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Grid computing systems are a cost-effective alternative to traditional high-performance computing systems. However, the computing resources of a grid are usually far apart and connected by Wide Area Networks resulting in considerable communication delays. Hence, efficient allocation of jobs to computing resources for load balancing is essential in these grid systems. In this paper, two price-based dynamic job allocation schemes for computational grids are proposed whose objective is to minimize the execution cost for the grid users' jobs. One scheme tries to provide a system-optimal solution so that the expected price for the execution of all the jobs in the grid system is minimized, while the other tries to provide a job-optimal solution so that all the jobs in the system of the same size will be charged approximately the same expected price independent of the computers allocated for their execution to provide fairness. The performance of the proposed dynamic schemes is compared with static job allocation schemes using simulations.