Decision SupportDynamic pricing, product and process innovation
Highlight
► We study dynamic pricing, product and process innovation. ► Under additive separable demand: price increases with quality and cost. ► Product and process innovation impact the pricing policy. ► Under multiplicative separable demand: price only increases with cost. ► Process innovation is the main determinant of the pricing policy.
Introduction
Many firms, especially in technological fields, simultaneously improve product quality by product innovation, and reduce production cost by process innovation. For example, a software that calculates more rapidly or better synchronises data is a result of product innovation, whereas a new machine tool that achieves the same output using less energy or with a lower reject rate is a result of process innovation. In parallel with its innovation policy, a firm determines the dynamic pricing policy. Pricing and innovation policies depend simultaneously on the dynamics of demand and supply. The former is connected to consumers’ preferences and the latter to the firm’s internal organisation (Saha, 2007).
This article poses the following question: what are the determinants of dynamic pricing policy for a firm that invests in both product innovation and process innovation? The literature on dynamic pricing and the literature on innovation include some response elements characterising the determinants of an innovative firm’s pricing policy.
The literature on dynamic pricing addresses innovation mainly by studying products sales over time. It models the diffusion effects on the level of demand and the learning effects on the level of supply (Kalish, 1983). Specifically, this literature focuses on the properties of demand functions (Kalish, 1983, Chatterjee, 2009) and gives robust results across different classes of demand functions. The literature on dynamic pricing ignored to deal explicitly with innovation management (Kalish, 1983, Chatterjee, 2009, Chenavaz and Leloup, 2011). Indeed, regarding the level of demand, the literature considers the diffusion of a supposedly innovative product with given characteristics. In regard to the level of supply, the literature on dynamic pricing models the effects of experience which reduces the cost of production. An explicit innovation policy incorporating the evolution of quality and cost is missing from the analysis.
The literature on innovation distinguishes between product innovation and process innovation (Utterback and Abernathy, 1975, Saha, 2007, Lambertini and Mantovani, 2009). In the product life cycle, product innovation precedes process innovation (Utterback and Abernathy, 1975, Klepper, 1996), even if firms pursue both types of innovation concurrently (Adner and Levinthal, 2001, Saha, 2007, Chenavaz, 2011). The combined analysis of both types of innovation has recently been initiated by Athey and Schmutzler, 1995, Mantovani, 2006, Lambertini and Mantovani, 2009 with many contributions in a static framework (Lambertini, 2003, Lin, 2004). While consumers’ preferences explain the division between product innovation and process innovation investments (Adner and Levinthal, 2001), the interactions between technological development and diverse consumer demands explain the technological change (Saha, 2007).
The effect of process innovation on pricing is predictable: when production cost decreases, the firm can lower the product price. There are two potential effects of product innovation on pricing. These effects play in opposite directions. On the one hand, when product quality increases, the firm may increase its profit markup by increasing the product price; the markup effect is positive. On the other hand, the firm may increase sales by lowering the product price; the sales effect is negative.
This paper focuses on a monopolistic market. This assumption characterises a firm after a new product release or a firm whose innovation is protected by a patent. The firm prices a product dynamically and invests in both product and process innovation. This research incorporates the general demand functions from the pricing literature. It generalises the product and process innovation functions from the innovation literature. The model accounts for both the demand of heterogeneous consumers and the dynamics of quality and cost. Price, product and process innovations are the decision variables, whereas current demand, product quality and production cost are the state variables.
Compared to the literature examining pricing and innovation issues simultaneously (Bayus, 1995, Teng and Thompson, 1996, Adner and Levinthal, 2001, Vörös, 2006), this work models quality and cost as results of explicit innovation policies. In contrast to papers based on numerical simulations (Bayus, 1995, Adner and Levinthal, 2001, Saha, 2007), this paper provides analytical results. This paper extends Chenavaz’s (2011) model to different classes of demand functions and to general innovation functions. It derives optimal price, product and process innovation policies and shows the interactions between these policies under different classes of demand specifications and gives new pricing rules. Moreover, the pricing rules are independent of the form of innovation. Furthermore, in the multiplicative separable demand case, this paper derives an easy to apply pricing rule: the dynamic pricing rule imitates the evolution of production cost and is independent of the evolution of product quality.
Section snippets
Model development
This article studies a monopoly and develops an optimal control model. The temporal horizon T is finite. The time t ∈ [0, T] is continuous.
Subclasses of the general formulation
The result (10) is robust as it is a direct consequence of (7a), the single first-order condition on p, and of its derivative with respect to t. It gives useful insights into the factors affecting dynamic pricing policies. Specifying demand functions gives stronger results. First, we discuss the case of additively separable demand functions. Next, we discuss the case of multiplicatively separable demand functions. In both cases, the general formulation for investment functions (1a), (1b) hold.
Conclusion
This article develops an optimal control model in which price, product innovation and process innovation levels are decision variables for a monopolist. Demand, quality and cost are state variables. The model establishes an analysis of optimal relationships between these variables under different classes of demand functions. The pricing rules depend on the sole price optimality condition. The pricing rules are therefore independent of the forms of innovation.
Given the analytical nature of the
Acknowledgements
The author thanks Philip Cartwright, Lydie Etienne, Christophe Schalck, and two anonymous referees for their helpful comments.
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