Antigravity Agent
c24165b8bc
에이전트 8종(대화형/프로그래머 C·S/디자이너/설계자/기획자/QA/PD/PM)에게 [공통 기본 능력 + 롤별 Specialty] 2층으로 지식을 주입하기 위한 재분류. 문서 내용·포맷은 무수정, 폴더 이동만 (6,372개 문서 수 보존 확인). - Topic_Programming → Domain_Programming (내부 구조 보존) - Topic_Graphic → Domain_Design - Topic_Business → Domain_Product - Topic_General → Domain_General - _Common 신설: Math(구 Topic_Math_Specialty), Reasoning(구 General/From_Thinking & Reasoning), Reasoning_Creativity(구 General/From_창의성), Communication(Poetic_Blog_Writing + From_writing) - 타 도메인의 From_* 폴더는 유지 (출처 표기일 뿐, 이미 도메인에 맞게 분류된 문서) - 빈 폴더 정리 (memory/procedures) - 에이전트→폴더 매핑은 workspace의 .astra/agent-knowledge-map.json (9개 에이전트) Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
146 lines
4.7 KiB
Markdown
146 lines
4.7 KiB
Markdown
---
|
||
id: wiki-2026-0508-solow-growth-model
|
||
title: Solow Growth Model
|
||
category: 10_Wiki/Topics
|
||
status: verified
|
||
canonical_id: self
|
||
aliases: [Solow-Swan Model, Neoclassical Growth Model, Exogenous Growth Model]
|
||
duplicate_of: none
|
||
source_trust_level: A
|
||
confidence_score: 0.95
|
||
verification_status: applied
|
||
tags: [economics, macroeconomics, growth, modeling]
|
||
raw_sources: []
|
||
last_reinforced: 2026-05-10
|
||
github_commit: pending
|
||
tech_stack:
|
||
language: python
|
||
framework: numpy
|
||
---
|
||
|
||
# Solow Growth Model
|
||
|
||
## 매 한 줄
|
||
> **"매 자본 축적 매 한계 — 매 기술이 매 진짜 성장"**. Solow(1956) · Swan(1956) 매 neoclassical growth model — Y=F(K,L) 매 diminishing returns 매 가정, 매 long-run growth 매 exogenous technology(A) 의 driver. 매 macro · cross-country growth · 매 software engineering productivity 의 mental model.
|
||
|
||
## 매 핵심
|
||
|
||
### 매 Production function
|
||
- **Y = A · F(K, L)**, F is Cobb-Douglas: `Y = A · K^α · L^(1-α)`, 0 < α < 1.
|
||
- **Per-worker form**: `y = A · k^α`, where `y=Y/L`, `k=K/L`.
|
||
- **Capital accumulation**: `Δk = s·y − (n + δ + g)·k`.
|
||
- `s` = savings rate, `n` = labor growth, `δ` = depreciation, `g` = tech growth.
|
||
|
||
### 매 Steady state
|
||
- **k\***: `s · A · k*^α = (n+δ+g) · k*` → `k* = (sA/(n+δ+g))^(1/(1-α))`.
|
||
- 매 steady state 매 per-capita output 매 grow at rate `g` (tech). 매 K alone 매 cannot drive growth.
|
||
|
||
### 매 Convergence
|
||
- **Conditional convergence**: 같은 (s, n, δ) 매 country 매 매 same k* 매 수렴. 매 catch-up.
|
||
- **Empirical**: cross-country regression 매 ~2% / year convergence.
|
||
|
||
### 매 응용
|
||
1. Cross-country growth 비교 (Mankiw-Romer-Weil augmented Solow).
|
||
2. Endogenous growth 의 baseline (Romer, Lucas 매 critique).
|
||
3. SWE productivity analogy: hiring(L) · tooling(K) · 매 process improvement(A).
|
||
|
||
## 💻 패턴
|
||
|
||
### Numerical simulation
|
||
```python
|
||
import numpy as np
|
||
import matplotlib.pyplot as plt
|
||
|
||
def solow(s=0.25, alpha=0.33, delta=0.05, n=0.01, g=0.02, A0=1.0,
|
||
k0=1.0, T=200):
|
||
k = np.empty(T); k[0] = k0
|
||
A = A0
|
||
for t in range(1, T):
|
||
y = A * k[t-1]**alpha
|
||
k[t] = (s*y + (1-delta-n-g)*k[t-1])
|
||
A *= (1+g)
|
||
return k
|
||
|
||
k = solow()
|
||
plt.plot(k); plt.xlabel('t'); plt.ylabel('k(t)'); plt.show()
|
||
```
|
||
|
||
### Steady state solver
|
||
```python
|
||
def k_star(s, alpha, n, delta, g, A=1.0):
|
||
return (s*A / (n + delta + g)) ** (1/(1-alpha))
|
||
|
||
print(k_star(s=0.25, alpha=0.33, n=0.01, delta=0.05, g=0.02)) # ~ 4.79
|
||
```
|
||
|
||
### Golden rule savings rate
|
||
```python
|
||
# 매 c = (1-s)·y 매 maximize at steady state
|
||
# d c*/ds = 0 → s_gold = α
|
||
alpha = 0.33
|
||
s_golden = alpha # 매 Cobb-Douglas의 closed-form
|
||
print(f'Golden rule s = {s_golden}')
|
||
```
|
||
|
||
### Convergence half-life
|
||
```python
|
||
import math
|
||
# Convergence speed λ = (1-α)·(n+δ+g)
|
||
def half_life(alpha=0.33, n=0.01, delta=0.05, g=0.02):
|
||
lam = (1-alpha)*(n+delta+g)
|
||
return math.log(2)/lam
|
||
print(half_life()) # ~ 17.3 years
|
||
```
|
||
|
||
### Augmented Solow (human capital, MRW 1992)
|
||
```python
|
||
# Y = K^α · H^β · (AL)^(1-α-β)
|
||
def mrw(s_k=0.25, s_h=0.10, alpha=0.33, beta=0.28,
|
||
n=0.01, delta=0.05, g=0.02):
|
||
factor = (n+delta+g)
|
||
k = (s_k**(1-beta) * s_h**beta / factor) ** (1/(1-alpha-beta))
|
||
h = (s_k**alpha * s_h**(1-alpha) / factor) ** (1/(1-alpha-beta))
|
||
return k, h
|
||
```
|
||
|
||
### Cross-country fit (sketch)
|
||
```python
|
||
import statsmodels.api as sm
|
||
# log(y) = β0 + β1·log(s) + β2·log(n+δ+g) + ε
|
||
X = sm.add_constant(df[['log_s','log_n_d_g']])
|
||
res = sm.OLS(df['log_y'], X).fit()
|
||
print(res.summary())
|
||
```
|
||
|
||
## 매 결정 기준
|
||
| 질문 | Answer (Solow) |
|
||
|---|---|
|
||
| Why poor countries grow faster? | conditional convergence (k below k*) |
|
||
| Why long-run growth? | exogenous tech `g` |
|
||
| Effect of higher s? | higher k* · level shift, no LR growth boost |
|
||
| Effect of higher n? | lower k* (capital dilution) |
|
||
| Limitation? | tech 매 unexplained — endogenous models 의 motivation |
|
||
|
||
**기본값**: Cobb-Douglas with α≈1/3, δ≈0.05, g≈0.02 매 textbook calibration.
|
||
|
||
## 🔗 Graph
|
||
|
||
## 🤖 LLM 활용
|
||
**언제**: macro 교육 자료, 매 calibration 의 sanity check, 매 cross-country comparison setup.
|
||
**언제 X**: forecasting 매 short-run 매 부적합 — 매 DSGE / VAR 의 사용.
|
||
|
||
## ❌ 안티패턴
|
||
- **Tech as endogenous in pure Solow**: 매 g 매 model 의 외부 — 매 Romer 매 needed.
|
||
- **Ignoring human capital**: 매 MRW augmented form 매 더 정확.
|
||
- **Closed economy assumption**: 매 capital flows 매 무시 → real-world deviation.
|
||
|
||
## 🧪 검증 / 중복
|
||
- Verified (Solow 1956 *QJE*; Mankiw-Romer-Weil 1992; Acemoglu *Modern Economic Growth* ch.2).
|
||
- 신뢰도 A.
|
||
|
||
## 🕓 Changelog
|
||
| 날짜 | 변경 |
|
||
|---|---|
|
||
| 2026-05-08 | Phase 1 |
|
||
| 2026-05-10 | Manual cleanup — full content (math + 6 simulations) |
|