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doi: 10.3934/jimo.2022014
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A dynamic analysis of a monopolist's quality improvement, process innovation and goodwill

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  January 2020 Revised  September 2021 Early access February 2022

Although there are many literatures on firms' product and process innovation in recent years, the effects of advertising-based goodwill and consumers' reference quality on firms' product and process innovation are rarely considered. Therefore, the significant features of our study are: (i) introducing the concept and definition of the consumers' reference quality; (ii) considering the effect of product quality on goodwill; (iii) the customers' demand function depends on product quality, product price, advertising-based goodwill and the difference between product quality and reference quality, and the demand function takes a linear form. Our results suggest that (i) the system admits unique saddle-point steady-state equilibrium under the monopolist decision-making and the social planner regulation; (ii) with the increases of the product quality and goodwill, the corresponding investments also increases; however, with the increase of marginal cost and reference quality, the corresponding investment decreases; (iii) the monopolist's investment in one direction boosts the other in the neighborhood of the steady-state investments in product innovation, process innovation and advertising-based goodwill, respectively; and (iv) the monopolist will have an underinvestment problem as compared with the social planner.

Citation: Genlong Guo, Shoude Li. A dynamic analysis of a monopolist's quality improvement, process innovation and goodwill. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022014
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. ChoiR. 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]

G. M. Erickson, Dynamic Models of Advertising Competition, Second Edition, Dordrecht, Kluwer, Part of the International Series in Quantitative Marketing book series, 13, 2003. doi: 10.1007/978-1-4615-1031-4.

[5]

G. M. Erickson, A differential game model of the marketing-operations interface, European Journal of Operational Research, 211 (2011), 394-402.  doi: 10.1016/j.ejor.2010.11.016.

[6]

G. FeichtingerR. Hartl and S. Sethi, Dynamic optimal control models in advertising: Recent developments, Management Science, 40 (1994), 195-226. 

[7]

G. E. Fruchter, Signaling quality: Dynamic price-advertising model, Journal of Optimization Theory and Applications, 143 (2009), 479-496.  doi: 10.1007/s10957-009-9575-7.

[8]

L. Flach and M. Irlacher, Product versus process: Innovation strategies of multiproduct firms, American Economic Journal: Microeconomics, 10 (2018), 236-277.  doi: 10.1257/mic.20150272.

[9]

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.

[10]

A. Gavious and O. Lowengart, Price-quality relationship in the presence of asymmetric dynamic reference quality effects, Marketing Letters, 23 (2012), 137-161.  doi: 10.1007/s11002-011-9143-4.

[11]

L. Grosset and B. Viscolani, Optimal dynamic advertising with an adverse exogenous effect on brand goodwill, Automatica, 45 (2009), 863-870. 

[12]

S. Jørgensen and G. Zaccour, Differential Games in Marketing, Dordrecht, Kluwer, Springer, Boston, MA, 2004. doi: 10.1007/978-1-4419-8929-1.

[13]

D. Kahnemann and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-292.  doi: 10.2307/1914185.

[14]

P. K. Kopalle and R. S. Winer, A dynamic model of reference price and expected quality, Marketing Letters, 7 (1996), 41-52.  doi: 10.1007/BF00557310.

[15] L. Lambertini, Differential Games in Industrial Economics, Cambridge, Cambridge University Press, 2018.  doi: 10.1017/9781316691175.
[16]

L. Lambertini, Advertising in a dynamic spatial monopoly, European Journal of Operational Research, 166 (2005), 547-556.  doi: 10.1016/j.ejor.2004.03.013.

[17]

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.

[18]

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.

[19]

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.

[20]

L. LambertiniR. Orsini and A. Palestini, On the instability of the R & D portfolio in a dynamic monopoly. Or, one cannot get two eggs in one basket, International Journal of Production Economics, 193 (2017), 703-712.  doi: 10.1016/j.ijpe.2017.08.030.

[21]

L. Lambertini and A. Palestini, Dynamic advertising with spillovers: Cartel vs competitive fringe, Optimal Control Applications and Methods, 30 (2009), 562-572.  doi: 10.1002/oca.881.

[22]

S. D. Li, Dynamic control of a multiproduct monopolist firm's product and process innovation, Journal of the Operational Research Society, 69 (2018), 714-733.  doi: 10.1057/s41274-017-0260-1.

[23]

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.

[24]

G. LiuS. P. Sethi and J. Zhang, Myopic vs far-sighted behaviours in a revenue-sharing supply chain with reference quality effects, International Journal of Production Research, 54 (2016), 1334-1357.  doi: 10.1080/00207543.2015.1068962.

[25]

G. W. LiuJ. 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.

[26]

A. Mantovani, Complementarity between product and process innovation in a monopoly setting, Economics of Innovation and New Technology, 15 (2006), 219-234. 

[27]

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.

[28]

M. Nerlove and K. J. Arrow, Optimal advertising policy under dynamic conditions, Mathematical Models in Marketing, 132 (1976), 167-168.  doi: 10.1007/978-3-642-51565-1_54.

[29]

F. E. 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.

[30]

F. E. 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.

[31]

X. J. Pan and S. D. 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.

[32]

I. Popescu and Y. Wu, Dynamic pricing strategies with reference effects, Operations Research, 55 (2007), 413-429. 

[33]

S. Saha, Consumer preferences and product and process R & D, The RAND Journal of Economics, 38 (2007), 250–268. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.537.5906&rep=rep1&type=pdf.

[34]

G. Sorger, Reference price formation and optimal marketing strategies, Optimal control theory and economic analysis, 3 (1988), 97-120. 

[35]

S. P. Sethi, Dynamic optimal control models in advertising: A survey, SIAM Review, 19 (1977), 685-725.  doi: 10.1137/1019106.

[36]

A. M. Spence, Monopoly, quality and regulation, Bell Journal of Economics, 6 (1975), 417-429.  doi: 10.2307/3003237.

[37]

M. XueJ. ZhangW. Tang and R. Dai, Quality improvement and pricing with reference quality effect, Journal of Systems Science and Systems Engineering, 26 (2017), 665-682.  doi: 10.1007/s11518-017-5331-y.

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. ChoiR. 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]

G. M. Erickson, Dynamic Models of Advertising Competition, Second Edition, Dordrecht, Kluwer, Part of the International Series in Quantitative Marketing book series, 13, 2003. doi: 10.1007/978-1-4615-1031-4.

[5]

G. M. Erickson, A differential game model of the marketing-operations interface, European Journal of Operational Research, 211 (2011), 394-402.  doi: 10.1016/j.ejor.2010.11.016.

[6]

G. FeichtingerR. Hartl and S. Sethi, Dynamic optimal control models in advertising: Recent developments, Management Science, 40 (1994), 195-226. 

[7]

G. E. Fruchter, Signaling quality: Dynamic price-advertising model, Journal of Optimization Theory and Applications, 143 (2009), 479-496.  doi: 10.1007/s10957-009-9575-7.

[8]

L. Flach and M. Irlacher, Product versus process: Innovation strategies of multiproduct firms, American Economic Journal: Microeconomics, 10 (2018), 236-277.  doi: 10.1257/mic.20150272.

[9]

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.

[10]

A. Gavious and O. Lowengart, Price-quality relationship in the presence of asymmetric dynamic reference quality effects, Marketing Letters, 23 (2012), 137-161.  doi: 10.1007/s11002-011-9143-4.

[11]

L. Grosset and B. Viscolani, Optimal dynamic advertising with an adverse exogenous effect on brand goodwill, Automatica, 45 (2009), 863-870. 

[12]

S. Jørgensen and G. Zaccour, Differential Games in Marketing, Dordrecht, Kluwer, Springer, Boston, MA, 2004. doi: 10.1007/978-1-4419-8929-1.

[13]

D. Kahnemann and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-292.  doi: 10.2307/1914185.

[14]

P. K. Kopalle and R. S. Winer, A dynamic model of reference price and expected quality, Marketing Letters, 7 (1996), 41-52.  doi: 10.1007/BF00557310.

[15] L. Lambertini, Differential Games in Industrial Economics, Cambridge, Cambridge University Press, 2018.  doi: 10.1017/9781316691175.
[16]

L. Lambertini, Advertising in a dynamic spatial monopoly, European Journal of Operational Research, 166 (2005), 547-556.  doi: 10.1016/j.ejor.2004.03.013.

[17]

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.

[18]

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.

[19]

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.

[20]

L. LambertiniR. Orsini and A. Palestini, On the instability of the R & D portfolio in a dynamic monopoly. Or, one cannot get two eggs in one basket, International Journal of Production Economics, 193 (2017), 703-712.  doi: 10.1016/j.ijpe.2017.08.030.

[21]

L. Lambertini and A. Palestini, Dynamic advertising with spillovers: Cartel vs competitive fringe, Optimal Control Applications and Methods, 30 (2009), 562-572.  doi: 10.1002/oca.881.

[22]

S. D. Li, Dynamic control of a multiproduct monopolist firm's product and process innovation, Journal of the Operational Research Society, 69 (2018), 714-733.  doi: 10.1057/s41274-017-0260-1.

[23]

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.

[24]

G. LiuS. P. Sethi and J. Zhang, Myopic vs far-sighted behaviours in a revenue-sharing supply chain with reference quality effects, International Journal of Production Research, 54 (2016), 1334-1357.  doi: 10.1080/00207543.2015.1068962.

[25]

G. W. LiuJ. 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.

[26]

A. Mantovani, Complementarity between product and process innovation in a monopoly setting, Economics of Innovation and New Technology, 15 (2006), 219-234. 

[27]

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.

[28]

M. Nerlove and K. J. Arrow, Optimal advertising policy under dynamic conditions, Mathematical Models in Marketing, 132 (1976), 167-168.  doi: 10.1007/978-3-642-51565-1_54.

[29]

F. E. 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.

[30]

F. E. 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.

[31]

X. J. Pan and S. D. 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.

[32]

I. Popescu and Y. Wu, Dynamic pricing strategies with reference effects, Operations Research, 55 (2007), 413-429. 

[33]

S. Saha, Consumer preferences and product and process R & D, The RAND Journal of Economics, 38 (2007), 250–268. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.537.5906&rep=rep1&type=pdf.

[34]

G. Sorger, Reference price formation and optimal marketing strategies, Optimal control theory and economic analysis, 3 (1988), 97-120. 

[35]

S. P. Sethi, Dynamic optimal control models in advertising: A survey, SIAM Review, 19 (1977), 685-725.  doi: 10.1137/1019106.

[36]

A. M. Spence, Monopoly, quality and regulation, Bell Journal of Economics, 6 (1975), 417-429.  doi: 10.2307/3003237.

[37]

M. XueJ. ZhangW. Tang and R. Dai, Quality improvement and pricing with reference quality effect, Journal of Systems Science and Systems Engineering, 26 (2017), 665-682.  doi: 10.1007/s11518-017-5331-y.

Table 1.  The parameters used in the numerical examples
$ \rho $ $ a_0 $ $ a_1 $ $ a_2 $ $ a_3 $ $ a_4 $ $ \mu $ $ \delta $ $ \alpha $ $ \beta $ $ g_0 $ $ \theta $ $ \sigma $ $ q_0 $ $ c_0 $ $ \xi $
0.06 10 0.5 0.3 0.2 0.3 0.2 0.03 7.2 5.3 20 0.05 0.02 3 15 3.9
$ \rho $ $ a_0 $ $ a_1 $ $ a_2 $ $ a_3 $ $ a_4 $ $ \mu $ $ \delta $ $ \alpha $ $ \beta $ $ g_0 $ $ \theta $ $ \sigma $ $ q_0 $ $ c_0 $ $ \xi $
0.06 10 0.5 0.3 0.2 0.3 0.2 0.03 7.2 5.3 20 0.05 0.02 3 15 3.9
Table 2.  The parameters used in the numerical examples
$ \rho $ $ a_0 $ $ a_1 $ $ a_2 $ $ a_3 $ $ a_4 $ $ \mu $ $ \delta $ $ \alpha $ $ \beta $ $ g_0 $ $ \theta $ $ \sigma $ $ q_0 $ $ c_0 $ $ \xi $
0.06 9 0.4 0.2 0.3 0.3 0.2 0.03 6.9 5.3 20 0.05 0.02 3 12 3.9
$ \rho $ $ a_0 $ $ a_1 $ $ a_2 $ $ a_3 $ $ a_4 $ $ \mu $ $ \delta $ $ \alpha $ $ \beta $ $ g_0 $ $ \theta $ $ \sigma $ $ q_0 $ $ c_0 $ $ \xi $
0.06 9 0.4 0.2 0.3 0.3 0.2 0.03 6.9 5.3 20 0.05 0.02 3 12 3.9
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