The traditional AJ model focused on the effects of technology spillover and directly assumes the cause of cost reduction is R&D efforts to simplify the efforts of R&D process. Thus, choosing the amount of cost reduction is equal to choose the level of R&D efforts. This assumption results in a theoretical confusion between R&D efforts and production cost reductions. We modify the traditional AJ model in this article by segregating the R&D department from the manufacturing and marketing department integrating. Different from AJ model, we focused on the R&D department and assume that the cost reduction is come from R&D efforts. Yet, the R&D efforts are the function of incentive rewards to R&D personnel and R&D budget determined by the firm’s head quarter.
While the two competitive firms set up the identical incentive contract for their R&D departments, we find that when spillover effect is greater than 1/2, the higher the spillover effect is lower the firm’s sales, sales profits, R&D outcome and total profits will be, but market price will increase. When the spillover effect is less than 1/2, the higher the spillover effect is, the lower the firm’s sales, sales profits, and total profits will increase, but market price and R&D outcome will decrease.
In terms of the influence of disutility of R&D effort, if the disutility of R&D is higher, the firm’s sales, R&D outcome, profit, and total profit will be lower, but market price will be higher.
This article explores the influence of exogenous factors on the firm’s R&D budget and incentive rewards. We find that when the spillover effect and disutility of R&D increase, the context of incentive contract of R&D budgets and incentive
rewards which is designed by head quarter should also be higher as well.
In addition, this article also discovers that if the optimal R&D outcome is unchanged, the R&D budgets promised to the R&D department by the head quarter and the incentive rewards provided by the head quarter exists a substitution relationship. In other words, when the head quarter purports the R&D personnel to obtain their optimal R&D outcome whether it is by improving the R&D budgets or increasing the incentive rewards, it can help the head quarter to get the same optimal R&D outcome.
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Appendix
Total differentiation of Eq. (A1)
i After rearranging Eq. (A2) yields:
i