2nd/10_Wiki/Topics/AI_and_ML/Willingness to Pay (WTP).md

id, title, category, status, canonical_id, aliases, duplicate_of, source_trust_level, confidence_score, verification_status, tags, raw_sources, last_reinforced, github_commit, tech_stack

id	title	category	status	canonical_id	aliases	duplicate_of	source_trust_level	confidence_score	verification_status	tags	raw_sources	last_reinforced	github_commit	tech_stack
wiki-2026-0508-willingness-to-pay-wtp	Willingness to Pay (WTP)	10_Wiki/Topics	verified	self	WTP Reservation Price Maximum Willingness to Pay	none	A	0.9	applied	pricing economics product-management conjoint van-westendorp		2026-05-10	pending	language framework Python/R pandas/scikit-learn/statsmodels

Willingness to Pay (WTP)

매 한 줄

"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.

매 핵심

매 정의

• WTP: consumer 가 매 specific good/service 에 매 indifferent point — 매 price > WTP 면 매 buy 안 함.
• Reservation price: synonym.
• Producer surplus: price − marginal cost. Consumer surplus: WTP − price. 매 둘의 합 = total surplus.

매 측정 methods

1. Direct ask (Gabor-Granger, van Westendorp): 매 가격 점진적으로 변화시키며 yes/no — cheap 그러나 매 hypothetical bias.
2. Conjoint (CBC, ACBC): 매 trade-off 를 force — 매 제일 실용적 quantitative method.
3. Auction (BDM, Vickrey): 매 incentive-compatible — 매 lab 에서 used.
4. Revealed preference / A-B test: 매 actual purchase data — gold standard but expensive.
5. Behavioral / ML inference: 매 click, scroll, abandonment 로 pricing model.

매 van Westendorp PSM (4 questions)

• "At what price would you consider this product too expensive to consider?" (TE)
• "At what price would you consider it expensive but still consider buying?" (Ex)
• "At what price would it be a bargain?" (B)
• "At what price would it be too cheap, raising quality concern?" (TC)
• 매 cumulative curves 의 intersection → optimal price point (OPP), point of marginal cheapness/expensiveness.

매 응용

1. SaaS pricing tier 결정.
2. Feature prioritization (어느 feature 가 매 WTP boost 매 큰가).
3. Discount / promo 효과 측정.
4. Bundling decisions.
5. Localized pricing (국가별 WTP 차이).

💻 패턴

1. van Westendorp PSM 분석 (Python)

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

# Survey responses: TE/Ex/B/TC for each respondent
df = pd.read_csv("psm_survey.csv")  # cols: too_exp, expensive, bargain, too_cheap

prices = np.linspace(0, 200, 401)

def cdf(series, prices, direction="leq"):
    if direction == "leq":
        return np.array([(series <= p).mean() for p in prices])
    return np.array([(series >= p).mean() for p in prices])

too_exp_curve = cdf(df.too_exp, prices, "leq")
expensive_curve = cdf(df.expensive, prices, "leq")
bargain_curve = cdf(df.bargain, prices, "geq")
too_cheap_curve = cdf(df.too_cheap, prices, "geq")

# Optimal Price Point: too_cheap == too_exp
opp_idx = np.argmin(np.abs(too_cheap_curve - too_exp_curve))
print(f"OPP: ${prices[opp_idx]:.2f}")

# Indifference Price: bargain == expensive
ip_idx = np.argmin(np.abs(bargain_curve - expensive_curve))
print(f"Indifference Price: ${prices[ip_idx]:.2f}")

2. Choice-Based Conjoint (CBC) — multinomial logit

import statsmodels.api as sm
import pandas as pd

# Long format: one row per alternative shown
# cols: respondent, task, alt, chosen, price, feature_a, feature_b
df = pd.read_csv("cbc.csv")

# Add chosen as outcome, group by task
X = df[["price", "feature_a", "feature_b"]]
X = sm.add_constant(X)
model = sm.MNLogit(df.chosen, X).fit()
print(model.summary())

# WTP for feature_a = -coef(feature_a) / coef(price)
wtp_a = -model.params["feature_a"][0] / model.params["price"][0]
print(f"WTP for feature A: ${wtp_a:.2f}")

3. Gabor-Granger curve

from scipy.optimize import curve_fit

# % of respondents willing to buy at each price
df = pd.DataFrame({
    "price": [9, 19, 29, 39, 49, 59, 69, 79],
    "willing_pct": [0.91, 0.78, 0.62, 0.45, 0.31, 0.18, 0.09, 0.04],
})

def demand(p, a, b):
    return 1 / (1 + np.exp(a * (p - b)))

(a, b), _ = curve_fit(demand, df.price, df.willing_pct, p0=[0.05, 40])
revenue = lambda p: p * demand(p, a, b)
optimal_price = max(np.linspace(0, 100, 1000), key=revenue)
print(f"Revenue-maximizing price: ${optimal_price:.2f}")

4. A/B test on price (revealed WTP)

# Backend: random price assignment per user cohort
import random
PRICE_LADDER = [9.99, 14.99, 19.99, 24.99, 29.99]

def assign_price(user_id: str) -> float:
    h = hash(user_id) % len(PRICE_LADDER)
    return PRICE_LADDER[h]

# Analysis: conversion × price = revenue per visitor (RPV)
import pandas as pd
log = pd.read_csv("checkout_log.csv")  # user, price, converted (0/1)
summary = log.groupby("price").agg(
    conv=("converted", "mean"),
    n=("converted", "size"),
)
summary["rpv"] = summary.index * summary.conv
print(summary.sort_values("rpv", ascending=False))

5. ML inference of WTP from behavior

# Predict propensity to convert at given price
from sklearn.ensemble import GradientBoostingClassifier
import numpy as np

X = events[["sessions", "time_on_pricing_page", "company_size", "industry_le"]]
y_at_price = {p: events[f"converted_{p}"] for p in [9, 19, 29, 49]}

models = {p: GradientBoostingClassifier().fit(X, y) for p, y in y_at_price.items()}
def expected_wtp(features):
    probs = {p: m.predict_proba([features])[0, 1] for p, m in models.items()}
    # WTP = highest price at which P(convert) >= 0.5
    over = [p for p, q in probs.items() if q >= 0.5]
    return max(over) if over else 0

6. Localized pricing (PPP-adjusted)

# OECD PPP factors (2025) — adjust list price per country
PPP = {"US": 1.0, "DE": 0.84, "JP": 0.91, "BR": 0.42, "IN": 0.29, "KR": 0.79}
def localize(usd: float, country: str) -> float:
    return round(usd * PPP.get(country, 1.0) * 0.99, 2)  # nudge to .99

매 결정 기준

상황	Approach
Pre-launch, new category	van Westendorp PSM (qualitative directional)
Feature trade-off, mature market	CBC conjoint
Granular dynamic pricing	A/B test + ML model
Bundling decisions	ACBC + reservation price model
Cross-country	PPP-adjust + per-country PSM
B2B enterprise	Sales-led discovery, value-based pricing matrix

기본값: 매 PSM 으로 ballpark → CBC 로 feature WTP → A/B test 로 final tier 검증.

🔗 Graph

• 부모: Behavioral Economics
• 변형: Reservation Price

🤖 LLM 활용

언제: 매 신제품 pricing tier 결정, 매 feature 의 monetization 평가, 매 international expansion pricing. 언제 X: 매 commodity (well-defined market price) 매 marginal cost-plus 가 더 simple. 매 매 sample size 매 작으면 PSM 매 noise.

❌ 안티패턴

• Direct ask 만 사용: 매 hypothetical bias — stated WTP 매 일반적으로 actual 의 1.5-2x.
• Single price point survey: 매 demand curve 그릴 수 없음 — 매 ladder / conjoint 필요.
• Confound feature with price: 매 conjoint design 매 price 와 feature 매 orthogonal 보장.
• Ignoring reference price: 매 경쟁사/대체재 매 anchor — 매 isolated WTP 매 misleading.
• PPP adjust 안 한 globally flat pricing: 매 emerging market 에서 매 piracy/churn 매 폭발.

🧪 검증 / 중복

• Verified (van Westendorp 1976, Sawtooth Software CBC docs, Nagle "Strategy and Tactics of Pricing").
• 신뢰도 A.

🕓 Changelog

날짜	변경
2026-05-08	Phase 1
2026-05-10	Manual cleanup — PSM/CBC/Gabor-Granger/ML behavioral inference