A model algorithm to provide practical insights into pricing mechanisms
- python 3.x
- numpy
- scipy
- matplotlib
- jupyter
(i) the number of potential customers is not
limited, and as a consequence, the size of the population is not a parameter of the
model
(ii) only one type of item is concerned
(iii) a monopoly situation is considered
(iv) customers buy items as soon as the price is less than or equal to
the price they are prepared to pay (myopic customers). A deterministic model with
time-dated items is presented and illustrated first.
For this model, the relationship between the price per item and demand is established. Then, the stochastic version of the same model is analyzed. A Poisson process generates customers’ arrivals. Finally, a stochastic model with salvage value where the price is a function of inventory level is considered
This provides an insight into mathematical pricing models.
That few convenient models exist without the assumptions presented above, that is to say a monopoly situation, an infinite number of potential customers who are myopic and no supply option. Negative exponential functions are often used to make the model manageable and few persuasive arguments are proposed to justify this choice: this is why we consider that most of these models are more useful to understand dynamic pricing than to treat real-life situations.