The impact of product substitution and retail capacity on the timing and depth of price promotions: theory and evidence
Bibliographic record
Abstract
We investigate the impact of store capacity and extent of inter-product substitution in a retailer’s assortment on the optimal timing and depth of price promotions. We develop a stylised model of a monopolistic retailer selling two substitutable products over time, where demand for each product in each period is a function of the prices of both products in that and earlier periods as well as the degree of substitution between the two periods. We present closed-form solutions to limiting cases of the model, and observe the following: When retailers optimise profits, (1) price promotions are relatively deeper in both absolute and relative terms at higher capacity stores than at low capacity stores, (2) price promotions for more expensive products are relatively deeper (shallower) in both absolute and relative terms than price promotions for cheaper products if the degree of substitution is low (high) and (3) the products are sequentially promoted if the degree of substitution is low, and simultaneously promoted if the degree of substitution is high. To confirm that these insights from a simple stylised two-product model are relevant in practice, we survey price promotions within the shampoo and detergent assortments of four mass-market retailers, and observe behaviour corresponding to the results from our stylised model.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.028 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".