Mathematical Modeling in Industry - A Workshop for Graduate Student, May 26-June 3, 2002

Optimal Pricing Strategy in Differentiated Durable-Goods Markets

Suzhou Huang
Ford Motor Company

We consider the problem of how to device an economic mechanism that implements the optimal pricing strategy for differentiated durable-goods in certain markets with imperfect competition. The pricing strategy has to be incentive compatible for all consumers, in the sense that each consumer, who has private information on his/her own preference, will end up choosing voluntarily the product that is intended for him/her by its producer. The optimality concept in a monopoly setting will be extended by the concept of Nash equilibrium in a competitive environment. Differentiated products imply that each product has a varied appeal to different consumers. So, the pricing strategy needs to accomodate substitutions and potential cannibalizations among products. Additional challenges arise when products are durable goods. Durability implies that any decision made today has a future ramification. Therefore, all decision making processes have to be modeled to avoid regrets for every market participant. Furthermore, a durable good can be sold, leased or bought as used, and often entails a non-negligible cost for each transaction.

Finding the solution to the problem posed above will rely heavily on game theory and optimization with inequality constraints. The complex setting for the problem provides an excellent opportunity to practice modeling skills: abstracting the essence of a realistic problem that would otherwise be too complicated to solve and then articulating it into mathematical equations.

References:

1) For background in economics: Hal Varian, "Microeconomic Analysis", 3rd Edition, Chapter 14 (Monopoly), Chapter 16 (Oligopoly)

2) For background in game theory: Hal Varian, "Microeconomic Analysis", 3rd Edition, Chapter 15 (Game Theory), Chapter 25 (Information)

3) For background in optimization: Hal Varian, "Microeconomic Analysis", 3rd Edition, Chapter 27 (Optimization)

4) For a more specific and detailed reference: S. Huang and D. Kuzyutin, "Incentive Compatible Pricing Strategies for Product Differentiation in Durable-Goods Markets", Ford Technical Report. PDF file attached. Students will be asked to consider situations that were not explicitly addressed by this paper.

 

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