Product innovation, process innovation and advertising-based goodwill: A dynamic analysis in a monopoly

Genlong Guo; Shoude Li

doi:10.3934/jimo.2021223

Article Contents

2023, Volume 19, Issue 2: 1152-1165. Doi: 10.3934/jimo.2021223

This issue Previous Article On convergence properties of the modified trust region method under Hölderian error bound condition Next Article Pricing strategy and product quality design with platform-investment

Product innovation, process innovation and advertising-based goodwill: A dynamic analysis in a monopoly

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: July 31, 2021

Revised: September 30, 2021

Published: February 2023

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Abstract

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.

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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

$ 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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