Abstract:We propose a new optimal model of product goodwill in a segmented market where the state variable is described by a partial differential equation of the Lotka-Sharp-McKendrick type. In order to maximize the sum of discounted profits over a finite time horizon, we control the advertising efforts which influence the state equation and the boundary condition. Moreover, we introduce the mathematical representation of consumer recommendations in a segmented market. Based on the semigroup approach, we prove the exis… Show more
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