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Reference price formation and optimal marketing strategies. (English) Zbl 0665.90056
Optimal control theory and economic analysis 3, Proc. 3rd Viennese Workshop, Vienna/Austria 1987, 97-120 (1988).

[For the entire collection see Zbl 0658.00019.]

We consider a monopolistic firm which produces a single product and maximizes its discounted future profits by a proper choice of the marketing instruments price and advertising. Although consumers permanently observe the price charged by the firm, they do not remember the exact price trajectory of the past. Instead, they convert their information on past prices into a reference price. This reference price is learnt adaptively in progression of time. Advertising activities of the firm generate a stock of goodwill. The demand function depends on the control variables price and advertising as well as on the state variables goodwill and reference price. It turns out that, depending on the quality of the consumers’ price memory, monotonical respectively oscillating marketing strategies are optimal.

MSC:
90B99Operations research and management science
91B62Growth models in economics
91B24Price theory and market structure