§15.2DTC 평생효용 + 자원
DTC Utility + Resources8 eq
(15.2)
DTC 평생효용
DTC Lifetime Utility
DRAFT
vc-passed
$$\int_0^{\infty} e^{-\rho t}\, \frac{C(t)^{1-\theta} - 1}{1-\theta}\, dt$$
Intuition
DRAFT — DTC 평생효용 (CRRA).
3세 비유
DRAFT — DTC 평생효용 (CRRA).
Genealogy
| 인물 | 저작 | note |
|---|
| Frank Ramsey (1928) | A Mathematical Theory of Saving | DRAFT — Euler/CRRA. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — DTC 평생효용 (CRRA).
(15.4)
자원제약
Resource Constraint
DRAFT
vc-passed
$$C(t) + X(t) + Z(t) \leq Y(t)$$
Intuition
DRAFT — DTC 자원제약.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — DTC 자원제약.
(15.5)
Skilled good production (expanding-variety)
Skilled Good Production (Expanding-Variety)
DRAFT
vc-passed
$$Y_L(t) = \frac{1}{1-\beta}\, \int_0^{N_L(t)} x_L(\nu, t)^{1-\beta}\, d\nu \cdot L^{\beta}$$
Intuition
비숙련 산출의 expanding-variety 형식. (ch18 (18.7)) 와 동일 구조 — N_L(t) 가 비숙련 노동용 중간재 종 수.
3세 비유
비숙련 노동용 도구가 N_L 종류 있고, 각각 x_L 양 사용. 도구 종 수가 늘면 생산성 상승.
Genealogy
| 인물 | 저작 | note |
|---|
| Paul Romer (1990) | Endogenous Technological Change | |
| Acemoglu (2002) | DTC 적용 | |
Civilizational Relevance
Romer 1990 expanding-variety 의 양면 (skilled/unskilled) 적용.
(15.6)
Y_H 생산
Y_H Production
DRAFT
vc-passed
$$Y_H(t) = \frac{1}{1-\beta}\, \int_0^{N_H(t)} x_H(\nu, t)^{1-\beta}\, d\nu \cdot H^{\beta}$$
Intuition
DRAFT — (15.5) 의 H-부문 사촌.
3세 비유
DRAFT — (15.5) 의 H-부문 사촌.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — (15.5) 의 H-부문 사촌.
(15.7)
Markets H sector
Markets H Sector
DRAFT
vc-passed
$$x^p_H(\nu, t)\ \forall \nu \in [0, N_H(t)]\ \text{markup pricing}$$
Intuition
DRAFT — H-부문 가격.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — H-부문 가격.
(15.8)
Variety value V_f
Variety Value V_f
DRAFT
vc-passed
$$V_f(\nu, t) = \int_t^{\infty} \exp\!\left(-\int_t^s r(s')\, ds'\right)\, \pi_f(\nu, s)\, ds$$
Intuition
DRAFT — ★ 변종 가치 — f ∈ {L, H}.
3세 비유
DRAFT — ★ 변종 가치 — f ∈ {L, H}.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ 변종 가치 — f ∈ {L, H}.
(15.9)
Profit π_f
Profit π_f
DRAFT
vc-passed
$$\pi_f(\nu, t) \equiv p^x_f\, x_f - \psi\, x_f$$
Intuition
DRAFT — 이윤 = 가격 × 수량 - 비용.
3세 비유
DRAFT — 이윤 = 가격 × 수량 - 비용.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — 이윤 = 가격 × 수량 - 비용.
(15.10)
Price 정규화 (CES)
Price Normalization (CES)
DRAFT
vc-passed
$$\bigl[\gamma_L^{\varepsilon}\, p_L(t)^{1-\varepsilon} + \gamma_H^{\varepsilon}\, p_H(t)^{1-\varepsilon}\bigr]^{\frac{1}{1-\varepsilon}} = 1$$
Intuition
CES dual price index = 1 정규화. unit cost function = ideal price index.
3세 비유
두 sector 가격의 CES 평균이 1로 고정 — numéraire 정규화.
Genealogy
| 인물 | 저작 | note |
|---|
| Diewert (1976) | Superlative index theory | |
Applications
- CPI calculation
- trade theory two-country
Civilizational Relevance
수치 정규화의 표준 도구.
§15.3균형 — markup, skill premium, growth
Equilibrium — Markup, Skill Premium, Growth19 eq
(15.11)
Equilibrium tuple
Equilibrium Tuple
DRAFT
vc-passed
$$[C(t), X(t), Z(t), N_L(t), N_H(t)]_{t=0}^{\infty}$$
Intuition
DRAFT — DTC 균형 변수.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — DTC 균형 변수.
(15.12)
H Sector Profit Max
H Sector Profit Max
DRAFT
vc-passed
$$\max_{H,\, x_H} p_H(t)\, Y_H(t) - w_H(t)\, H - \int x_H \cdot p^x_H\, d\nu$$
Intuition
DRAFT — H-부문 이윤 max.
3세 비유
DRAFT — H-부문 이윤 max.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — H-부문 이윤 max.
(15.13)
L Sector demand
L Sector Demand
DRAFT
vc-passed
$$x_L(\nu, t) = \left(\frac{p_L(t)}{p^x_L}\right)^{1/\beta}\, L$$
Intuition
DRAFT — L-부문 수요.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — L-부문 수요.
(15.14)
H Sector demand
H Sector Demand
DRAFT
vc-passed
$$x_H(\nu, t) = \left(\frac{p_H(t)}{p^x_H}\right)^{1/\beta}\, H$$
Intuition
DRAFT — H-부문 수요.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — H-부문 수요.
(15.15)
Limit pricing both
Limit Pricing Both
DRAFT
vc-passed
$$p^x_L = p^x_H = 1,\ x_L = p_L^{1/\beta}\, L,\ x_H = p_H^{1/\beta}\, H$$
Intuition
DRAFT — ★ 양 부문 동일 markup.
3세 비유
DRAFT — ★ 양 부문 동일 markup.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ 양 부문 동일 markup.
(15.16)
Y_L closed
Y_L Closed
DRAFT
vc-passed
$$Y_L(t) = \frac{1}{1-\beta}\, p_L(t)^{(1-\beta)/\beta}\, N_L(t)\, L$$
Intuition
DRAFT — Y_L 닫힌 형태.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — Y_L 닫힌 형태.
(15.17)
Y_H closed
Y_H Closed
DRAFT
vc-passed
$$Y_H(t) = \frac{1}{1-\beta}\, p_H(t)^{(1-\beta)/\beta}\, N_H(t)\, H$$
Intuition
DRAFT — Y_H 닫힌 형태.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — Y_H 닫힌 형태.
(15.18) ★
★ Relative price p
★ Relative Price p
DRAFT
vc-passed
$$p(t) \equiv \frac{p_H(t)}{p_L(t)} = \gamma\, \left(\frac{Y_H}{Y_L}\right)^{-1/\varepsilon}$$
Intuition
DRAFT — ★ DTC 상대가격 — CES inverse.
3세 비유
DRAFT — ★ DTC 상대가격 — CES inverse.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ DTC 상대가격 — CES inverse.
(15.19) ★
★ Skill premium ω
★ Skill Premium ω
DRAFT
vc-passed
$$\omega(t) \equiv \frac{w_H(t)}{w_L(t)} = p(t)^{1/\beta}\, \frac{N_H}{N_L} = \gamma^{\varepsilon\sigma}\, \cdots$$
Intuition
DRAFT — ★ ★ DTC 의 핵심 — 임금 premium 분해.
3세 비유
DRAFT — ★ ★ DTC 의 핵심 — 임금 premium 분해.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ DTC 의 핵심 — 임금 premium 분해.
(15.20)
Equilibrium R&D allocation (skill bias)
Equilibrium R&D Allocation
DRAFT
vc-passed
$$\frac{N_H(t)}{N_L(t)} = \eta^*\, \left(\frac{H}{L}\right)^{\sigma}$$
Intuition
★★ DTC 의 핵심 결과. 균형에서 skilled 기술 종 수 / unskilled 기술 종 수 = (H/L)^σ. σ > 1: 노동 공급이 늘면 그 노동을 보강하는 기술 종 수 증가.
3세 비유
고학력자 비율이 높은 사회 → 고학력 보강 기술이 더 많이 발명됨. **공급이 기술 방향 결정**.
Genealogy
| 인물 | 저작 | note |
|---|
| Acemoglu (2002) | Directed Technical Change (Theorem) | |
| Acemoglu·Zilibotti (2001) | Cross-country implications | |
Applications
- ★ 미국 1970-2010 대학생 비율 증가 → AI·소프트웨어 (skill-biased) 폭발
- 한국 1990-2020 4년제 진학률 → IT·금융 발전
- AI 가 white-collar 보강하는 economic logic
Civilizational Relevance
★★★ '시장이 기술 방향 결정' 의 수학. 정책 (교육, R&D 보조금) 의 기술적 영향 framework.
(15.21)
Free-entry both H/L
Free-Entry Both
DRAFT
vc-passed
$$\eta_H\, V_H \leq 1,\ Z_H \geq 0,\ \eta_H V_H = 1\ \text{if } Z_H > 0$$
Intuition
DRAFT — H-부문 free-entry (대칭).
3세 비유
DRAFT — H-부문 free-entry (대칭).
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — H-부문 free-entry (대칭).
(15.22)
Consumption Euler
Consumption Euler
DRAFT
vc-passed
$$\frac{\dot C}{C} = \frac{1}{\theta}\, (r(t) - \rho)$$
Intuition
DRAFT — ★ CRRA Euler.
3세 비유
DRAFT — ★ CRRA Euler.
Genealogy
| 인물 | 저작 | note |
|---|
| Frank Ramsey (1928) | A Mathematical Theory of Saving | DRAFT — Euler/CRRA. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ CRRA Euler.
(15.23)
TVC
Transversality
DRAFT
vc-passed
$$\lim_{t\to\infty} \exp\!\left(-\int_0^t r(s)\, ds\right) (N_L V_L + N_H V_H) = 0$$
Intuition
DRAFT — ★ DTC TVC.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ DTC TVC.
(15.24) ★
BGP V_L, V_H
BGP V_L, V_H
DRAFT
vc-passed
$$V_L = \frac{\beta\, p_L^{1/\beta}\, L}{r^*},\ V_H = \frac{\beta\, p_H^{1/\beta}\, H}{r^*}$$
Intuition
DRAFT — ★ ★ BGP value formulae.
3세 비유
DRAFT — ★ ★ BGP value formulae.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ BGP value formulae.
(15.25) ★
★ V_H/V_L ratio
★ V_H/V_L Ratio
DRAFT
vc-passed
$$\frac{V_H}{V_L} = \gamma^{\varepsilon\sigma}\, \left(\frac{N_H}{N_L}\right)^{-1/\sigma}\, \left(\frac{H}{L}\right)^{\sigma}$$
Intuition
DRAFT — ★ ★ DTC value ratio — direction of innovation.
3세 비유
DRAFT — ★ ★ DTC value ratio — direction of innovation.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ DTC value ratio — direction of innovation.
(15.26)
σ vs ε relationship
σ vs ε Relationship
DRAFT
vc-passed
$$\sigma > 1 \Leftrightarrow \varepsilon > 1\ \text{(strong induced innovation)}$$
Intuition
DRAFT — ★ market-size vs price effect.
3세 비유
DRAFT — ★ market-size vs price effect.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ market-size vs price effect.
(15.27) ★
★ ★ N_H/N_L equilibrium
★ ★ N_H/N_L Equilibrium
DRAFT
vc-passed
$$\left(\frac{N_H}{N_L}\right)^* = \eta^{\sigma}\, \gamma^{\varepsilon}\, \left(\frac{H}{L}\right)^{\sigma - 1}$$
Intuition
DRAFT — ★ ★ ★ DTC 정전 — H 가 큰 사회는 H-augmenting tech 만든다 (σ>1).
3세 비유
DRAFT — ★ ★ ★ DTC 정전 — H 가 큰 사회는 H-augmenting tech 만든다 (σ>
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ ★ DTC 정전 — H 가 큰 사회는 H-augmenting tech 만든다 (σ>1).
(15.28) ★
★ DTC growth rate
★ DTC Growth Rate
DRAFT
vc-passed
$$g^* = \frac{1}{\theta}\, [\beta\, \gamma^{\varepsilon}\, H(\eta_H H)^{\sigma-1} + \gamma^{\varepsilon}\, L(\eta_L L)^{\sigma-1} - \rho]$$
Intuition
DRAFT — ★ ★ DTC growth — 양 부문 합성.
3세 비유
DRAFT — ★ ★ DTC growth — 양 부문 합성.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ DTC growth — 양 부문 합성.
(15.29)
Aggregate growth
Aggregate Growth
DRAFT
vc-passed
$$g^* = \frac{1}{\theta}\, [\beta\, \gamma^{\varepsilon}\, H(\eta_H H)^{\sigma-1} + \gamma^{\varepsilon}\, L(\eta_L L)^{\sigma-1} - \rho]$$
Intuition
DRAFT — (15.28) 동일.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — (15.28) 동일.
§15.4Knowledge spillover variant
Knowledge Spillover Variant10 eq
(15.30)
Skilled wage premium (long-run)
Long-Run Skilled Wage Premium
DRAFT
vc-passed
$$\frac{w_H}{w_L} = \eta\, \left(\frac{H}{L}\right)^{\sigma-2}$$
Intuition
★ DTC 의 long-run prediction. **공급 H/L 가 늘면 임금 premium 도 σ>2 면 증가** (역 직관!). 미국 1980s post-college 폭증의 설명: 고학력자 늘었는데 premium 도 늘었다 → σ > 2.
3세 비유
대학생 늘어났는데 대학 임금 프리미엄도 늘었다 — DTC 의 "역직관적" 핵심 결과.
Genealogy
| 인물 | 저작 | note |
|---|
| Acemoglu (2002) | DTC long-run | |
Applications
- Goldin-Katz 2008 "Race between Education and Technology" 핵심 framework
- AI 가 college premium 어떻게 영향 줄까 분석
Civilizational Relevance
★ 21세기 inequality 폭발 설명의 정전.
(15.31) ★
★ Spillover R&D function
★ Spillover R&D Function
DRAFT
vc-passed
$$\dot N_L = \eta_L\, N_L^{(1+\delta)/2}\, N_H^{(1-\delta)/2}\, S_L(t)$$
Intuition
DRAFT — ★ knowledge spillover δ.
3세 비유
DRAFT — ★ knowledge spillover δ.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ knowledge spillover δ.
(15.32)
Scientist constraint
Scientist Constraint
DRAFT
vc-passed
$$S_L(t) + S_H(t) \leq S$$
Intuition
DRAFT — scientist 자원.
3세 비유
DRAFT — scientist 자원.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — scientist 자원.
(15.33)
Free-entry L (spillover)
Free-Entry L (Spillover)
DRAFT
vc-passed
$$\eta_L\, N_L^{(1+\delta)/2}\, N_H^{(1-\delta)/2}\, V_L \leq w_S(t)$$
Intuition
DRAFT — L spillover free-entry.
3세 비유
DRAFT — L spillover free-entry.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — L spillover free-entry.
(15.34)
Free-entry H (spillover)
Free-Entry H (Spillover)
DRAFT
vc-passed
$$\eta_H\, N_L^{(1-\delta)/2}\, N_H^{(1+\delta)/2}\, V_H \leq w_S(t)$$
Intuition
DRAFT — H spillover free-entry.
3세 비유
DRAFT — H spillover free-entry.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — H spillover free-entry.
(15.35)
Profit ratio identity
Profit Ratio Identity
DRAFT
vc-passed
$$\eta_L\, N_L^{\delta}\, \pi_L = \eta_H\, N_H^{\delta}\, \pi_H$$
Intuition
DRAFT — ★ 균형 직교 조건.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ 균형 직교 조건.
(15.36) ★
★ N_H/N_L (spillover)
★ N_H/N_L (Spillover)
DRAFT
vc-passed
$$\left(\frac{N_H}{N_L}\right)^* = \eta^{\sigma/(1-\delta\sigma)}\, \gamma^{(1-\delta)\varepsilon/(1-\delta\sigma)}\, \cdots$$
Intuition
DRAFT — ★ DTC spillover N ratio.
3세 비유
DRAFT — ★ DTC spillover N ratio.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ DTC spillover N ratio.
(15.37) ★
★ ω* spillover
★ ω* Spillover
DRAFT
vc-passed
$$\omega^* \equiv \frac{w_H^*}{w_L^*} = \eta^{(\sigma-1)/(1-\delta\sigma)}\, \gamma^{(1-\delta)\varepsilon/\beta(1-\delta\sigma)}\, \cdots$$
Intuition
DRAFT — ★ DTC spillover skill premium.
3세 비유
DRAFT — ★ DTC spillover skill premium.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ DTC spillover skill premium.
(15.38)
S* allocation
S* Allocation
DRAFT
vc-passed
$$\eta_H\, N_H^{\delta - 1}\, S_H = \eta_L\, N_L^{\delta - 1}\, S_L,\ \eta^{(1-\sigma)/(1-\delta\sigma)}\, \cdots$$
Intuition
DRAFT — scientist allocation.
3세 비유
DRAFT — scientist allocation.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — scientist allocation.
(15.39)
Wellposed
Wellposed
DRAFT
vc-passed
$$(1 - \theta)\, \eta_L \eta_H (N_H/N_L)^{\delta} < \rho$$
Intuition
DRAFT — ★ wellposedness.
3세 비유
DRAFT — ★ wellposedness.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ wellposedness.
§15.5Jones-style spillover (g*=n/(1-λ))
Jones-style Spillover6 eq
(15.40)
★ Jones-style spillover
★ Jones-style Spillover
DRAFT
vc-passed
$$\dot N_L = \eta_L\, N_L^{\lambda}\, S_L,\ \dot N_H = \eta_H\, N_H^{\lambda}\, S_H$$
Intuition
DRAFT — ★ Jones critique 의 DTC 사촌.
3세 비유
DRAFT — ★ Jones critique 의 DTC 사촌.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ Jones critique 의 DTC 사촌.
(15.41) ★
★ Population-driven g*
★ Population-Driven g*
DRAFT
vc-passed
$$g^* = \frac{n}{1 - \lambda}$$
Intuition
DRAFT — ★ ★ Jones-style g — 인구로만 결정.
3세 비유
DRAFT — ★ ★ Jones-style g — 인구로만 결정.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Jones-style g — 인구로만 결정.
(15.42)
Innovation balance
Innovation Balance
DRAFT
vc-passed
$$\eta_L\, N_L^{\lambda}\, \pi_L = \eta_H\, N_H^{\lambda}\, \pi_H$$
Intuition
DRAFT — ★ 두 부문 균형.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ 두 부문 균형.
(15.43)
★ N_H/N_L (Jones)
★ N_H/N_L (Jones)
DRAFT
vc-passed
$$\left(\frac{N_H}{N_L}\right)^* = \eta^{\sigma/(1-\lambda\sigma)}\, \gamma^{\varepsilon/(1-\lambda\sigma)}\, (H/L)^{\sigma-1}/(1-\lambda\sigma)$$
Intuition
DRAFT — ★ Jones DTC ratio.
3세 비유
DRAFT — ★ Jones DTC ratio.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ Jones DTC ratio.
(15.44)
★ ω* (Jones)
★ ω* (Jones)
DRAFT
vc-passed
$$\omega^* = \eta^{(\sigma-1)/(1-\lambda\sigma)}\, \gamma^{\varepsilon/\beta(1-\lambda\sigma)}\, (H/L)^{(\sigma-2)/(1-\lambda\sigma)}$$
Intuition
DRAFT — ★ Jones DTC premium.
3세 비유
DRAFT — ★ Jones DTC premium.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ Jones DTC premium.
(15.45)
Closing prop
Closing Proposition
DRAFT
vc-passed
$$N_H/N_L\ \text{rises with } H,\ \omega^*\ \text{can rise or fall}$$
Intuition
DRAFT — Proposition 15.10 결과.
3세 비유
DRAFT — Proposition 15.10 결과.
Genealogy
| 인물 | 저작 | note |
|---|
| Daron Acemoglu (1998) | Why Do New Technologies Complement Skills? (QJE) | DRAFT — directed technical change 정전. |
| Daron Acemoglu (2002) | Directed Technical Change (RES) | DRAFT — DTC framework 정립. |
| John Hicks (1932) | The Theory of Wages | DRAFT — induced innovation hypothesis 시작. |
| William Kennedy (1964) | Induced Bias in Innovation | DRAFT — Kennedy induced innovation. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — Proposition 15.10 결과.
§15.7Frechet aggregation (Kortum-Eaton)
Frechet Aggregation8 eq
(15.49)
Leontief firm
Leontief Firm
DRAFT
vc-passed
$$Y_i(t) = \min\{b_i\, K(t),\, a_i\, L(t)\}$$
Intuition
DRAFT — ★ Leontief micro production.
3세 비유
DRAFT — ★ Leontief micro production.
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ Leontief micro production.
(15.50) ★
★ Pareto draw G(b,a)
★ Pareto Draw G(b,a)
DRAFT
vc-passed
$$G(b, a) \equiv \Pr(a_i \geq a, b_i \geq b) = b^{-\beta/\gamma_b}\, a^{-\alpha/\gamma_a}$$
Intuition
DRAFT — ★ Pareto distribution of techs.
3세 비유
DRAFT — ★ Pareto distribution of techs.
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Pareto distribution of techs.
(15.51)
Output distribution H(y)
Output Distribution H(y)
DRAFT
vc-passed
$$H(y) \equiv \Pr[\tilde Y_i \leq y] = 1 - \Pr[a_i\, L \geq y, b_i\, K \geq y]$$
Intuition
DRAFT — ★ output Pareto inversion.
3세 비유
DRAFT — ★ output Pareto inversion.
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ output Pareto inversion.
(15.52)
Y aggregator
Y Aggregator
DRAFT
vc-passed
$$\tilde Y(t; N(t)) \equiv \max_{i = 1, \ldots, N(t)} \min\{b_i\, K(t),\, a_i\, L(t)\}$$
Intuition
DRAFT — ★ best-of-N choice.
3세 비유
DRAFT — ★ best-of-N choice.
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ best-of-N choice.
(15.53) ★
★ Aggregate distribution
★ Aggregate Distribution
DRAFT
vc-passed
$$\Pr[\tilde Y \leq y] = H(y)^{N(t)}$$
Intuition
DRAFT — ★ N independent Paretos.
3세 비유
DRAFT — ★ N independent Paretos.
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ N independent Paretos.
(15.54) ★
★ Frechet normalization
★ Frechet Normalization
DRAFT
vc-passed
$$n(t) \equiv (\gamma\, N(t)\, K^{\beta}\, L^{\alpha})^{1/(\alpha+\beta)}$$
Intuition
DRAFT — ★ ★ Frechet normalization const.
3세 비유
DRAFT — ★ ★ Frechet normalization const.
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Frechet normalization const.
(15.55) ★
★ ★ Frechet limit
★ ★ Frechet Limit
DRAFT
vc-passed
$$\lim_{N\to\infty} \Pr[\tilde Y \leq (\gamma\, N\, K^{\beta}\, L^{\alpha})^{1/(\alpha+\beta)}\, y] = e^{-y^{-(\alpha+\beta)}}$$
Intuition
DRAFT — ★ ★ ★ extreme value theorem → Cobb-Douglas at macro.
3세 비유
DRAFT — ★ ★ ★ extreme value theorem → Cobb-Douglas at macr
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ ★ extreme value theorem → Cobb-Douglas at macro.
(15.56) ★
★ CD macro emergent
★ CD Macro Emergent
DRAFT
vc-passed
$$\tilde Y(t; N(t)) \approx \varepsilon(t)\, \gamma^{1/(\alpha+\beta)}\, N(t)^{1/(\alpha+\beta)}\, K^{\beta/(\alpha+\beta)}\, L^{\alpha/(\alpha+\beta)}$$
Intuition
DRAFT — ★ ★ ★ Cobb-Douglas at aggregate from Leontief micro!
3세 비유
DRAFT — ★ ★ ★ Cobb-Douglas at aggregate from Leontief micr
Genealogy
| 인물 | 저작 | note |
|---|
| Kortum (1997) | Research, Patenting, and Technological Change (Econometrica) | DRAFT — Frechet distribution growth model. |
| Eaton & Kortum (2002) | Technology, Geography and Trade (Econometrica) | DRAFT — Frechet 분포 trade 응용. |
| Acemoglu (2009) | Introduction to Modern Economic Growth (Ch.15.6) | DRAFT — Frechet 합산. |
Applications
- Acemoglu 1998 directed technical change
- Acemoglu 2002/2003 induced innovation
- Hicks 1932 induced innovation
- Eaton-Kortum 2002 trade
- skill-biased technical change empirics
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ ★ Cobb-Douglas at aggregate from Leontief micro!