Optimal control of a diffusion model of new product acceptance with price‐dependent total market potential

This paper deals with the problem of finding an optimal pricing policy for the dynamics of an innovator-imitator diffusion model of new product acceptance. Total market potential is assumed to be a linearly-decreasing function of price, and the objective of the firm is to maximize the present value of the profit stream over an infinite horizon. By using Green's theorem, one can show that the optimal policy is to approach long-run stationary equilibrium sales (the turnpike) as fast as possible followed by a permanent stay on the turnpike.

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