agents, grid task agents; and a grid market that regulates the prices based on the observed aggregate excess demand. In order to solve the problem of heterogeneous demand in the grid, grid users' preferences are summarized by means of their utility functions. We consider budget and complete times as constraints of optimization problem. The objective of the optimization problem is to determine the amount of resources under different constraints to maximize the users' utilities. This paper proves the existence of a solution of the optimization problem, it also specify an iterative algorithm that is used by the grid market to update the prices, and it leads to an allocation that is close to a solution of the optimization problem in a finite number of iterations. The experiments are made to study characteristics of the utility directed allocation algorithm under budget constraint and under completed time constraint in terms of completion time and resource allocation efficiency.