Competition for exclusive customers: comparing equilibrium and welfare under one‐part and two‐part pricing
Bibliographic record
Abstract
Abstract. This paper compares one‐part and two‐part pricing in a discrete‐continuous choice model, providing more extensive welfare results than prior literature. Under two‐part pricing, firms may set fixed fees with or without ‘unit‐price commitment,’ where the lack of unit‐price commitment is consistent with ‘after‐market monopolization.’ We find that two‐part pricing with unit‐price commitment is firms’ dominant unilateral and joint pricing policy. Two‐part pricing without unit‐price commitment is the least desirable policy from a welfare standpoint. Under appropriate conditions, one‐part pricing produces the highest consumer and social welfare, but the lowest profits.
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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 | 0.005 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 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".