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Research Papers

# Should Designers Worry About Market Systems?

[+] Author and Article Information
Ching-Shin Norman Shiau

Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213cshiau@cmu.edu

Jeremy J. Michalek

Department of Mechanical Engineering, and Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213jmichalek@cmu.edu

A company store (also called factory store) is a retail store owned by a specific manufacturer so that wholesale price and retail price are equal. Such a channel configuration is also referred to as vertical integration (9).

A franchised retailer (also called exclusive store) is a retail store owned by a private company that sells products from only one manufacturer.

A common retailer is a retailer who sells products produced by multiple manufacturers.

Vertical Nash, first defined by Choi (24), is the Nash competition scenario between manufacturer and retailer players. Similarly, a manufacturer Stackelberg game treats manufacturer players as Stackelberg leaders and retailer players as Stackelberg followers.

We assume that manufacturers can offer different wholesale prices to different retailers.

The FOC approach is more efficient than the sequential iteration method used in Ref. 22. The sequential iteration method requires iterative solution of a series of nonlinear programming (NLP) problems for each manufacturer until Nash equilibrium is reached, while the FOC approach is a single step NLP execution for a local solution. The differences between two algorithms are discussed by Shiau and Michalek (23).

The detailed derivations of all FOC equations for the MCR scenario are shown in the supplemental document that is available by contacting the authors.

Note also that for the special case of traditional profit maximization of a product line for a single producer with fixed competitors (outside good) and no retail structure (CS case), this implies that under logit linear in price all products in the line will be identical at the optimum.

We assume that automotive manufacturers are capable of adjusting engine power and final drive gear ratio on their existing engines and gearboxes without complete redesign from scratch. Therefore automakers compete on both vehicle design and price in a static timeframe.

The mean and standard deviation of a lognormal distribution are $exp(η+σ2∕2)$ and $[(exp(σ2)−1)exp(2η+σ2)]1∕2$, respectively.

Besanko et al. (12) and Sudhir (13) used zero utility as outside good in their estimations for the market data.

There is no active constraint for the solutions in all cases.

Under assumptions of constant marginal cost and identical fixed cost, Anderson et al. (29) proved that under multinomial logit in an oligopolistic model there exists a unique and symmetric price equilibrium when the profit function is strictly quasiconcave.

In the Nash game, the number of players in the game affects the price and profit at equilibrium. For example, a monopoly results in higher profit and prices than an oligopoly (35).

A saddle point is found in the MCR model, which has identical solutions across manufacturers and retailers ($w=19,275$, $m=8990$, $x1=2.22$, and $x2=1.16$). It satisfies the first-order criterion but fails in Nash equilibrium verification.

Anderson et al. (29) showed that under logit a producer’s margin is proportional to the inverse of number of producers minus 1 . Therefore, including more producers would reduce the margin and price.

J. Mech. Des 131(1), 011011 (Dec 15, 2008) (9 pages) doi:10.1115/1.3013848 History: Received December 04, 2007; Revised September 03, 2008; Published December 15, 2008

## Abstract

We examine how profit-maximizing designs are influenced by two structural aspects of market systems: (1) the structure of manufacturer-retailer interactions and (2) the structure of heterogeneity in consumer preference modeling. We first model firms as players in a profit-seeking game that compete on product attributes and prices offered. We then model the interactions of manufacturers and retailers in Nash competition under alternative channel structures and compare the equilibrium conditions for each case. We find that under linear logit consumer choice, optimal design can be decoupled from the game, and design decisions can be made without regard to price, competition, or channel structure. However, when consumer preference coefficients are heterogeneous over the population, channel structure is key to determining which designs are most profitable. We examine the extent of this influence in a vehicle design case study from the literature and find that the presence of heterogeneity leads different channel structures to imply different profit-maximizing designs. These findings imply that the common assumption that manufacturers set retail prices may produce suboptimal designs with respect to alternative channel structures. The results highlight the need for coordination between engineering design and product planning decision-makers and the importance that the structure of market systems plays in making design tradeoffs optimally.

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## Figures

Figure 1

Channel structure scenarios: (a) company store, (b) franchised retailer, (c) single common retailer, and (d) multiple common retailers

Figure 2

Interaction between manufacturer and retailer in the vertical Nash game

Figure 3

Distributions of consumer preference coefficients

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