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Manufacturer-dealer Joint-profit Maximizing Level Of Promotion Function

The marginal cost of promoting Toyota (derivative of C with respect to S) equals the marginal probability of making a Toyota sale due to additional promotion (derivative of p with respect to S) multiplied by the sum of the dealer's and manufacturer's profit from selling a Toyota(M superscript D subscript T less M superscript M subscript T)

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Updated June 25, 2015