algo-price-van-westendorp

asgard-ai-platform ｜ 商業與營運 ｜ 原文 ｜ MIT

用四個價格問題的問卷找出可接受的價格區間

---
name: "algo-price-van-westendorp"
description: "進行 Van Westendorp 價格敏感度量表（Price Sensitivity Meter）分析，找出可接受的價格區間。當使用者需要替新產品訂出價格邊界、找出最佳價格點與無差異價格點、或做問卷式定價研究時使用，即使他們說的是「我們該收多少錢」、「價格敏感度問卷」或「可接受的價格區間」也一樣。"
metadata:
  category: "WP-39 定價演算法"
  tags: ["pricing", "van-westendorp", "survey", "price-sensitivity"]
---

# Van Westendorp 價格敏感度量表

## 概述

Van Westendorp PSM 用四個價格感知問題，透過交叉點分析找出可接受的價格區間。產出：邊際便宜點（PMC）、邊際昂貴點（PME）、無差異價格點（IPP）和最佳價格點（OPP）。需要 100 位以上受訪者的問卷資料。

## 何時使用

**觸發條件：**
- 要替新產品或新服務訂初始價格
- 要從消費者感知找出可接受的價格區間
- 想做快速的定價研究，不用複雜的實驗設計

**何時不要用：**
- 需要衡量屬性之間的取捨時（用聯合分析）
- 需要估計需求曲線時（用價格彈性）

## 演算法

```
鐵律：Van Westendorp 找出的是「可接受的區間」，不是最佳價格。它不考慮競爭、成本，也不考慮大規模下的願付價格。它告訴你價格落在哪裡會被認為合理，不會告訴你什麼價格能讓營收最大。把它當成定價策略的輸入，不要當成最終答案。
```

### 階段 1：輸入驗證
針對 100 位以上的目標客戶，在不同價格點上問四個問題：
1. 太便宜（會懷疑品質）？  2. 很划算（超值）？  3. 變貴了（但還會考慮）？  4. 太貴了（不會買）？
**關卡：** 100 份以上回覆、四條曲線都畫得出來。

### 階段 2：核心演算法
1. 對每個價格點，計算每個問題的累積百分比
2. 畫出四條曲線：「太便宜」（遞減）、「便宜／划算」（遞減）、「貴」（遞增）、「太貴」（遞增）
3. 找出交叉點：
   - OPP = 「太便宜」和「太貴」的交叉點（最佳價格點）
   - IPP = 「便宜」和「貴」的交叉點（無差異價格點）
   - PMC = 「太便宜」和「貴」的交叉點（邊際便宜點）
   - PME = 「便宜」和「太貴」的交叉點（邊際昂貴點）
4. 可接受區間 = [PMC, PME]

### 階段 3：驗證
檢查：PMC < OPP < IPP < PME（預期的順序）。所有交叉點都落在調查的價格範圍內。
**關卡：** 四個點的順序合乎邏輯、區間在商業上可行。

### 階段 4：輸出
回傳各價格點和可接受區間。

## 輸出格式

```json
{
  "price_points": {"opp": 299, "ipp": 349, "pmc": 199, "pme": 449},
  "acceptable_range": {"min": 199, "max": 449},
  "metadata": {"respondents": 250, "currency": "TWD", "product": "..."}
}
```

## 範例

### 輸入輸出範例
**輸入：** 一個 SaaS 產品的 200 份問卷回覆，測試的價格範圍：$5-$50/月
**預期：** PMC=$12、OPP=$18、IPP=$22、PME=$35。可接受區間：$12-$35。

### 邊界情況
| 輸入 | 預期 | 原因 |
|-------|----------|-----|
| 曲線沒有交叉 | 擴大調查的範圍 | 測試的價格點太窄 |
| IPP < OPP | 不常見但有可能 | 檢查資料品質，可能代表受訪者搞混了 |
| 區間非常寬 | 價格敏感度低 | 這個產品類別的容忍度高 |

## 常見陷阱

- **假設性偏誤**：人們說會付的價格，會比實際願意付的高。Van Westendorp 會系統性高估願付價格。
- **沒有競爭情境**：受訪者是孤立地回答。真實的購買決策會考慮替代方案。要搭配競爭分析補強。
- **樣本代表性**：結果只對被調查的族群有效。B2B 與 B2C、早期採用者與主流用戶，區間都會不同。
- **Newton-Miller-Smith 延伸**：在 OPP 和 IPP 加上購買意願的問題，能得到更可行動的營收估計。標準的 Van Westendorp 本身缺少這一塊。
- **受訪者必須理解產品**：受訪者要知道自己在替什麼定價。新穎的產品要附上清楚的概念說明。

## 參考資料

- Newton-Miller-Smith 購買意願延伸，見 `references/nms-extension.md`
- 問卷設計最佳實務，見 `references/survey-design.md`

---
name: "algo-price-van-westendorp"
description: "Conduct Van Westendorp Price Sensitivity Meter analysis to identify acceptable price ranges. Use this skill when the user needs to determine price boundaries for a new product, find the optimal and indifference price points, or survey-based pricing research — even if they say 'what should we charge', 'price sensitivity survey', or 'acceptable price range'."
metadata:
  category: "WP-39 定價演算法"
  tags: ["pricing", "van-westendorp", "survey", "price-sensitivity"]
---

# Van Westendorp Price Sensitivity Meter

## Overview

Van Westendorp PSM uses four price perception questions to identify an acceptable price range through intersection analysis. Produces: Point of Marginal Cheapness (PMC), Point of Marginal Expensiveness (PME), Indifference Price Point (IPP), and Optimal Price Point (OPP). Requires survey data from 100+ respondents.

## When to Use

**Trigger conditions:**
- Setting initial price for a new product or service
- Identifying the acceptable price range from consumer perception
- Quick pricing research without complex experimental design

**When NOT to use:**
- When you need to measure attribute trade-offs (use conjoint analysis)
- When you need demand curve estimation (use price elasticity)

## Algorithm

```
IRON LAW: Van Westendorp Identifies an ACCEPTABLE Range, Not Optimal Price
It doesn't account for competition, costs, or willingness to pay at
scale. It tells you WHERE prices are perceived as reasonable, not
what maximizes revenue. Use as input to pricing strategy, not as the
final answer.
```

### Phase 1: Input Validation
Survey 100+ target customers with four questions at various price points:
1. Too cheap (quality suspect)?  2. A bargain (great deal)?  3. Getting expensive (but would consider)?  4. Too expensive (would not buy)?
**Gate:** 100+ responses, all four curves plottable.

### Phase 2: Core Algorithm
1. For each price point, compute cumulative percentages for each question
2. Plot four curves: "too cheap" (descending), "cheap/bargain" (descending), "expensive" (ascending), "too expensive" (ascending)
3. Find intersections:
   - OPP = intersection of "too cheap" and "too expensive" (optimal price point)
   - IPP = intersection of "cheap" and "expensive" (indifference price point)
   - PMC = intersection of "too cheap" and "expensive" (marginal cheapness)
   - PME = intersection of "cheap" and "too expensive" (marginal expensiveness)
4. Acceptable range = [PMC, PME]

### Phase 3: Verification
Check: PMC < OPP < IPP < PME (expected ordering). All intersections exist within surveyed range.
**Gate:** Four-point ordering is logical, range is commercially viable.

### Phase 4: Output
Return price points and acceptable range.

## Output Format

```json
{
  "price_points": {"opp": 299, "ipp": 349, "pmc": 199, "pme": 449},
  "acceptable_range": {"min": 199, "max": 449},
  "metadata": {"respondents": 250, "currency": "TWD", "product": "..."}
}
```

## Examples

### Sample I/O
**Input:** 200 survey responses for a SaaS product, price range tested: $5-$50/month
**Expected:** PMC=$12, OPP=$18, IPP=$22, PME=$35. Acceptable range: $12-$35.

### Edge Cases
| Input | Expected | Why |
|-------|----------|-----|
| Curves don't intersect | Extend surveyed range | Price points tested were too narrow |
| IPP < OPP | Unusual but possible | Check data quality, may indicate confused respondents |
| Very wide range | Low price sensitivity | Product category has high tolerance |

## Gotchas

- **Hypothetical bias**: People say they'd pay more than they actually would. Van Westendorp systematically overestimates willingness to pay.
- **No competitive context**: Respondents answer in isolation. Real purchase decisions consider alternatives. Supplement with competitive analysis.
- **Sample representativeness**: Results are only valid for the surveyed population. B2B vs B2C, early adopters vs mainstream — all give different ranges.
- **Newton-Miller-Smith extension**: Add purchase intent questions at OPP and IPP for more actionable revenue estimates. Standard Van Westendorp alone lacks this.
- **Product must be understood**: Respondents need to understand what they're pricing. For novel products, include a clear concept description.

## References

- For Newton-Miller-Smith purchase intent extension, see `references/nms-extension.md`
- For survey design best practices, see `references/survey-design.md`