Optimal Allocation of Competitive Marketing Efforts Revisited
Optimal Allocation of Competitive Marketing Efforts Revisited
Philippe Naert
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M = q/Q P = average market price S. ■ competitiors ' advertising outlays excluding brand i's X = average product - quality index p* = i's relative price, i. E. P*"p/P s* = i's relative advertising, i. E. S* » s/S. X* = i's relative quality, i. E. X* = x/X n = -(9q/9p) (p/q) = i's absolute price elasticity y p9q/3s " i's absolute marginal revenue product of advertising n = i's absolute advertising - sales elasticity a = r„" .. V — = i's absolute product quality elasticity x v. OC/dxy q n * = -(9...m/3p*) (p*/m) = i's market share elasticity with respect to i's relative price n ^ = (9m/9s*) (s*/m) = i's market share elasticity with respect to i's relative advertising outlay. n^ •= (9m/9x*) (x*/m) ■= i's market share elasticity with respect to i's relative quality Other symbols will be defined when needed. - 4 - The market share optimization rule Brand i's profit function can be written as IT = pq - qc - s (1) or IT = q(p, s, x) fp - c(q(p, s, x), x)j - s (2) The Dorfman-Steiner theorem Is simply the optimization of equation (2) with respect to absolute price, advertising and quality.
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