Article Contents
Article Contents

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

• * Corresponding author: Shoude Li
• 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.

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

 Citation:

• 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

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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