الفهرس 
Analytical solutions to the dynamic pricing problem for time-normalized revenue
Table of ContentsOnly 14 pages are availabe for public view
 |  | from | 134 |  |  |
| | | from | 134 | | |
Abstract
The majority of research on dynamic pricing considers optimizing revenue or profit. However, for most firms what matters most is how much revenue or profit is achieved in a certain time frame, for example per year. In this work we have considered a normalized revenue or profit function, in other words revenue or profit per unit time. This changes the problem qualitatively and methodologically. We have developed a new dynamic pricing model for this formulation, applicable to replenishable assets that have to be sold within a certain time frame. We have derived an analytical solution to the pricing problem in the form of a simple-to-solve ordinary differential equation (ODE) equation. The trajectory of this ODE gives the optimal pricing curve. Unlike many of the models existing in the literature that rely on computationally demanding dynamic programming type solutions, our model is very simple to solve. Also, we have applied the derived equation to two commonly used demand price-demand functions (the exponential and the power functions), and have derived closed-form pricing curves for these functions. Also we have derived a closed-form pricing curve for two time-dependent demand elasticity function (the exponential and the power functions with exponential decay with time). And finally, we considered the problem of maximizing the profit of mobile calls using dynamic pricing, and we derived optimal solution for it