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

  • * Corresponding author: Shoude Li

    * Corresponding author: Shoude Li
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  • 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:

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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
     | Show Table
    DownLoad: CSV
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