§12.3혁신과 독점이윤 (Patent)
Innovation Surplus and Monopoly6 eq
(12.1) ★
★ Innovation surplus SI
Innovation Surplus SI
DRAFT
vc-passed
$$S^I = \int_{\psi/\lambda^{-1}}^{\psi} D(p)\, dp - \mu = \int [D(p) - D(\psi)]\, dp + D(\psi)\, \lambda^{-1}(\lambda - 1)\, \psi - \mu$$
Intuition
DRAFT — ★ 혁신 사회잉여 — 가격 인하분의 적분 + 표준 잉여 + 비용 μ. Arrow 1962 의 핵심 식.
3세 비유
DRAFT — 혁신으로 가격 내려가서 사회가 얻는 이득 - 발명 비용.
Genealogy
| 인물 | 저작 | note |
|---|
| Kenneth Arrow (1962) | Economic Welfare and the Allocation of Resources for Invention | DRAFT — innovation surplus, replacement effect. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction. |
| William Nordhaus (1969) | Invention, Growth, and Welfare | DRAFT — patent welfare 분석. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ 혁신 사회잉여 — 가격 인하분의 적분 + 표준 잉여 + 비용 μ. Arrow 1962 의 핵심 식.
(12.2)
Monopoly price (CES)
Monopoly Price (CES)
DRAFT
vc-passed
$$p^M \equiv \lambda^{-1}\psi (1-\varepsilon)\, D(p^M)^{-1}$$
Intuition
DRAFT — 독점 가격 — CES 수요에서 도출.
3세 비유
DRAFT — 독점 가격 = 한계비용 × markup.
Genealogy
| 인물 | 저작 | note |
|---|
| Kenneth Arrow (1962) | Economic Welfare and the Allocation of Resources for Invention | DRAFT — innovation surplus, replacement effect. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction. |
| William Nordhaus (1969) | Invention, Growth, and Welfare | DRAFT — patent welfare 분석. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — 독점 가격 — CES 수요에서 도출.
(12.3) ★
★ Monopoly profit (innov)
Monopoly Profit (Innovation)
DRAFT
vc-passed
$$\hat{\pi}^I_1 = D(p^M)(p^M - \lambda^{-1}\psi) - \mu$$
Intuition
DRAFT — ★ 혁신가의 독점이윤 — 가격 차이 × 수량 - 비용 μ.
3세 비유
DRAFT — 혁신 후 1년차 이익 = 마진 × 수량 - 발명 비용.
Genealogy
| 인물 | 저작 | note |
|---|
| Kenneth Arrow (1962) | Economic Welfare and the Allocation of Resources for Invention | DRAFT — innovation surplus, replacement effect. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction. |
| William Nordhaus (1969) | Invention, Growth, and Welfare | DRAFT — patent welfare 분석. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ 혁신가의 독점이윤 — 가격 차이 × 수량 - 비용 μ.
(12.4)
Innovation profit floor
Innovation Profit Floor
DRAFT
vc-passed
$$\pi^I_1 = D(\psi)\, \lambda^{-1}(\lambda - 1)\, \psi - \mu < \hat{\pi}^I_1$$
Intuition
DRAFT — patent 없을 때의 마진 < 독점 마진.
3세 비유
DRAFT — 특허 없을 때 이익 < 특허 있을 때.
Genealogy
| 인물 | 저작 | note |
|---|
| Kenneth Arrow (1962) | Economic Welfare and the Allocation of Resources for Invention | DRAFT — innovation surplus, replacement effect. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction. |
| William Nordhaus (1969) | Invention, Growth, and Welfare | DRAFT — patent welfare 분석. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — patent 없을 때의 마진 < 독점 마진.
(12.5) ★
★ Social innovation surplus
Social Innovation Surplus
DRAFT
vc-passed
$$S^I_1 = D(p^M)(p^M - \lambda^{-1}\psi) + \int_{p^M}^{\psi} D(p)\, dp - \mu$$
Intuition
DRAFT — ★ 사회 잉여 = 독점 이익 + 가격하락 잉여 - 비용. Arrow 1962 의 social value of invention.
3세 비유
DRAFT — 사회 전체 입장의 발명 가치.
Genealogy
| 인물 | 저작 | note |
|---|
| Kenneth Arrow (1962) | Economic Welfare and the Allocation of Resources for Invention | DRAFT — innovation surplus, replacement effect. |
| Joseph Schumpeter (1942) | Capitalism, Socialism, and Democracy | DRAFT — creative destruction. |
| William Nordhaus (1969) | Invention, Growth, and Welfare | DRAFT — patent welfare 분석. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ 사회 잉여 = 독점 이익 + 가격하락 잉여 - 비용. Arrow 1962 의 social value of invention.
(12.6)
Monopoly price closed-form
Monopoly Price Closed-Form
DRAFT
vc-passed
$$\hat{p}^M \equiv \frac{\varepsilon}{\varepsilon - 1}\, \lambda^{-1}\psi$$
Intuition
DRAFT — ★ ε / (ε-1) markup formula — Dixit-Stiglitz 표준.
3세 비유
DRAFT — 독점 가격 = 한계비용 × ε/(ε-1).
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ ε / (ε-1) markup formula — Dixit-Stiglitz 표준.
§12.4Dixit-Stiglitz CES + Markup
Dixit-Stiglitz CES + Markup10 eq
(12.7)
★ DS 효용 함수
Dixit-Stiglitz Utility
DRAFT
vc-passed
$$U(c_1, \ldots, c_N, y) = u(C, y)$$
Intuition
DRAFT — ★ 합성 재화 C 와 numeraire y — 별개 재화의 aggregator.
3세 비유
DRAFT — 내가 좋아하는 다양한 상품 + 다른 것 = 행복.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ 합성 재화 C 와 numeraire y — 별개 재화의 aggregator.
(12.8) ★
★ ★ CES aggregator
CES Aggregator
DRAFT
vc-passed
$$C \equiv \left(\sum_{i=1}^N c_i^{(\varepsilon-1)/\varepsilon}\right)^{\varepsilon/(\varepsilon-1)}$$
Intuition
DRAFT — ★ ★ Dixit-Stiglitz 1977 의 정전 — N 개 재화의 CES 합성. ε 는 substitution elasticity.
3세 비유
DRAFT — 다양한 상품을 묶는 표준 방법 — 사람들이 다양성 좋아함.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Dixit-Stiglitz 1977 의 정전 — N 개 재화의 CES 합성. ε 는 substitution elasticity.
(12.9)
Budget constraint
Budget Constraint
DRAFT
vc-passed
$$\sum_{i=1}^N p_i\, c_i + y \leq m$$
Intuition
DRAFT — 예산제약 — N 재화 가격합 + y ≤ 소득.
3세 비유
DRAFT — 내 소득 = 모든 상품 가격 합.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — 예산제약 — N 재화 가격합 + y ≤ 소득.
(12.10)
★ DS 수요 — 단일 재화
DS Demand — Single Good
DRAFT
vc-passed
$$\frac{c_i}{C} \cdot \varepsilon^{-1} = \frac{p_i}{P}$$
Intuition
DRAFT — ★ DS 수요 식 — 재화 i 의 share = 가격 ratio (역).
3세 비유
DRAFT — 내가 사는 비율은 가격 비율 역.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ DS 수요 식 — 재화 i 의 share = 가격 ratio (역).
(12.11) ★
★ ★ DS 가격지수
Dixit-Stiglitz Price Index
DRAFT
vc-passed
$$P \equiv \left(\sum_{i=1}^N p_i^{1-\varepsilon}\right)^{1/(1-\varepsilon)}$$
Intuition
DRAFT — ★ ★ Dixit-Stiglitz 가격지수 — CES dual. 무역·R&D·growth 의 표준.
3세 비유
DRAFT — 여러 상품 가격을 하나로 묶는 방식.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Dixit-Stiglitz 가격지수 — CES dual. 무역·R&D·growth 의 표준.
(12.12)
Two-stage budget
Two-stage Budget
DRAFT
vc-passed
$$u(C, y)\ \text{s.t.}\ P\, C + y \leq m$$
Intuition
DRAFT — Stage 1: aggregator 와 numeraire 사이 결정.
3세 비유
DRAFT — 먼저 다양성 묶음 vs 다른 거 사이에서 정한다.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — Stage 1: aggregator 와 numeraire 사이 결정.
(12.13)
★ Two-stage FOC
Two-stage FOC
DRAFT
vc-passed
$$\frac{\partial u/\partial y}{\partial u/\partial C} = \frac{1}{P},\quad y = g(P, m),\ C = (m - g(P, m))/P$$
Intuition
DRAFT — ★ 두 단계 최적 — y 와 C 분배.
3세 비유
DRAFT — 두 단계 결정의 최적 조건.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ 두 단계 최적 — y 와 C 분배.
(12.14)
★ 기업 가격 결정
Firm Pricing
DRAFT
vc-passed
$$\max_{p_i \geq 0} \left(\frac{p_i}{P}\right)^{-\varepsilon} C\, (p_i - \psi)$$
Intuition
DRAFT — ★ 기업 i 의 이윤극대 — 수요탄력성 ε 가 markup 결정.
3세 비유
DRAFT — 기업이 가격 정할 때 — 수요 탄력성 보고.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ 기업 i 의 이윤극대 — 수요탄력성 ε 가 markup 결정.
(12.15) ★
★ ★ DS 등가 가격
DS Symmetric Price
DRAFT
vc-passed
$$p_i = p = \frac{\varepsilon}{\varepsilon - 1}\, \psi\quad \forall i = 1, \ldots, N$$
Intuition
DRAFT — ★ ★ DS 의 핵심 결과 — 모든 기업이 같은 가격, 한계비용에 ε/(ε-1) markup. Krugman 1980 무역 모형 의 출발.
3세 비유
DRAFT — 모든 회사 동일 가격 = 비용 × markup.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ DS 의 핵심 결과 — 모든 기업이 같은 가격, 한계비용에 ε/(ε-1) markup. Krugman 1980 무역 모형 의 출발.
(12.16) ★
★ DS 가격지수 (대칭)
DS Symmetric Price Index
DRAFT
vc-passed
$$P = N^{-1/(\varepsilon-1)} \cdot \frac{\varepsilon}{\varepsilon - 1}\, \psi$$
Intuition
DRAFT — ★ N 개 재화 합성 가격 — N 늘면 P 감소 (다양성 효과).
3세 비유
DRAFT — 재화 종류 늘면 종합 가격 ↓.
Genealogy
| 인물 | 저작 | note |
|---|
| Avinash Dixit & Joseph Stiglitz (1977) | Monopolistic Competition and Optimum Product Diversity (AER) | DRAFT — CES variety preference 의 정전. |
| Edward Chamberlin (1933) | The Theory of Monopolistic Competition | DRAFT — 독점 경쟁의 시발점. |
| Paul Krugman (1980) | Scale Economies, Product Differentiation, and the Pattern of Trade (AER) | DRAFT — Dixit-Stiglitz 의 무역 응용. |
Applications
- Dixit-Stiglitz 1977 monopolistic competition
- Krugman 1980 trade model
- Romer 1990 endogenous innovation
- Aghion-Howitt creative destruction
- Acemoglu directed technical change
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ N 개 재화 합성 가격 — N 늘면 P 감소 (다양성 효과).