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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:

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##### References:
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
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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