Optimal Pricing and Inventory Planning with Charitable Donations
Bibliographic record
Abstract
Problem definition: This paper investigates firms’ optimal operational decisions and after-tax profits with regard to tax deduction for charitable donations. Academic/practical relevance: Motivated by the steady growth in noncash donations from U.S. companies, our work is the first to provide theoretical guidance on operational planning under tax deduction for both precommitted donations and end-of-season donations. Methodology: We analyze the impact of tax deduction for a profit-driven firm under a two-period price-markdown newsvendor model and characterize the firm’s optimal price and quantity decisions. Results: The firm’s optimal donation behavior is driven by two factors—fixed cost and demand uncertainty. Specifically, a positive fixed cost can induce precommitted donation during the regular selling season, and demand uncertainty can induce end-of-season donation during the clearance period. Managerial insights: The enhanced tax deduction that is designed to encourage charitable donations results in unexpected behavior by the firm. For example, the firm’s optimal clearance price can increase with the amount of leftover inventory, and the firm’s optimal after-tax profit can increase as the tax rate increases. While the value of the deduction is tied to the fair market value (and the price) of the product, surprisingly, the firm may find it more profitable to charge a lower price, because the lower price may scale up the demand uncertainty and consequently increase the expected tax subsidy under the enhanced tax deduction. Our analysis reveals important insights about the impact of the tax law on a monopolist’s optimal operational decisions and profit. The online appendix is available at https://doi.org/10.1287/msom.2017.0676 .
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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 | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.010 | 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".