Dynamic analysis of a firm's green and process innovation under green-based price regulation in a monopoly market with network externality

Huiquan Li; Lijia Ge; Junfang Xi; Shoude Li; Huiquan Li; Lijia Ge; Junfang Xi; Shoude Li

doi:10.3934/jimo.2026028

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 1: 776-805. doi: 10.3934/jimo.2026028

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Dynamic analysis of a firm's green and process innovation under green-based price regulation in a monopoly market with network externality

Huiquan Li ¹,
Lijia Ge ^{2
,
,},
Junfang Xi ^{3
,
,},
Shoude Li ³

1.
School of Finance and Economics, Qinghai University, Xining 810016, Qinghai, P. R. China
2.
School of Business Administration and Customs Affairs, Shanghai Customs University, Shanghai 201204, P. R. China
3.
Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, P. R. China

Received: 14 October 2025 Revised: 27 November 2025 Accepted: 16 December 2025 Published: 25 December 2025
49N90, 37N40

This paper attempts to explore a firm's green and process innovation under green-based price regulation in a dynamic monopolistic market with network externality. In our work, the product price is linked to the green design quality, and the effects of green performance and network externality on demand structure are explicitly incorporated. Our findings mainly show that (ⅰ) in both settings of monopolist decision-making and social planning, there exists a unique saddle point steady-state equilibrium over the whole admissible parameter constellations; (ⅱ) at steady-state equilibrium of the dynamical system, the monopolist's efforts for green and process innovation are lower under monopolist decision-making than that under planning; (ⅲ) the monopolist undersupplies green performance compared with the socially optimal level, while the marginal production cost remains socially efficient; (ⅳ) whether the network scale under monopolist decision-making is larger than that under social planning depends on factors such as the fixed and variable strength of network externalities, but it is independent of the pollutant dynamics.
- dynamic control,
- green innovation,
- network externality,
- price regulation
Citation: Huiquan Li, Lijia Ge, Junfang Xi, Shoude Li. Dynamic analysis of a firm's green and process innovation under green-based price regulation in a monopoly market with network externality[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 776-805. doi: 10.3934/jimo.2026028

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Abstract

This paper attempts to explore a firm's green and process innovation under green-based price regulation in a dynamic monopolistic market with network externality. In our work, the product price is linked to the green design quality, and the effects of green performance and network externality on demand structure are explicitly incorporated. Our findings mainly show that (ⅰ) in both settings of monopolist decision-making and social planning, there exists a unique saddle point steady-state equilibrium over the whole admissible parameter constellations; (ⅱ) at steady-state equilibrium of the dynamical system, the monopolist's efforts for green and process innovation are lower under monopolist decision-making than that under planning; (ⅲ) the monopolist undersupplies green performance compared with the socially optimal level, while the marginal production cost remains socially efficient; (ⅳ) whether the network scale under monopolist decision-making is larger than that under social planning depends on factors such as the fixed and variable strength of network externalities, but it is independent of the pollutant dynamics.

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