A dynamic analysis of a monopolist's quality improvement, process innovation and goodwill

Genlong Guo; Shoude Li

doi:10.3934/jimo.2022014

Article Contents

2023, Volume 19, Issue 3: 1714-1733. Doi: 10.3934/jimo.2022014

This issue Previous Article Stochastic production planning with regime switching Next Article Aggregation and Adjustment mechanisms for disaster relief task allocation with uneven distribution

A dynamic analysis of a monopolist's quality improvement, process innovation and goodwill

Genlong Guo^1, and
Shoude Li^2, ,

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
^* Corresponding author: Shoude Li

Received: January 2020

Revised: September 2021

Early access: February 2022

Published: March 2023

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Abstract

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.

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Mathematics Subject Classification: Primary: 37N35, 37N40; Secondary: 93C95.

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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

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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

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