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This paper derives a two-tier supply chain model with many firms in each tier. The upstream firms engage in cost-reducing R&D activities. Under the case of R&D competition, the paper discusses how the changes in R&D spillover, R&D efficiency and the numbers of the manufacturers and the suppliers affect the R&D expenditures, the quantities and the profits. Then, R&D cooperation is considered. And what effects arise with the changes in the R&D spillover and the degree of cooperation are studied.