§14.1AH 1992 — 기본 생산 + R&D
Aghion-Howitt 1992 Production + R&D7 eq
(14.1)
Aghion-Howitt creative destruction
Aghion-Howitt Creative Destruction
DRAFT
vc-passed
$$Y(t) = A(t)\, x(t)^{\alpha}\, L^{1-\alpha}$$
Intuition
★ 한 종류의 중간재 (quality ladder). A(t) 가 누적 quality. 새 발명 → A 점프 (creative destruction).
3세 비유
한 종류의 도구가 점점 좋아진다 — 새 버전이 나오면 옛 버전 무용지물.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion · Peter Howitt (1992) | A Model of Growth through Creative Destruction (Econometrica) | |
Applications
- Schumpeterian growth empirics
- industry dynamics
Civilizational Relevance
★ Joseph Schumpeter (1942) 의 "창조적 파괴" 의 수학.
(14.4)
균형 변수 (AH)
Equilibrium Variables (AH)
DRAFT
vc-passed
$$[C(t), X(t), Z(t), N(t)]_{\nu, t=0}^{\infty}$$
Intuition
DRAFT — AH 균형 변수 정의.
3세 비유
DRAFT — AH 균형 변수 정의.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — AH 균형 변수 정의.
(14.5)
Quality jump (innovation)
Quality Jump
DRAFT
vc-passed
$$A(t) = \lambda^{n(t)}$$
Intuition
★ 누적 quality = (jump factor λ > 1)^(누적 발명 수 n(t)). 매 발명마다 λ 배 향상.
3세 비유
100번 발명이 일어나면 처음보다 λ^100 배 좋다.
Genealogy
| 인물 | 저작 | note |
|---|
| Aghion-Howitt (1992) | | |
Civilizational Relevance
discrete jump growth model.
(14.6) ★
Limit pricing
Limit Pricing
DRAFT
vc-passed
$$p_x(\nu, t \mid q) = q(\nu, t)$$
Intuition
DRAFT — ★ 한계 가격 = 품질 — 진입 위협 받침.
3세 비유
DRAFT — ★ 한계 가격 = 품질 — 진입 위협 받침.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ 한계 가격 = 품질 — 진입 위협 받침.
(14.7)
수요 = L
Demand = L
DRAFT
vc-passed
$$x(\nu, t \mid q) = L$$
Intuition
DRAFT — (14.6) limit price 의 균형 수량.
3세 비유
DRAFT — (14.6) limit price 의 균형 수량.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — (14.6) limit price 의 균형 수량.
(14.8)
이윤 (general q)
Profit (general q)
DRAFT
vc-passed
$$\pi(\nu, t \mid q) = (1-\beta)\, q(\nu, t)\, L$$
Intuition
DRAFT — ★ 이윤 = (1-β) q L — 품질 비례.
3세 비유
DRAFT — ★ 이윤 = (1-β) q L — 품질 비례.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ 이윤 = (1-β) q L — 품질 비례.
(14.9) ★
Aggregate Y (Q form)
Aggregate Y (Q form)
DRAFT
vc-passed
$$Y(t) = \frac{1}{1-\beta}\, Q(t)\, L$$
Intuition
DRAFT — ★ Q 형 — Romer (13.12) 의 quality 사촌.
3세 비유
DRAFT — ★ Q 형 — Romer (13.12) 의 quality 사촌.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Q 형 — Romer (13.12) 의 quality 사촌.
§14.2AH 균형 특성화 (HJB)
AH Equilibrium (HJB)10 eq
(14.10)
Poisson innovation arrival
Poisson Innovation Arrival Rate
DRAFT
vc-passed
$$\Pr(\text{innovation in } [t, t+dt)) = \mu\, Z(t)\, dt$$
Intuition
★★ 발명은 Poisson process 로 모델링. arrival rate μZ(t) — R&D 투입에 비례. **확률적 도착의 physics 차용 (radioactive decay 와 동형)**.
3세 비유
발명이 "무작위로 도착" — 마치 라디오 활성 입자가 무작위로 붕괴하듯.
Genealogy
| 인물 | 저작 | note |
|---|
| Siméon Denis Poisson (1837) | Recherches sur la probabilité des jugements | |
| Aghion-Howitt (1992) | Innovation Poisson process | |
Applications
- ★ patent arrival data
- 한국 IP filing 모델
Civilizational Relevance
★★ Mirowski case — Poisson process (Physics 1837) 가 economics 에 차용.
(14.11)
Aggregate X
Aggregate X
DRAFT
vc-passed
$$X(t) = (1-\beta)\, Q(t)\, L$$
Intuition
DRAFT — 총 중간재 비용.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 총 중간재 비용.
(14.12)
Aggregate w
Aggregate Wage
DRAFT
vc-passed
$$w(t) = \frac{\beta}{1-\beta}\, Q(t)$$
Intuition
DRAFT — ★ 임금 = (β/(1-β))Q.
3세 비유
DRAFT — ★ 임금 = (β/(1-β))Q.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ 임금 = (β/(1-β))Q.
(14.13) ★
★ HJB-style asset eq
HJB-style Asset Equation
DRAFT
vc-passed
$$r(t)\, V(\nu, t \mid q) - \dot V = \pi(\nu, t \mid q) - z(\nu, t \mid q)\, V(\nu, t \mid q)$$
Intuition
DRAFT — ★ Schumpeterian asset value HJB — z 가 Poisson 도전 hazard.
3세 비유
DRAFT — ★ Schumpeterian asset value HJB — z 가 Poisson 도전 h
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Schumpeterian asset value HJB — z 가 Poisson 도전 hazard.
(14.14)
Free-entry (AH)
Free-Entry (AH)
DRAFT
vc-passed
$$\eta\, V(\nu, t \mid q) \leq \lambda^{-1}\, q(\nu, t)$$
Intuition
DRAFT — AH free-entry — 비용 < 가치.
3세 비유
DRAFT — AH free-entry — 비용 < 가치.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — AH free-entry — 비용 < 가치.
(14.15)
Consumption Euler
Consumption Euler
DRAFT
vc-passed
$$\frac{\dot C}{C} = \frac{1}{\theta}\, (r(t) - \rho)$$
Intuition
DRAFT — ★ CRRA Euler 표준.
3세 비유
DRAFT — ★ CRRA Euler 표준.
Genealogy
| 인물 | 저작 | note |
|---|
| Frank Ramsey (1928) | A Mathematical Theory of Saving | DRAFT — RCK Euler. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ CRRA Euler 표준.
(14.16)
TVC (AH)
Transversality (AH)
DRAFT
vc-passed
$$\lim_{t\to\infty} \exp\!\left(-\int_0^t r(s)\, ds\right) \int_0^1 V(\nu, t \mid q)\, d\nu = 0$$
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — TVC.
(14.17)
V proportional to q
V Proportional to q
DRAFT
vc-passed
$$V(\nu, t \mid q) = q(\nu, t)\, v(t)$$
Intuition
DRAFT — ★ V 가 quality q 에 비례.
3세 비유
DRAFT — ★ V 가 quality q 에 비례.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ V 가 quality q 에 비례.
(14.18) ★
★ V BGP form
V BGP Form
DRAFT
vc-passed
$$V(\nu, t \mid q) = \frac{\beta\, q(\nu, t)\, L}{r^* + z^*}$$
Intuition
DRAFT — ★ ★ AH BGP 자산가치 — 이윤 / (이자 + Poisson hazard).
3세 비유
DRAFT — ★ ★ AH BGP 자산가치 — 이윤 / (이자 + Poisson hazard).
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ AH BGP 자산가치 — 이윤 / (이자 + Poisson hazard).
(14.19) ★
★ AH no-arb
AH No-Arbitrage
DRAFT
vc-passed
$$r^* + z^* = \lambda\, \eta\, \beta\, L$$
Intuition
DRAFT — ★ ★ AH no-arbitrage — 이자 + 도전 hazard = R&D 한계.
3세 비유
DRAFT — ★ ★ AH no-arbitrage — 이자 + 도전 hazard = R&D 한계.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ AH no-arbitrage — 이자 + 도전 hazard = R&D 한계.
§14.3AH BGP + Pareto
AH BGP + Pareto10 eq
(14.20)
Schumpeterian BGP
Schumpeterian BGP Growth
DRAFT
vc-passed
$$g^* = \mu\, \frac{Z^*}{L}\, \ln \lambda$$
Intuition
★ Schumpeterian BGP — 성장률 = 발명 빈도 × log(quality jump). Romer (linear in scale) 와 차이.
3세 비유
성장 속도 = 발명 자주 + 발명마다 큰 향상.
Genealogy
| 인물 | 저작 | note |
|---|
| Aghion-Howitt (1992) | | |
Applications
- growth empirics: 미국 1980s-2010s tech innovation rate
Civilizational Relevance
★ Schumpeterian framework 의 BGP.
(14.21)
Y growth = Q growth
Y Growth = Q Growth
DRAFT
vc-passed
$$\frac{\dot Y(t)}{Y(t)} = \frac{\dot Q(t)}{Q(t)}$$
Intuition
DRAFT — Y 와 Q 성장률 동일.
3세 비유
DRAFT — Y 와 Q 성장률 동일.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Y 와 Q 성장률 동일.
(14.22) ★
★ g* = (λ-1) z*
★ g* = (λ-1) z*
DRAFT
vc-passed
$$g^* = (\lambda - 1)\, z^*$$
Intuition
DRAFT — ★ ★ AH 결과 — 성장률 = 품질 jump 크기 × Poisson 강도.
3세 비유
DRAFT — ★ ★ AH 결과 — 성장률 = 품질 jump 크기 × Poisson 강도.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ AH 결과 — 성장률 = 품질 jump 크기 × Poisson 강도.
(14.23) ★
★ ★ AH g*
★ ★ AH Growth Rate
DRAFT
vc-passed
$$g^* = \frac{\lambda\, \eta\, \beta\, L - \rho}{\theta + (\lambda - 1)^{-1}}$$
Intuition
DRAFT — ★ ★ ★ AH 정전 — Schumpeterian g*.
3세 비유
DRAFT — ★ ★ ★ AH 정전 — Schumpeterian g*.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ ★ AH 정전 — Schumpeterian g*.
(14.24)
Pareto x
Pareto x
DRAFT
vc-passed
$$x^S(\nu, t \mid q) = \psi^{-1/\beta}\, L = (1-\beta)^{-1/\beta}\, L$$
Intuition
DRAFT — 사회계획 x — markup 제거.
3세 비유
DRAFT — 사회계획 x — markup 제거.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 사회계획 x — markup 제거.
(14.25)
Pareto Y - X
Pareto Y - X
DRAFT
vc-passed
$$\tilde{Y}^S(t) \equiv Y^S(t) - X^S(t) = (\text{cleaner expr})$$
Intuition
DRAFT — Pareto 순산출.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Pareto 순산출.
(14.26)
★ Pareto Q evolution
Pareto Q Evolution
DRAFT
vc-passed
$$\dot Q^S(t) = \eta\, (\lambda - 1)\, Z^S(t)$$
Intuition
DRAFT — ★ Pareto Q 동학.
3세 비유
DRAFT — ★ Pareto Q 동학.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ Pareto Q 동학.
(14.27)
Pareto Hamiltonian
Pareto Hamiltonian
DRAFT
vc-passed
$$\hat H(Q^S, C^S, \mu^S) = \frac{(C^S)^{1-\theta} - 1}{1-\theta} + \mu^S\, [\eta(\lambda - 1)(1-\beta)^{-1/\beta} \cdots]$$
Intuition
DRAFT — 사회계획 Hamiltonian.
3세 비유
DRAFT — 사회계획 Hamiltonian.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 사회계획 Hamiltonian.
(14.28)
Quality ladder Y (single)
Quality Ladder Y (single)
DRAFT
vc-passed
$$Y(t) = \frac{1}{1-\beta}\, x(t \mid q)^{1-\beta}\, q(t)^{\beta}\, L^{\beta}$$
Intuition
DRAFT — 단일 quality ladder Y.
3세 비유
DRAFT — 단일 quality ladder Y.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 단일 quality ladder Y.
(14.29)
★ AH L*_R
★ AH L*_R (Lab Eq)
DRAFT
vc-passed
$$L^*_R = \frac{\lambda(1-\beta)\, \eta\, L - \rho}{\cdots}$$
Intuition
DRAFT — ★ Lab equipment R&D 노동.
3세 비유
DRAFT — ★ Lab equipment R&D 노동.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ Lab equipment R&D 노동.
§14.4Aghion 2001 step-by-step duopoly
Aghion 2001 Step-by-step Duopoly27 eq
(14.30)
Cleansing recessions
Cleansing Recessions
DRAFT
vc-passed
$$\text{Recessions} \Rightarrow \uparrow Z(t) \Rightarrow \uparrow A(t+\tau)$$
Intuition
Schumpeter 의 'cleansing recessions' — 경기침체기에 비효율 기업 퇴출 + R&D 증가 → 장기 성장.
3세 비유
불황이 "청소 효과" — 약한 기업 정리하고 새 기술 도입.
Genealogy
| 인물 | 저작 | note |
|---|
| Joseph Schumpeter (1942) | Capitalism, Socialism and Democracy | |
Civilizational Relevance
거시 변동의 long-run 효과 framework.
(14.31)
AH → modern firm dynamics
AH → Modern Firm Dynamics
DRAFT
vc-passed
$$\eta(L_R(q))\, V(\lambda q) = w(q)$$
Intuition
DRAFT — ★ R&D 노동 free-entry.
3세 비유
DRAFT — ★ R&D 노동 free-entry.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion & Peter Howitt (1992) | A Model of Growth Through Creative Destruction (Econometrica) | DRAFT — Schumpeterian growth 의 정전. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction concept. |
| Grossman & Helpman (1991) | Quality Ladders in the Theory of Growth (RES) | DRAFT — quality ladder 평행 모형. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ R&D 노동 free-entry.
(14.32) ★
Two-firm Aghion duopoly
Two-firm Aghion Duopoly
DRAFT
vc-passed
$$\eta(L^1_R)\, V_2(\lambda q) = w(q),\ \eta(L^2_R)\, V_1(\lambda q) = w(q)$$
Intuition
DRAFT — ★ Aghion 2001 duopoly.
3세 비유
DRAFT — ★ Aghion 2001 duopoly.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Aghion 2001 duopoly.
(14.33)
★ Aghion Y (continuum)
Aghion Y (continuum)
DRAFT
vc-passed
$$Y(t) = \frac{1}{1-\beta}\, \int_0^1 q(\nu, t)^{\beta}\, x(\nu, t \mid q)^{1-\beta}\, d\nu \cdot L^{\beta}$$
Intuition
DRAFT — ★ Aghion 2001 통합 Y.
3세 비유
DRAFT — ★ Aghion 2001 통합 Y.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ Aghion 2001 통합 Y.
(14.34)
η decreasing returns
η Decreasing Returns
DRAFT
vc-passed
$$\lim_{z \to \infty} \eta(z) = 0,\ \lim_{z \to 0} \eta(z) = \infty$$
Intuition
DRAFT — ★ R&D 의 한계 감소.
3세 비유
DRAFT — ★ R&D 의 한계 감소.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ R&D 의 한계 감소.
(14.35)
Total Z
Total Z
DRAFT
vc-passed
$$Z(t) = \int_0^1 [z(\nu, t) + \hat z(\nu, t)]\, d\nu$$
Intuition
DRAFT — 총 R&D = leader + follower.
3세 비유
DRAFT — 총 R&D = leader + follower.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 총 R&D = leader + follower.
(14.36)
Demand (Aghion)
Demand (Aghion)
DRAFT
vc-passed
$$x(\nu, t \mid q) = p_x(\nu, t \mid q)^{-1/\beta}\, q(\nu, t)\, L$$
Intuition
DRAFT — Aghion 수요.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Aghion 수요.
(14.37)
Step-by-step κ
Step-by-step κ
DRAFT
vc-passed
$$\kappa \geq \frac{1}{1-\beta}\, \frac{1}{1-\beta} \cdots$$
Intuition
DRAFT — ★ κ step-size.
3세 비유
DRAFT — ★ κ step-size.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ κ step-size.
(14.38)
Limit price
Aghion Limit Price
DRAFT
vc-passed
$$p_x(\nu, t \mid q) = 1$$
Intuition
DRAFT — Aghion limit price.
3세 비유
DRAFT — Aghion limit price.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Aghion limit price.
(14.39)
x = q L
x = q L
DRAFT
vc-passed
$$x(\nu, t \mid q) = q\, L$$
Intuition
DRAFT — Aghion 수량.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Aghion 수량.
(14.40) ★
★ Aghion HJB
★ Aghion HJB
DRAFT
vc-passed
$$r(t)\, V(\nu, t \mid q) - \dot V = \max_{z \geq 0} \{\pi - z V\}$$
Intuition
DRAFT — ★ ★ Aghion HJB.
3세 비유
DRAFT — ★ ★ Aghion HJB.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Aghion HJB.
(14.41)
Free-entry (general)
Free-Entry (Aghion)
DRAFT
vc-passed
$$\eta(\hat z)\, V(\nu, t \mid \kappa q) \leq q(\nu, t)$$
Intuition
DRAFT — Aghion free-entry.
3세 비유
DRAFT — Aghion free-entry.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Aghion free-entry.
(14.42)
Innovator value diff
Innovator Value Diff
DRAFT
vc-passed
$$\varphi[V(\nu, t \mid \lambda q) - V(\nu, t \mid q)] \leq q(\nu, t)$$
Intuition
DRAFT — ★ Aghion 도전자 free-entry.
3세 비유
DRAFT — ★ Aghion 도전자 free-entry.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ Aghion 도전자 free-entry.
(14.43)
Innovator equality
Innovator Equality
DRAFT
vc-passed
$$\varphi[V(\lambda q) - V(q)] = q$$
Intuition
DRAFT — free-entry binding.
3세 비유
DRAFT — free-entry binding.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — free-entry binding.
(14.44)
Aghion firm description
Aghion Firm Description
DRAFT
vc-passed
$$\text{firm with quality } q,\ \text{leader value } V(q),\ \text{follower } V(q/\lambda)$$
Intuition
DRAFT — Aghion firm value 표.
3세 비유
DRAFT — Aghion firm value 표.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Aghion firm value 표.
(14.45)
Aghion BGP V
Aghion BGP V
DRAFT
vc-passed
$$V(q) = \frac{q}{\kappa\, \eta(\hat z)}$$
Intuition
DRAFT — ★ Aghion BGP V form.
3세 비유
DRAFT — ★ Aghion BGP V form.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ Aghion BGP V form.
(14.46)
Aghion BGP V (alt)
Aghion BGP V (alt)
DRAFT
vc-passed
$$V(q) = \frac{\beta L\, q}{r^* + \hat z^*\, \eta(\hat z^*)}$$
Intuition
DRAFT — ★ alternative BGP V.
3세 비유
DRAFT — ★ alternative BGP V.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ alternative BGP V.
(14.47) ★
★ Aghion no-arb
★ Aghion No-Arbitrage
DRAFT
vc-passed
$$r^* = \varphi(\lambda - 1)\, \beta L - \hat z^*\, \eta(\hat z^*)$$
Intuition
DRAFT — ★ Aghion no-arb.
3세 비유
DRAFT — ★ Aghion no-arb.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Aghion no-arb.
(14.48) ★
★ ★ Aghion g*
★ ★ Aghion Growth Rate
DRAFT
vc-passed
$$g^* = \frac{1}{\theta}\, [\varphi(\lambda - 1)\, \beta L - \hat z^*\, \eta(\hat z^*) - \rho]$$
Intuition
DRAFT — ★ ★ Aghion duopoly g*.
3세 비유
DRAFT — ★ ★ Aghion duopoly g*.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Aghion duopoly g*.
(14.49)
Q evolution (transition)
Q Evolution (Transition)
DRAFT
vc-passed
$$Q(t + dt) = \lambda\, \varphi z(t)\, dt\, Q(t) + \kappa\, \hat z(t)\, \eta(\hat z(t))\, dt\, Q(t)$$
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Q 동학.
(14.50)
z-bar definition
z-bar definition
DRAFT
vc-passed
$$z(t) \equiv \frac{1}{Q(t)}\, \int_0^1 z(\nu, t \mid q)\, q(\nu, t)\, d\nu$$
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — z-bar.
(14.51) ★
★ Q growth (Aghion)
★ Q Growth (Aghion)
DRAFT
vc-passed
$$\frac{\dot Q}{Q} = (\lambda - 1)\, \varphi z(t) + (\kappa - 1)\, \hat z(t)\, \eta(\hat z(t))$$
Intuition
DRAFT — ★ Aghion Q 성장률 — 두 채널.
3세 비유
DRAFT — ★ Aghion Q 성장률 — 두 채널.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Aghion Q 성장률 — 두 채널.
(14.52) ★
★ Aghion BGP g*
★ Aghion BGP g*
DRAFT
vc-passed
$$g^* = (\lambda - 1)\, \varphi z^* + (\kappa - 1)\, \hat z^*\, \eta(\hat z^*)$$
Intuition
DRAFT — ★ ★ Aghion duopoly final g*.
3세 비유
DRAFT — ★ ★ Aghion duopoly final g*.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Aghion duopoly final g*.
(14.53)
Aghion wellposed
Aghion Wellposed
DRAFT
vc-passed
$$\varphi(\lambda - 1)\beta L - (\theta(\kappa - 1) + 1)\, \hat z^*\, \eta(\hat z^*) > \rho$$
Intuition
DRAFT — wellposed 조건.
3세 비유
DRAFT — wellposed 조건.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — wellposed 조건.
(14.54)
Quality jump prob
Quality Jump Prob
DRAFT
vc-passed
$$x(\nu, t + dt \mid q) = \begin{cases} \lambda x & \text{w/p } \varphi z\, dt \\ x & \text{else} \end{cases}$$
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 확률 분포.
(14.55)
Patent fee + V
Patent Fee + V
DRAFT
vc-passed
$$\eta(\hat z^*)\, V(\kappa q) = (1 + \tau_e)\, q,\ V(q) = \frac{q\, (1 + \tau_e)}{\kappa\, \eta(\hat z^*)}$$
Intuition
DRAFT — ★ 정책 — patent fee.
3세 비유
DRAFT — ★ 정책 — patent fee.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ 정책 — patent fee.
(14.56)
Tax distortion (1+τe)/(1+τi)
Tax Distortion
DRAFT
vc-passed
$$\frac{\varphi(\lambda - 1)\, (1 + \tau_e)}{\kappa\, \eta(\hat z^*)\, (1 + \tau_i)} = 1$$
Intuition
DRAFT — ★ 조세 distortion 합성.
3세 비유
DRAFT — ★ 조세 distortion 합성.
Genealogy
| 인물 | 저작 | note |
|---|
| Philippe Aghion et al. (2001) | Competition, Imitation and Growth with Step-by-Step Innovation (RES) | DRAFT — Aghion-Bloundell duopoly model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — duopoly 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ 조세 distortion 합성.
§14.4.1Klette-Kortum 2004 multi-firm setup
Klette-Kortum 2004 Multi-firm19 eq
(14.57)
KK 평생효용
KK Lifetime Utility
DRAFT
vc-passed
$$\int_0^{\infty} e^{-\rho t}\, \log C(t)\, dt$$
Intuition
DRAFT — Klette-Kortum log utility.
3세 비유
DRAFT — Klette-Kortum log utility.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — Klette-Kortum log utility.
(14.58)
★ Log Euler g(t)=r(t)-ρ
★ Log Euler
DRAFT
vc-passed
$$g(t) \equiv \frac{\dot C}{C} = \frac{\dot Y}{Y} = r(t) - \rho$$
Intuition
DRAFT — ★ KK log Euler.
3세 비유
DRAFT — ★ KK log Euler.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK log Euler.
(14.59) ★
★ Cobb-Douglas Y (KK)
★ Cobb-Douglas Y (KK)
DRAFT
vc-passed
$$Y(t) = \exp\!\left(\int_0^1 \log y(\nu, t)\, d\nu\right)$$
Intuition
DRAFT — ★ Klette-Kortum Cobb-Douglas Y.
3세 비유
DRAFT — ★ Klette-Kortum Cobb-Douglas Y.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Klette-Kortum Cobb-Douglas Y.
(14.60)
Demand y_i
Demand y_i
DRAFT
vc-passed
$$y(\nu, t) = \frac{Y(t)}{p_y(\nu, t)}$$
Intuition
DRAFT — 단위탄력성 수요.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 단위탄력성 수요.
(14.61)
Production y_i = q l_i
Production y_i = q l_i
DRAFT
vc-passed
$$y_i(\nu, t) = q_i(\nu, t)\, l_i(\nu, t)$$
Intuition
DRAFT — labor-only 생산.
3세 비유
DRAFT — labor-only 생산.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — labor-only 생산.
(14.62)
Marginal cost
Marginal Cost
DRAFT
vc-passed
$$MC_i(\nu, t) = \frac{w(t)}{q_i(\nu, t)}$$
Intuition
DRAFT — 한계비용 = 임금/품질.
3세 비유
DRAFT — 한계비용 = 임금/품질.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 한계비용 = 임금/품질.
(14.63) ★
★ KK Limit price
★ KK Limit Price
DRAFT
vc-passed
$$p^y_i(\nu, t) = \frac{w(t)}{q_{-i}(\nu, t)}$$
Intuition
DRAFT — ★ Bertrand limit price = 도전자 비용.
3세 비유
DRAFT — ★ Bertrand limit price = 도전자 비용.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Bertrand limit price = 도전자 비용.
(14.64)
★ KK firm output
★ KK Firm Output
DRAFT
vc-passed
$$y_i(\nu, t) = \frac{q_{-i}(\nu, t)}{w(t)}\, Y(t)$$
Intuition
DRAFT — ★ KK firm 산출.
3세 비유
DRAFT — ★ KK firm 산출.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK firm 산출.
(14.65)
Innovation prob = h
Innovation Prob = h
DRAFT
vc-passed
$$z_i(\nu, t) = (h_i(\nu, t))$$
Intuition
DRAFT — innovation 확률 = R&D h.
3세 비유
DRAFT — innovation 확률 = R&D h.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — innovation 확률 = R&D h.
(14.66)
Innovation cost h_bar
Innovation Cost h_bar
DRAFT
vc-passed
$$\bar h \text{ defined as average R\&D}$$
Intuition
DRAFT — h-bar 정의.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — h-bar 정의.
(14.67) ★
★ KK quality ladder
★ KK Quality Ladder
DRAFT
vc-passed
$$q_{-i}(\nu, t) = \lambda^{n_{-i}(\nu, t)}$$
Intuition
DRAFT — ★ 도전자 품질 = λ^n.
3세 비유
DRAFT — ★ 도전자 품질 = λ^n.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ 도전자 품질 = λ^n.
(14.68) ★
Markov n evolution
Markov n Evolution
DRAFT
vc-passed
$$n(\nu, t + dt) = \begin{cases} n + 1 & \text{w/p } z_i\, dt \\ 0 & \text{w/p } z_{-i}\, dt + \kappa \end{cases}$$
Intuition
DRAFT — ★ KK quality gap Markov chain.
3세 비유
DRAFT — ★ KK quality gap Markov chain.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ KK quality gap Markov chain.
(14.69)
Profit (KK)
KK Profit
DRAFT
vc-passed
$$\pi_i(\nu, t) = (p^y_i - MC_i)\, y_i = \frac{w(t)}{q_{-i}} \cdot \frac{Y(t)}{p^y_i}$$
Intuition
DRAFT — ★ KK 이윤.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK 이윤.
(14.70)
ξ definition
ξ Definition
DRAFT
vc-passed
$$\xi_n(t) \equiv z_n(t),\ p^y_i,\ y_i,\ \xi_{-n}(t) \equiv z_{-n}(t)$$
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — 표기 정리.
(14.71)
★ Aggregate R&D
★ Aggregate R&D
DRAFT
vc-passed
$$h_n(t) = G(z_n(t)) + G(z_{-n}(t))$$
Intuition
DRAFT — ★ KK aggregate R&D = 양쪽 합.
3세 비유
DRAFT — ★ KK aggregate R&D = 양쪽 합.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK aggregate R&D = 양쪽 합.
(14.72)
Resource constraint
Resource Constraint (KK)
DRAFT
vc-passed
$$1 \geq \sum_{n=0}^{\infty} \mu_n(t)\, [\omega(t)\, \lambda^{-n} + G(z_n) + G(z_{-n})]$$
Intuition
DRAFT — ★ KK 자원 제약.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK 자원 제약.
(14.73)
Wage share ω
Wage Share ω
DRAFT
vc-passed
$$\omega(t) \equiv \frac{w(t)}{Y(t)}$$
Intuition
DRAFT — ★ KK wage share.
3세 비유
DRAFT — ★ KK wage share.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK wage share.
(14.74)
log Q definition
log Q Definition
DRAFT
vc-passed
$$\log Q(t) \equiv \int_0^1 \log q(\nu, t)\, d\nu$$
Intuition
DRAFT — ★ Cobb-Douglas log Q.
3세 비유
DRAFT — ★ Cobb-Douglas log Q.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ Cobb-Douglas log Q.
(14.75)
Wage formula
Wage Formula
DRAFT
vc-passed
$$w(t) = Q(t)\, \lambda^{-\sum n\, \mu_n(t)}$$
Intuition
DRAFT — ★ KK wage equilibrium.
3세 비유
DRAFT — ★ KK wage equilibrium.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK wage equilibrium.
§14.4.3KK steady-state HJB + Markov chain
KK Steady-State HJB + Markov chain17 eq
(14.76) ★
★ KK steady-state HJB
★ KK Steady-State HJB
DRAFT
vc-passed
$$r(t)\, V_n(t) - \dot V_n = \pi_n + z_n[V_{n+1} - V_n] + [z_{-n} + \kappa][V_0 - V_n]$$
Intuition
DRAFT — ★ KK steady-state HJB.
3세 비유
DRAFT — ★ KK steady-state HJB.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ KK steady-state HJB.
(14.77)
v_n definition
v_n Definition
DRAFT
vc-passed
$$v_n(t) \equiv V_n(t)/Y(t)$$
Intuition
DRAFT — ★ KK 정규화.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK 정규화.
(14.78)
v_n max problem
v_n Max Problem
DRAFT
vc-passed
$$\rho v_n = \max_{z_n} \{(1 - \lambda^{-n}) - \omega^*\, G(z_n) + z_n[v_{n+1} - v_n] - [z^*_{-n} + \kappa][v_n - v_0]\}$$
Intuition
DRAFT — ★ KK Bellman.
3세 비유
DRAFT — ★ KK Bellman.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK Bellman.
(14.79)
v_0 max
v_0 Max
DRAFT
vc-passed
$$\rho v_0 = \max_{z_0} \{-\omega^*\, G(z_0) + z_0[v_1 - v_0] + z^*_0[v_{-1} - v_0]\}$$
Intuition
DRAFT — v_0 Bellman.
3세 비유
DRAFT — v_0 Bellman.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — v_0 Bellman.
(14.80)
v_-1 max
v_-1 Max
DRAFT
vc-passed
$$\rho v_{-1} = \max_{z_{-1}} \{-\omega^*\, G(z_{-1}) + [z_{-1} + \kappa][v_0 - v_{-1}]\}$$
Intuition
DRAFT — v_-1 Bellman.
3세 비유
DRAFT — v_-1 Bellman.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — v_-1 Bellman.
(14.81)
z*_n FOC
z*_n FOC
DRAFT
vc-passed
$$z^*_n = \max\!\left\{G'^{-1}\!\left(\frac{v_{n+1} - v_n}{\omega^*}\right), 0\right\}$$
Intuition
DRAFT — ★ R&D FOC.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ R&D FOC.
(14.82)
z*_-1 FOC
z*_-1 FOC
DRAFT
vc-passed
$$z^*_{-1} = \max\!\{G'^{-1}((v_0 - v_{-1})/\omega^*), 0\}$$
Intuition
DRAFT — z*_-1 FOC.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — z*_-1 FOC.
(14.83)
z*_0 FOC
z*_0 FOC
DRAFT
vc-passed
$$z^*_0 = \max\!\{G'^{-1}((v_1 - v_0)/\omega^*), 0\}$$
Intuition
DRAFT — z*_0 FOC.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — z*_0 FOC.
(14.84)
Stationary distribution n+1
Stationary Distribution n+1
DRAFT
vc-passed
$$(z^*_{n+1} + z^*_{-1} + \kappa)\, \mu^*_{n+1} = z^*_n\, \mu^*_n$$
Intuition
DRAFT — ★ stationary distribution.
3세 비유
DRAFT — ★ stationary distribution.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ stationary distribution.
(14.85)
Stationary distribution n=1
Stationary Distribution n=1
DRAFT
vc-passed
$$(z^*_1 + z^*_{-1} + \kappa)\, \mu^*_1 = 2\, z^*_0\, \mu^*_0$$
Intuition
DRAFT — stat dist n=1.
3세 비유
DRAFT — stat dist n=1.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — stat dist n=1.
(14.86)
Stationary distribution n=0
Stationary Distribution n=0
DRAFT
vc-passed
$$2\, z^*_0\, \mu^*_0 = z^*_{-1} + \kappa$$
Intuition
DRAFT — stat dist n=0.
3세 비유
DRAFT — stat dist n=0.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — stat dist n=0.
(14.87)
Resource binding
Resource Binding
DRAFT
vc-passed
$$1 \geq \sum_{n=0}^{\infty} \mu^*_n\, [\omega^*\, \lambda^{-n} + G(z^*_n) + G(z^*_{-n})]$$
Intuition
DRAFT — ★ KK resource binding.
3세 비유
DRAFT — ★ KK resource binding.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK resource binding.
(14.88) ★
★ ★ KK growth rate
★ ★ KK Growth Rate
DRAFT
vc-passed
$$g^* = \log \lambda\, \cdot \left(2\mu^*_0\, z^*_0 + \sum_{n} \mu^*_n\, z^*_n\right)$$
Intuition
DRAFT — ★ ★ KK Schumpeterian growth — quality jump × innovation rate 합.
3세 비유
DRAFT — ★ ★ KK Schumpeterian growth — quality jump × innov
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ KK Schumpeterian growth — quality jump × innovation rate 합.
(14.89)
z* monotone
z* Monotone
DRAFT
vc-passed
$$z^*_{n+1} \leq z^*_n\quad \forall n$$
Intuition
DRAFT — ★ R&D 강도 leader 가 따라잡혀 갈수록 감소.
3세 비유
DRAFT — ★ R&D 강도 leader 가 따라잡혀 갈수록 감소.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ R&D 강도 leader 가 따라잡혀 갈수록 감소.
(14.90)
Aux: ρ-bar Bellman
Aux: ρ-bar Bellman
DRAFT
vc-passed
$$\bar\rho\, v_n = \max_{z_n} \{(1 - \lambda^{-n}) - \omega^*\, G(z_n) + z_n[v_{n+1} - v_n]\}$$
Intuition
DRAFT — ★ ρ̄ Bellman.
3세 비유
DRAFT — ★ ρ̄ Bellman.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ ρ̄ Bellman.
(14.91)
ρ-bar definition
ρ-bar Definition
DRAFT
vc-passed
$$\bar\rho \equiv \rho + z^*_{-1} + \kappa$$
Intuition
DRAFT — ★ effective discount.
3세 비유
DRAFT — ★ effective discount.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ effective discount.
(14.92)
ρ-bar δ inequality
ρ-bar δ Inequality
DRAFT
vc-passed
$$\bar\rho\, \delta_{n+1} \leq \lambda^{-n}(1 - \lambda^{-1}) + z^*_{n+1}(\delta_{n+2} - \delta_{n+1})$$
Intuition
DRAFT — ★ KK 단조성 증명.
3세 비유
DRAFT — ★ KK 단조성 증명.
Genealogy
| 인물 | 저작 | note |
|---|
| Tor Klette & Samuel Kortum (2004) | Innovating Firms and Aggregate Innovation (JPE) | DRAFT — multi-firm Schumpeterian model. |
| Aghion & Howitt (1992) | A Model of Growth Through Creative Destruction | DRAFT — KK 의 토대. |
Applications
- Aghion-Howitt 1992 creative destruction
- Klette-Kortum 2004 multi-firm
- Aghion 2001 step-by-step duopoly
- Schumpeter 1942 creative destruction
- modern firm dynamics empirics
Civilizational Relevance
DRAFT — ★ KK 단조성 증명.