Article ID: | iaor20061386 |
Country: | Germany |
Volume: | 127 |
Issue: | 3 |
Start Page Number: | 565 |
End Page Number: | 577 |
Publication Date: | Dec 2005 |
Journal: | Journal of Optimization Theory and Applications |
Authors: | Bhargava Hemant K., Fan Y.Y., Natsuyama H.H. |
Keywords: | control processes |
This article specifies an efficient numerical scheme for computing optimal dynamic prices in a setting where the demand in a given period depends on the price in that period, cumulative sales up to the current period, and remaining market potential. The problem is studied in a deterministic and monopolistic context with a general form of the demand function. While traditional approaches produce closed-form equations that are difficult to solve due to the boundary conditions, we specify a computationally tractable numerical procedure by converting the problem to an initial-value problem based on a dynamic programming formulation. We find also that the optimal price dynamics preserves certain properties over the planning horizon: the unit revenue is linearly proportional to the demand elasticity of price; the unit revenue is constant over time when the demand elasticity is constant; and the sales rate is constant over time when the demand elasticity is linear in the price.