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doi: 10.3934/jimo.2021223
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## Product innovation, process innovation and advertising-based goodwill: A dynamic analysis in a monopoly

 1 School of Economics and Management, Shanxi Normal University, Taiyuan 030002, China 2 Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China

* Corresponding author: Shoude Li

Received  August 2021 Revised  October 2021 Early access December 2021

In this paper, we develop a dynamic control model to investigate a monopolist's investment strategies in product innovation, process innovation and advertising-based goodwill. The significant features of our study are: (ⅰ) considering the effect of product quality on goodwill; (ⅱ) considering the instantaneous cost of producing a quality using machinery and/or skilled labour; (ⅲ) the customers' demand function depends on product quality, product price and goodwill in a separable multiplicative way between the state variables and control variables. Our results suggest that (ⅰ) the system admits unique saddle-point steady-state equilibrium under the monopolist optimum and the social optimum; (ⅱ) and the monopolist will have an underinvestment problem as compared with the social planner; and (ⅲ) although the product price is still determined by the monopolist under the social planner optimum, the product price is higher under the monopolist optimum than that under the social planner optimum.

Citation: Genlong Guo, Shoude Li. Product innovation, process innovation and advertising-based goodwill: A dynamic analysis in a monopoly. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021223
##### References:
 [1] R. Cellini and L. Lambertini, Dynamic R & D with spillovers: Competition vs cooperation, Journal of Economic Dynamics & Control, 33 (2009), 568-582.  doi: 10.1016/j.jedc.2008.08.006. [2] R. Chenavaz, Dynamic pricing, product and process innovation, European Journal of Operational Research, 222 (2012), 553-557.  doi: 10.1016/j.ejor.2012.05.009. [3] K. Choi, R. Narasimhanb and S. W. Kim, Opening the technological innovation black box: The case of the electronics industry in Korea, European Journal of Operational Research, 250 (2016), 192-203.  doi: 10.1016/j.ejor.2015.08.054. [4] P. De Giovanni, Quality improvement vs. advertising support: Which strategy works better for a manufacturer?, European Journal of Operational Research, 208 (2011), 119-130.  doi: 10.1016/j.ejor.2010.08.003. [5] L. Lambertini and A. Mantovani, Process and product innovation by a multiproduct monopolist: A dynamic approach, International Journal of Industrial Organization, 27 (2009), 508-518.  doi: 10.1016/j.ijindorg.2008.12.005. [6] L. Lambertini and A. Mantovani, Process and product innovation: A differential game approach to product life cycle, International Journal of Economic Theory, 6 (2010), 227-252.  doi: 10.1111/j.1742-7363.2010.00132.x. [7] L. Lambertini and R. Orsini, Quality improvement and process innovation in monopoly: A dynamic analysis, Operations Research Letters, 43 (2015), 370-373.  doi: 10.1016/j.orl.2015.04.009. [8] P. Lin and K. Saggi, Product differentiation, process R & D, and the nature of market competition, European Economic Review, 46 (2002), 201-211.  doi: 10.1016/S0014-2921(00)00090-8. [9] G. W. Liu, J. X. Zhang and W. S. Tang, Strategic transfer pricing in a marketing-operations interface with quality level and advertising dependent goodwill, Omega, 56 (2015), 1-15.  doi: 10.1016/j.omega.2015.01.004. [10] A. Mantovani, Complementarity between product and process innovation in a monopoly setting, Economics of Innovation and New Technology, 15 (2006), 219-234.  doi: 10.1080/10438590500197315. [11] A. Nair and R. Narasimhan, Dynamics of competing with quality-and advertising-based goodwill, European Journal of Operational Research, 175 (2006), 462-474.  doi: 10.1016/j.ejor.2005.05.015. [12] M. Nerlove and K. J. Arrow, Optimal advertising policy under dynamic conditions, Economica, 29 (1962), 129-142.  doi: 10.2307/2551549. [13] F. El Ouardighi and F. Pasin, Quality improvement and goodwill accumulation in a dynamic duopoly, European Journal of Operational Research, 175 (2006), 1021-1032.  doi: 10.1016/j.ejor.2005.06.020. [14] F. El Ouardighi and C. S. Tapiero, Quality and the diffusion of innovations, European Journal of Operational Research, 106 (1998), 31-38.  doi: 10.1016/S0377-2217(97)00158-6. [15] X. Pan and S. Li, Dynamic optimal control of process-product innovation with learning by doing, European Journal of Operational Research, 248 (2016), 136-145.  doi: 10.1016/j.ejor.2015.07.007. [16] S. Saha, Consumer preferences and product and process R & D, The RAND Journal of Economics, 38 (2007), 250-268.  doi: 10.1111/j.1756-2171.2007.tb00054.x.

show all references

##### References:
 [1] R. Cellini and L. Lambertini, Dynamic R & D with spillovers: Competition vs cooperation, Journal of Economic Dynamics & Control, 33 (2009), 568-582.  doi: 10.1016/j.jedc.2008.08.006. [2] R. Chenavaz, Dynamic pricing, product and process innovation, European Journal of Operational Research, 222 (2012), 553-557.  doi: 10.1016/j.ejor.2012.05.009. [3] K. Choi, R. Narasimhanb and S. W. Kim, Opening the technological innovation black box: The case of the electronics industry in Korea, European Journal of Operational Research, 250 (2016), 192-203.  doi: 10.1016/j.ejor.2015.08.054. [4] P. De Giovanni, Quality improvement vs. advertising support: Which strategy works better for a manufacturer?, European Journal of Operational Research, 208 (2011), 119-130.  doi: 10.1016/j.ejor.2010.08.003. [5] L. Lambertini and A. Mantovani, Process and product innovation by a multiproduct monopolist: A dynamic approach, International Journal of Industrial Organization, 27 (2009), 508-518.  doi: 10.1016/j.ijindorg.2008.12.005. [6] L. Lambertini and A. Mantovani, Process and product innovation: A differential game approach to product life cycle, International Journal of Economic Theory, 6 (2010), 227-252.  doi: 10.1111/j.1742-7363.2010.00132.x. [7] L. Lambertini and R. Orsini, Quality improvement and process innovation in monopoly: A dynamic analysis, Operations Research Letters, 43 (2015), 370-373.  doi: 10.1016/j.orl.2015.04.009. [8] P. Lin and K. Saggi, Product differentiation, process R & D, and the nature of market competition, European Economic Review, 46 (2002), 201-211.  doi: 10.1016/S0014-2921(00)00090-8. [9] G. W. Liu, J. X. Zhang and W. S. Tang, Strategic transfer pricing in a marketing-operations interface with quality level and advertising dependent goodwill, Omega, 56 (2015), 1-15.  doi: 10.1016/j.omega.2015.01.004. [10] A. Mantovani, Complementarity between product and process innovation in a monopoly setting, Economics of Innovation and New Technology, 15 (2006), 219-234.  doi: 10.1080/10438590500197315. [11] A. Nair and R. Narasimhan, Dynamics of competing with quality-and advertising-based goodwill, European Journal of Operational Research, 175 (2006), 462-474.  doi: 10.1016/j.ejor.2005.05.015. [12] M. Nerlove and K. J. Arrow, Optimal advertising policy under dynamic conditions, Economica, 29 (1962), 129-142.  doi: 10.2307/2551549. [13] F. El Ouardighi and F. Pasin, Quality improvement and goodwill accumulation in a dynamic duopoly, European Journal of Operational Research, 175 (2006), 1021-1032.  doi: 10.1016/j.ejor.2005.06.020. [14] F. El Ouardighi and C. S. Tapiero, Quality and the diffusion of innovations, European Journal of Operational Research, 106 (1998), 31-38.  doi: 10.1016/S0377-2217(97)00158-6. [15] X. Pan and S. Li, Dynamic optimal control of process-product innovation with learning by doing, European Journal of Operational Research, 248 (2016), 136-145.  doi: 10.1016/j.ejor.2015.07.007. [16] S. Saha, Consumer preferences and product and process R & D, The RAND Journal of Economics, 38 (2007), 250-268.  doi: 10.1111/j.1756-2171.2007.tb00054.x.
The parameters used in the numerical examples
 $r$ $a_0$ $a_1$ $a_2$ $a_3$ $\mu$ $\delta$ $\alpha$ $\beta$ $g_0$ $\theta$ $\sigma$ $q_0$ $c_0$ $\xi$ $\nu$ 0.06 10 0.5 0.3 0.2 0.2 0.03 7.2 5.3 20 0.05 0.02 3 15 3.9 9.2
 $r$ $a_0$ $a_1$ $a_2$ $a_3$ $\mu$ $\delta$ $\alpha$ $\beta$ $g_0$ $\theta$ $\sigma$ $q_0$ $c_0$ $\xi$ $\nu$ 0.06 10 0.5 0.3 0.2 0.2 0.03 7.2 5.3 20 0.05 0.02 3 15 3.9 9.2
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