Antigravity Agent
209 lines
8.0 KiB
Markdown
209 lines
8.0 KiB
Markdown
---
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id: wiki-2026-0508-willingness-to-pay-wtp
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title: Willingness to Pay (WTP)
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category: 10_Wiki/Topics
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status: verified
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canonical_id: self
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aliases: [WTP, Reservation Price, Maximum Willingness to Pay]
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duplicate_of: none
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source_trust_level: A
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confidence_score: 0.9
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verification_status: applied
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tags: [pricing, economics, product-management, conjoint, van-westendorp]
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raw_sources: []
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last_reinforced: 2026-05-10
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github_commit: pending
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tech_stack:
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language: Python/R
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framework: pandas/scikit-learn/statsmodels
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---
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# Willingness to Pay (WTP)
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## 매 한 줄
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> **"매 customer 가 매 product/feature 에 매 max 얼마까지 지불할 의사가 있는가 — 매 demand curve 의 점 1개"**. 매 price-setting 의 foundation 이지만 매 측정 매 hard (stated WTP 매 over-report, revealed WTP 매 expensive). 2026 현재 매 conjoint analysis (CBC), van Westendorp PSM, MaxDiff, 매 ML-driven 실시간 personalized pricing 이 매 standard toolkit.
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## 매 핵심
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### 매 정의
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- **WTP**: consumer 가 매 specific good/service 에 매 indifferent point — 매 price > WTP 면 매 buy 안 함.
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- **Reservation price**: synonym.
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- **Producer surplus**: price − marginal cost. **Consumer surplus**: WTP − price. 매 둘의 합 = total surplus.
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### 매 측정 methods
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1. **Direct ask (Gabor-Granger, van Westendorp)**: 매 가격 점진적으로 변화시키며 yes/no — cheap 그러나 매 hypothetical bias.
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2. **Conjoint (CBC, ACBC)**: 매 trade-off 를 force — 매 제일 실용적 quantitative method.
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3. **Auction (BDM, Vickrey)**: 매 incentive-compatible — 매 lab 에서 used.
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4. **Revealed preference / A-B test**: 매 actual purchase data — gold standard but expensive.
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5. **Behavioral / ML inference**: 매 click, scroll, abandonment 로 pricing model.
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### 매 van Westendorp PSM (4 questions)
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- "At what price would you consider this product **too expensive** to consider?" (TE)
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- "At what price would you consider it expensive but still consider buying?" (Ex)
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- "At what price would it be a bargain?" (B)
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- "At what price would it be **too cheap**, raising quality concern?" (TC)
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- 매 cumulative curves 의 intersection → optimal price point (OPP), point of marginal cheapness/expensiveness.
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### 매 응용
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1. SaaS pricing tier 결정.
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2. Feature prioritization (어느 feature 가 매 WTP boost 매 큰가).
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3. Discount / promo 효과 측정.
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4. Bundling decisions.
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5. Localized pricing (국가별 WTP 차이).
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## 💻 패턴
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### 1. van Westendorp PSM 분석 (Python)
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```python
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import pandas as pd
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import numpy as np
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import matplotlib.pyplot as plt
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# Survey responses: TE/Ex/B/TC for each respondent
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df = pd.read_csv("psm_survey.csv") # cols: too_exp, expensive, bargain, too_cheap
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prices = np.linspace(0, 200, 401)
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def cdf(series, prices, direction="leq"):
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if direction == "leq":
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return np.array([(series <= p).mean() for p in prices])
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return np.array([(series >= p).mean() for p in prices])
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too_exp_curve = cdf(df.too_exp, prices, "leq")
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expensive_curve = cdf(df.expensive, prices, "leq")
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bargain_curve = cdf(df.bargain, prices, "geq")
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too_cheap_curve = cdf(df.too_cheap, prices, "geq")
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# Optimal Price Point: too_cheap == too_exp
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opp_idx = np.argmin(np.abs(too_cheap_curve - too_exp_curve))
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print(f"OPP: ${prices[opp_idx]:.2f}")
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# Indifference Price: bargain == expensive
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ip_idx = np.argmin(np.abs(bargain_curve - expensive_curve))
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print(f"Indifference Price: ${prices[ip_idx]:.2f}")
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```
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### 2. Choice-Based Conjoint (CBC) — multinomial logit
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```python
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import statsmodels.api as sm
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import pandas as pd
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# Long format: one row per alternative shown
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# cols: respondent, task, alt, chosen, price, feature_a, feature_b
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df = pd.read_csv("cbc.csv")
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# Add chosen as outcome, group by task
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X = df[["price", "feature_a", "feature_b"]]
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X = sm.add_constant(X)
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model = sm.MNLogit(df.chosen, X).fit()
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print(model.summary())
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# WTP for feature_a = -coef(feature_a) / coef(price)
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wtp_a = -model.params["feature_a"][0] / model.params["price"][0]
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print(f"WTP for feature A: ${wtp_a:.2f}")
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```
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### 3. Gabor-Granger curve
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```python
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from scipy.optimize import curve_fit
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# % of respondents willing to buy at each price
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df = pd.DataFrame({
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"price": [9, 19, 29, 39, 49, 59, 69, 79],
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"willing_pct": [0.91, 0.78, 0.62, 0.45, 0.31, 0.18, 0.09, 0.04],
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})
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def demand(p, a, b):
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return 1 / (1 + np.exp(a * (p - b)))
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(a, b), _ = curve_fit(demand, df.price, df.willing_pct, p0=[0.05, 40])
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revenue = lambda p: p * demand(p, a, b)
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optimal_price = max(np.linspace(0, 100, 1000), key=revenue)
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print(f"Revenue-maximizing price: ${optimal_price:.2f}")
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```
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### 4. A/B test on price (revealed WTP)
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```python
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# Backend: random price assignment per user cohort
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import random
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PRICE_LADDER = [9.99, 14.99, 19.99, 24.99, 29.99]
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def assign_price(user_id: str) -> float:
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h = hash(user_id) % len(PRICE_LADDER)
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return PRICE_LADDER[h]
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# Analysis: conversion × price = revenue per visitor (RPV)
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import pandas as pd
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log = pd.read_csv("checkout_log.csv") # user, price, converted (0/1)
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summary = log.groupby("price").agg(
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conv=("converted", "mean"),
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n=("converted", "size"),
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)
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summary["rpv"] = summary.index * summary.conv
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print(summary.sort_values("rpv", ascending=False))
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```
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### 5. ML inference of WTP from behavior
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```python
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# Predict propensity to convert at given price
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from sklearn.ensemble import GradientBoostingClassifier
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import numpy as np
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X = events[["sessions", "time_on_pricing_page", "company_size", "industry_le"]]
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y_at_price = {p: events[f"converted_{p}"] for p in [9, 19, 29, 49]}
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models = {p: GradientBoostingClassifier().fit(X, y) for p, y in y_at_price.items()}
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def expected_wtp(features):
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probs = {p: m.predict_proba([features])[0, 1] for p, m in models.items()}
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# WTP = highest price at which P(convert) >= 0.5
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over = [p for p, q in probs.items() if q >= 0.5]
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return max(over) if over else 0
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```
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### 6. Localized pricing (PPP-adjusted)
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```python
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# OECD PPP factors (2025) — adjust list price per country
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PPP = {"US": 1.0, "DE": 0.84, "JP": 0.91, "BR": 0.42, "IN": 0.29, "KR": 0.79}
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def localize(usd: float, country: str) -> float:
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return round(usd * PPP.get(country, 1.0) * 0.99, 2) # nudge to .99
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```
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## 매 결정 기준
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| 상황 | Approach |
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| Pre-launch, new category | van Westendorp PSM (qualitative directional) |
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| Feature trade-off, mature market | CBC conjoint |
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| Granular dynamic pricing | A/B test + ML model |
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| Bundling decisions | ACBC + reservation price model |
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| Cross-country | PPP-adjust + per-country PSM |
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| B2B enterprise | Sales-led discovery, value-based pricing matrix |
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**기본값**: 매 PSM 으로 ballpark → CBC 로 feature WTP → A/B test 로 final tier 검증.
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## 🔗 Graph
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- 부모: [[Pricing Strategy]] · [[Behavioral Economics]] · [[Microeconomics]]
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- 변형: [[Reservation Price]] · [[Hedonic Pricing]] · [[Value-Based Pricing]]
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- 응용: [[SaaS Pricing]] · [[Conjoint Analysis]] · [[Revenue Optimization]]
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- Adjacent: [[Demand Curve]] · [[Consumer Surplus]] · [[Price Elasticity]]
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## 🤖 LLM 활용
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**언제**: 매 신제품 pricing tier 결정, 매 feature 의 monetization 평가, 매 international expansion pricing.
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**언제 X**: 매 commodity (well-defined market price) 매 marginal cost-plus 가 더 simple. 매 매 sample size 매 작으면 PSM 매 noise.
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## ❌ 안티패턴
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- **Direct ask 만 사용**: 매 hypothetical bias — stated WTP 매 일반적으로 actual 의 1.5-2x.
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- **Single price point survey**: 매 demand curve 그릴 수 없음 — 매 ladder / conjoint 필요.
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- **Confound feature with price**: 매 conjoint design 매 price 와 feature 매 orthogonal 보장.
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- **Ignoring reference price**: 매 경쟁사/대체재 매 anchor — 매 isolated WTP 매 misleading.
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- **PPP adjust 안 한 globally flat pricing**: 매 emerging market 에서 매 piracy/churn 매 폭발.
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## 🧪 검증 / 중복
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- Verified (van Westendorp 1976, Sawtooth Software CBC docs, Nagle "Strategy and Tactics of Pricing").
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- 신뢰도 A.
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## 🕓 Changelog
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| 날짜 | 변경 |
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| 2026-05-08 | Phase 1 |
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| 2026-05-10 | Manual cleanup — PSM/CBC/Gabor-Granger/ML behavioral inference |
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