A Note on Willingness to Spend and Customer Lifetime Value for Firms with Limited Capacity
Bibliographic record
Abstract
The paper draws a distinction between customer lifetime value (CLV) and willingness to spend (WTS). By WTS we mean the maximum amount the firm should be willing to spend to acquire (retain) the customer relationship. In order to avoid the double counting of cash flows when summing the CLVs of customers, we suggest including only direct cash flows in the formulation of CLV. This convention means that CLV will equal WTS if (and, for the most part, only if) the firm's relationships with customers are independent. By independent we mean that the acquisition (retention) of Jane Doe has no effect on the cash flows of any other current or future customers. In contrast to well-understood demand-side dependencies among customer relationships (such as referrals), this paper highlights a particular kind of supply-side dependency—that created when the firm is limited in the number of customers it can serve. Using an extended version of the model of Blattberg and Deighton (“Manage Marketing by the Customer Equity Test, ” Harvard Business Review, July–August 1996, 136–144) of customer equity, we demonstrate that, for a firm at capacity (in this model), CLV is no longer relevant to marketing spending decisions and the firm can prefer a lower-CLV customer.
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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 | 0.002 | 0.019 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.010 | 0.000 |
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".