Optimal promotional time for maximum sales response with an initial market share in internet marketing

Most products usually have an initial market share at the beginning in marketing. In order to increase and maximize sales response, sellers can set an optimal promotional time limit. This paper aims to explain how an existing initial market share with vital parameters affects the range and shape of sales response curve to reach optimal promotional time. We use two opposite negative exponential growth functions to build a mathematical model, apply decision calculus to determine parameters, and optimize promotional time limits for maximum sales response. We demonstrate real numerical examples of e-mail marketing by using functions with or without an initial response. Furthermore, we also conduct sensitivity analyses to compare different optimal time limits by various response rates. This paper contributes to the field by providing a sales response model with an initial market share and can be applied to the general one force or two forces cases with vital capacity parameter and exponential growth coefficient to get more elastic, adequate, and complete results.   Key words: Sales response, initial market share, diffusion function, decision calculus, optimal promotional time limits, negative exponential growth.