Bundling and pricing of product with after-sale services
Summary (3 min read)
1 Introduction
- Integration of service with product is considered as one of the innovative supply chain initiatives of the next decade (Anderson and Delattre, 2002).
- Study by Cohen (Cohen et al., 1997) indicate that manufacturers in electronics/computing industry are acting aggressively for service revenue (through maintenance contracts) after relatively short warranty periods.
- The decision making framework for the monopoly situation is considered in Section 4 and the duopoly game model is solved in Section 5.
- The model assumes that consumers valuation for the product is deterministically known to the manufacturers.
2 Integration of Manufacturing and Service
- The service industry is difficult to define because it includes many diverse activities.
- Many manufacturing firms are increasing the proportion of their turnover earned from selling services by bundling, as a single package or as add-ons to products at different times.
- In (Viswanadham et al., 2005), manufacturing and service were integrated in a single network to investigate the impact of manufacturing and service phases on each other, when product-service bundles are being offered.
- The conditions under which bundling is an optimal strategy was investigated in (McAfee et al., 1989) for a multiproduct monopolist.
- This leads to the use of game theory as the decision tool.
3.1 Product and Service Markets
- The product P is not identified by its brand or model but by its type, which explains its usage.
- In any city, one can find several electrical equipment service centers for repairing refrigerators and air conditioners of various brands and models.
- Let w be the total cost a consumer is willing to pay for servicing the product during its lifetime.
- This is because the independent service providers do not service the product for its entire lifetime for a previously agreed upon cost.
- A consumer can thus choose to buy the service from the manufacturer or can avail it across different independent service providers during the lifetime.
3.2 Manufacturing Firm and the Consumers
- Let the constant marginal cost of providing the lifetime service for the firm be cS ∈ [W,W ].
- If the firm provides the lifetime service for price β, then all the consumers with WTP w ≥ β will buy the service from the manufacturer for the entire product lifetime.
- Since the money value would change during the lifetime of the product, they are assumed to be suitably discounted using a common discounting factor for both the manufacturer and consumers.
- The offering P & PS means that the firm can sell the product alone and also as a bundle with the service.
- Given the above setup, the authors consider two scenarios in the product market: monopoly and duopoly.
4 Monopoly in Product Market
- The firm faces no competition and hence the decision making is an optimization problem with the objective of maximizing the payoff.
- The payoff πj for the offering j depends on the price of the offering.
- Hence the optimal price α∗ = v and the total payoff to the firm is πP = v − cP (2) The firm, being a monopoly, is best off by charging the maximum price and the consumers are worse off in this scenario.
- The other consumers (with w < β) will buy the service from the independent service providers at their respective w.
- A consumer can buy only the bundle.
5 Duopoly in the Product Market
- In this section the authors consider the duopoly in the product market.
- The authors focus here is similar as the whether the firms that manufacture P should bundle along with it the S. Consider two firms 1 and 2, which manufacture the same product and the valuation for the products manufactured by these two firms are the same v for the consumers.
- Both the firms are aware of the advantages of entering the service market.
- These games are played sequentially by the same players, and the total payoffs from the sequence of games will be evaluated using the sequence of outcomes in the games that were played.
- Both firms choose the price simultaneously without the knowledge of the price chosen by the competing firm.
5.1 The Two-stage Game
- Following are the assumptions of the two stage game: 1. Both the firms have the same constant marginal cost of producing the product cP and the same constant marginal cost of providing the service (for the lifetime) cS .
- The second assumption is more of a realistic constraint where a firm need not provide service to its competing product.
- This may also be due to the technological constraints.
- The firms 1 and 2 are capable of producing the product P and providing the service S. In the first stage, both the firms choose the offering.
- There are nine possible pricing games, one for each of the nine possible outcomes of the stage 1.
5.2 Pricing Subgames
- Stage 2 has nine pricing subgames, but due to the symmetry of the firms in terms of costs and offerings, only six distinct games need to be examined.
- The Nash equilibrium of each of them are determined in the following.
- The proof is based on the lines of Bertrand Duopoly (Varian, 1992) situation.
- If both firms can cooperate, then they both can charge the highest possible price and share the profits equally, leaving the consumers worse-off.
5.6 Offerings Game
- The row strategies are for firm 1 and the column strategies are for firm 2.
- Note that these ordered pair entries are NE outcomes of the corresponding pricing games of stage 2.
- Thus is can be easily seen that the NE strategies are (P, PS) and (PS, P ), both earning nonzero profits to both the firms.
- Without loss of generality, let firm 1 enter the market first, followed by firm 2.
6 Heterogeneous Preferences for the Product Market
- It can be easily seen that Proposition 1 holds true with the above assumption.
- In the following, the authors graphically analyze the the three symmetric pricing subgames.
- The horizontal and vertical axes in figures 2-4 are for the product and service, respectively.
7 Conclusions
- Integration of service with product is considered as one of the innovative supply chain initiatives of the next decade.
- A consumer’s WTP for the lifetime service was assumed to be uniformly distributed.
- The firms were assumed to be non-cooperative and hence the interactions were modeled as a two stage non-cooperative game.
- It is worth investigating the model where both the firms have different production and service costs.
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References
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...Bundling was suggested as an alternative technique for price discrimination for monopolists (Stigler, 1968), which was further analyzed in (Adams and Yellen, 1976)....
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..., 1996); optimality of bundling for monopolists (Adams and Yellen, 1976; Schmalensee, 1982); and equilibrium theory of bundling (Chen, 1997)....
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"Bundling and pricing of product wit..." refers background in this paper
...The conditions under which bundling is an optimal strategy was investigated in (McAfee et al., 1989) for a multiproduct monopolist....
[...]