Imagine there is an online auction business selling 1000+ varieties of fruits. The demand for these fruits change over time, and the prices of these fruits is set by the seller.
Supposed I am interested in tracking the profit margin per fruit over time. Each variety has different profit margin. Let's say the profitability has jumped +10% in the past week.
Question: Is there an elegant way to quantify how much of the jump is due to sellers changing their profit margin systematically, or by the shift in the demand distribution for the fruits varieties (mix shift effect)?
Some thoughts:
- This is a simplified example, so in reality there may be interactions between the demand shift and sellers. Let's assume they are independent. Also there may be many different dimensions (say fruit size, color, etc).
- The most straightforward solution is to apply matching to force the distribution of varieties to be similar. However, I think this only works on adhoc basis, since you need to pick a time to match the distribution, and recompute the metric.
- Is there a way to derive one or more 'normalized' metrics to allows quick comparison between any time periods?
