ˆ CGE ž ž ˆ 2 CGE 2 1 ˆ n = 1,, n n ˆ k f = 1,, k ˆ ˆ ˆ 3
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1 CGE 2 * Date: 2018/07/24, Verson * : Webste: 1
2 ˆ CGE ž ž ˆ 2 CGE 2 1 ˆ n = 1,, n n ˆ k f = 1,, k ˆ ˆ ˆ 3 2 2
3 n k y = f (x 1, x 2,, x n, v 1,, v k ) = f (x, v ) (1) y x v f f p f p F f π π = p f (x, v ) p x + p F f v f (2) f π f (x, v ) = p p = 0 x x (3) π f (x, v ) = p p F f = 0 v f v f (4) CGE n k u = g(d 1,, d n ) = g(d) (5) max u = g(d) (6) d s.t. p d = m (7) m d (p, m) 1 v f m = f p F f v f (8) 3
4 2. 1: y = (x, v ) {y } =1,,n f (x, v ) p p = 0 {x } =1,,n,=1,,n x f (x, v ) p p F f = 0 {v f } =1,,n,f=1,,k v f y = x + d (p, m) {p } =1,,n v f = v f {p F f } f=1,,k m = f p F f v f {m} y = x + d (p, m) (9) p v f = v f (10) p F f n + n n + n k + n + k + 1 = 2n + n 2 + nk + k + 1 {y } n {x } n n {v f } n k {p } n {p F f } k {m} CGE 4
5 2. n + n n + n k + n + k + 1 = 2n + n 2 + nk + k ˆ ˆ ˆ ˆ ˆ 1 CGE ˆ ˆ ˆ d (p, m)
6 ) 2) Walras' law 0 = p x + d (p, m) y (11) f p F f v f v f (12) VED VED = p x + d (p, m) y + f p F f v f v f (13) [ ] 0 (13) 0 (13) 0 (13) VED = p d (p, m) p F f v f p y p x + p F f v f (14) f f [ ] bndng 0 [ ] [ ] 0 1 : bndng 6
7 2. 2 : (14) 1 VED = p x + d (p, m) y + f p F f v f v f = 0 (15) k (15) p x + d (p, m) y + p F f v f v f = p F k v k v k f k n + k 1 v kf = v k k n + k n + k 1 n + k n + k n + n 2 + nk + k + 1 2n + n 2 + nk + k < 2n + n 2 + nk + k CGE 0 CGE 5 4 CGE CES 1 CGE 5 1 7
8 y x v f p pf f m λ > 0 p = λp pf f = λpf f m = λm y x v f p p F f m (3) (4) (9) 0 d ( p, m) = d (λp, λm ) = d (p, m ) (8) m = λm = λ f p F f v f = f λp F f v f = f p F f v f 0 6 CGE CGE CGE p 1 1 {p 2,, p n, p F 1,, p F m, m} 1 1 numerare {1, p + 2,, p+ n, p F + 1,, p F + m, m +, y +, x+, v+ f } {2, 2p + 2,, 2p+ n, 2p F + 1,, 2p F + m, 2m +, y +, x+, v+ f }
9 ˆ ˆ ˆ λ λ CGE 0 CGE CGE 0 CGE y = f (x 1, x 2,, x n, v 1,, v k ) = f (x, v ) (16) 7 9
10 2. CGE y = f y (x, v a ) (17) v a = f v (v ) (18) f y ( ) f v( ) f v( ) v a v a y = f (x, v ) y = f y (x, f v(v )) ˆ y = f y (x, v a) ˆ v a = f v(v ) π y = p f y (x, v a ) p x p va v a (19) p va π y x = p f y x p = 0 (20) π y v a = p f y v a 2 {x } v a p va = 0 (21) π va = p va f v (v ) f p F f v f π va v f = p va f v v f p F f = 0 v f 10
11 y = f y (x, f v (v )) 2: 2 y = f y (x, v a ) {y } =1,,n p f y (x, v a ) x p = 0 {x },=1,,n p f y (x, v a ) v a p va = 0 {v a } =1,,n p va f v(v ) p F f = 0 {v f } =1,,n,f=1,,k v f y = x + d (p, m) {p } =1,,n f v (v ) = v a {p va } =1,,n v f {p F f } f=1,,k v f = d m = f p F f v f {m} 3 2 dual approach CGE ˆ Mas-Colell et al. (1995) Varan (1992)? ˆ Dxt and Norman (1980) 11
12 c (p, p F ) mn z,z F p z + f p = {p 1,, p n } p F = {p F 1,, p F k } π = [ p c (p, p F ) ] y π y = p c (p, p F ) = 0 p F f zf f F (z, z F ) = 1 1 Shephard a (p, p F ) = c (p, p F ) p a F f(p, p F ) = c (p, p F ) p F f a (p, p F ) a F f (p, pf ) f a (p, p F )y a F f(p, p F )y 3.2 e(p, u) mn h [ ] p h g(h) = u m e(p, u) = m Shephard h (p, u) = e(p, u) p 2 m = f p F f v f 12
13 y = a (p, p F )y + h (p, u) v f = a F f(p, p F )y : p c (p, p F ) = 0 {y } =1,,n a = c (p, p F ) p {a } =1,,n,=1,,n a F f = c (p, p F ) p F f {a F f } f=1,,k,=1,,n e(p, u) h = {h } =1,,n p y = a y + h {p } =1,,n v f = a F fy {p F f } f=1,,k e(p, u) = m {u} m = p F f v f {m} f n + n 2 + nk + n + n + k = 3n + n 2 + nk + k + 2 {y } n {a } n 2 {a F f } nk {h } n {p } n {p F f } k {u} 1 {m} 1 n + n 2 + nk + n + n + k = 3n + n 2 + nk + k CGE 1) 2) CGE CGE 13
14 3. 4: c (p, p F ) = p e(p, u) = m a (p, p F ) = c (p, p F ) h (p, u) = p a F f(p, p F ) = c (p, p F ) p F f e(p, u) p CGE 4 CGE CGE CES CGE CES CGE CGE 14
15 3. CGE CGE MIT EPPA (Paltsev et al., 2005) 8 EPA ADAGE 9 ZEW PACE 10 CGE (, 2010) 11 AIM CGE CGE 12 CGE Thomas F. Rutherford Chrstoph Böhrnger CGE 13 CGE CGE 3.6 (17) (18) c y (p, pva ) mn z,z a p z + p va z a f y (z, z a ) = 1 π y = [p c y (p, pva )] y π y y = p c y (p, pva ) = 0 a (p, p va ) = cy (p, pva ) p a v (p, p va ) = cy (p, pva ) GAMS MPSGE MPSGE GAMS CGE MPSGE 13 p va 15
16 c va (p F ) mn z F f p F f zf f F v (z F ) = 1 π va = [ p va c va (p F ) ] v a π va v a = p va c va (p F ) = 0 a F f(p F ) = cva (p F ) p F f : 2 p c y (p, pva ) = 0 {y } =1,,n p va c va (p F ) = 0 {v a } =1,,n (p, pva ) a = cy {a } =1,,n,=1,,n p a v = cy (p, pva ) p va a F f = cva (p F ) p F f {a v } =1,,n {a F f } =1,,k,=1,,n e(p, u) h = {h } =1,,n p y = a y + h {p } =1,,n v a = a v y {p va } =1,,n v f = a F fv a {p F f } f=1,,k e(p, u) = m {u} m = f p F f v f {m} 16
17 4. 4 CES 2.6 CES 1 A-1 y = f y (x, v a ) = α(x x ) σ 1 σ + a v (v a ) σ 1 σ σ σ 1 v a = f v (v ) = f βf(v v σ v 1 σ f ) v σ v σ v 1 u = g(d 1,, d n ) = [ γ (d ) σc 1 σ c ] σ c σ c y = α(x x ) σ 1 σ + a v (v a ) σ 1 σ σ σ 1 {y } =1,,n 1 σ p y α(x x ) 1 σ p = 0 {x } =1,,n,=1,,n 1 σ p y α v (v a ) 1 σ p va = 0 {v a } =1,,n p va (v a ) 1 σ v βf(v v f ) 1 σ v p F f = 0 {v f } =1,,n,f=1,,k y = f x + [ ] σ c γ p βf(v v σ v 1 σ f ) v m (γ ) σc (p ) 1 σc {p } =1,,n σ v σ v 1 = v a {p va } =1,,n v f = v f {p F f } f=1,,k m = f p F f v f {m}
18 (α x ) σ (p ) 1 σ + (α v ) σ (p va ) 1 σ 1 1 σ p = 0 {y } =1,,n (22) f (βf) v σv (p F f ) 1 σv 1 1 σ v p va = 0 {v a } =1,,n (23) [ α x ] [ ] σ σ a x = (αl) x σ (p l ) 1 σ + (α v ) σ (p va ) 1 σ a v = a F f = h = p [ ] [ α v σ p va l [ β v f p F f [ ] σ c γ p l ] σ v [ k 1 σ 1 σ ] σ (αl) x σ (p l ) 1 σ + (α v ) σ (p va ) 1 σ (β v k) σv (p F k ) 1 σv ] σv 1 σ v {a x },=1,,n (24) {a v } =1,,n (25) {a F f} f=1,,k,=1,,n (26) 1 1 σ c (γ ) σc (p ) 1 σc u {h } =1,,n (27) y = a x y + h {p } =1,,n (28) v a = a v y {p va } =1,,n (29) v f = a F fv a {p F f } f=1,,k (30) [ ] 1 1 σ c u (γ ) σc (p ) 1 σc = m {u} (31) m = f p F f v f {m} (32) Dxt, Avnash K. and Vctor Norman (1980) Theory of Internatonal Trade: A Dual General Equlbrum Approach, Cambrdge: Cambrdge Unversty Press. Mas-Colell, Andreu, Mchael D. Whnston, and Jerry R. Green (1995) Mcroeconomc Theory, New York: Oxford Unversty Press. Paltsev, Sergey V., John M. Relly, Henry D. Jacoby, Rchard S. Eckaus, James R. Mcfarland, Marcus Sarom, Malcolm Asadooran, and Mustafa H. Babker (2005) The MIT Emssons Predcton and Polcy Analyss (EPPA) Model: Verson 4, URL: / Varan, Hal R. (1992) edton. Mcroeconomc Analyss, New York: W. W. Norton Company, 3rd 18
19 5. (2010) CGE CO Cobb-Douglas y = f y (x, v a ) = ϕ y (x ) αx (v a ) αv v a = f v (v ) = ϕ v (v f ) βv f f u = g(d 1,, d n ) = ϕ c (d ) γ 2 (22) (32) 0 p pva p F f m p + = λp pva+ = λp va p F + f = λp F f m+ = λm p + pva+ m + 3 p F + f (22) (32) v f λ (22) (32) 1 v f 6 ˆ : ˆ : ˆ : ˆ : ˆ : 19
CGE 12 * Date: 2018/07/24, Verson 1.1.1 1 2 2 2 3 Armngton 4 3.1 Armngton.................................. 4 3.2 Armngton................................ 5 3.3..........................................
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CGE Part 12 * Date: 2016/04/03, Verson 1.0.0 1 2 2 2 3 Armngton 4 3.1 Armngton.................................. 4 3.2 Armngton................................ 5 3.3..........................................
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