: Harberger Conenton ˆ CGE ˆ CGE ˆ 2 CGE 2.1 CGE CGE CES constant elastcty of substtuton Cob

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1 CGE Part 8 Date: 2015/11/21, Verson CGE CES CES CGE : : CGE Harberger Conenton Calbrated Share Form CES Calbrated Share Form CES Calbrated share form Calbrated share form Calbrated share form Calbrated Share Form Calbrated Share Form Calbrated Share Form Cobb-Douglas Calbrated share form : 1

2 : Harberger Conenton ˆ CGE ˆ CGE ˆ 2 CGE 2.1 CGE CGE CES constant elastcty of substtuton Cobb-Douglas Leontef CES 1) 2) CES CES homothetc 1 CES CES Part 7 CES CES 2

3 2.2 CES 2.2 CES y = f(x) = β (x ) σ 1 σ ] σ σ 1 Part 1 CES σ y = h(z 11,, z m1, z 12,, z m2,, z 1n,, z mn ) h {z j } CES f g CES h y = h(z 11,, z m1, z 12,, z m2,, z 1n,, z mn ) = f(g 1 (z 11,, z m1 ), g 2 (z 12,, z m2 ),, g n (z 1n,, z mn )) CES CES ] σ σ 1 y = f(x 1,, x n ) = β (x ) σ 1 σ x = g (z 1,, z m ) = j σ x 1 σ δ j (z j ) x σ x σ x 1 CGE x j x l σ x x j x lk σ CES CGE CES CES CES MIT EPPA Paltse et al. (2005) 2.3 CES CGE CES CES CES 3 3

4 2.3 CES ˆ CDE constant derence of elastctes ˆ Stone-Geary ˆ Translog GTAP (Hertel, 1999) CDE constant derence of elastctes functon, Hertel et al CDE e(p, u) mplct γ σ ] 1 σ p u (1 σ )β = 1 e(p, u) σ = σ β = 1 CES CDE CES GTAP 2 Stone-Geary u = g(d 1,, d n ) = ϕ (d γ ) α (1) Cobb-Douglas γ Cobb-Douglas 1 γ Stone-Geary Cobb-Douglas γ CGE Sotne-Geary ˆ OECD ENV-Lnkages (Burnaux et al., 2008) ˆ GEM-E3 2 ˆ World Bank LINKAGE (an der Mensbrugghe, 2005) ˆ IFPRI (Lofgren et al., 2002) 3 ˆ PEP (Robchaud et al., 2012) CGE 2 translog ADAGE EPA IGEM 5 translog translog CGE 1 Stone-Geary Cobb-Douglas {γ 1,, γ n}

5 3 CGE 3.1 CES CES CGE ˆ ˆ ˆ Part 5 & 6 Part 5 & 6 CGE CGE benchmark equlbrum CGE 3.2 : Gérard Debreu Kenneth J. Arrow CGE CGE CGE 5

6 3.3 : CGE CGE CGE 3.3 : CGE Part 8 CGE CGE CGE John B. Shoen John Whalley 6 CGE Herbert Scarf Scarf CGE (Shoen and Whalley, 1992) Scarf (1991) Scarf CGE CGE CGE CGE CGE GAMS CGE GAMS CGE Part 5 c = j (α x j) σ (p j ) 1 σ + (α ) σ (p a ) 1 σ 1 1 σ {c } =1,,n (2) 6 Ballard et al. (1985) 7 MPSGE CGE 6

7 4.1 c a = f (β f) σ (1 + t F f )p F f ] 1 σ 1 1 σ {c a } =1,,n (3) c p = 0 {y } =1,,n (4) c a p a = 0 { a } =1,,n (5) α x ] a x j c σ j = {a x a = p j α c p a j},j=1,,n (6) ] σ {a } =1,,n (7) x j = a x jy j {x j },j=1,,n (8) a F f = β f (1 + t F f )pf f ca ] σ {a F f} =1,,n,f=1,,m (9) f = a F f a { f } f=1,,m,=1,,n (10) 1 e = (γ j ) 1 σ σc (1 + t C ] 1 σ c j )p j u j {e} (11) ] σ c γ (e/u) d = (1 + t C )p u {d } =1,,n (12) y = j a = a y f = a x jy j + d {p } =1,,n (13) {p a } =1,,n (14) a F f a {p F f } f=1,,m (15) m = f p F f f + t C p C d +,f t F fp F f f {m} (16) e = m {u} (17) Part 5 c c a e Part 5 ˆ αj x α σ βf σ ˆ γ σ c CES ˆ ˆ CGE 1) 2) 7

8 4.2 CGE 1: SAM 2: 1 2 Part A-1 SAM (6) (7) α x j α α x j c ā x j = p j α x j = (āx j ) 1 σ ] σ ā = ] α σ c p a 1 σ pj α = (ā ) c c p a θ x j p jā x j c = p j ā x j l p lā x l + pa ā θ pa ā = c p a ā l p lā x l + pa ā 8

9 4.3 αj x = θj x (āx ) 1 σ σ j α = θ (ā ) 1 σ σ (18) (18) α x j α α x j = β f = (āx j ) 1 σ c α = (ā ) 1 σ c ( ā F f γ = ) 1 σ c a pj p a ( d /ū ) 1 σ c ē p F f = θj x (āx ) 1 σ σ j (19) = θ (ā ) 1 σ σ (20) = θf F (āf ) 1 σ σ f (21) p c ū = θ c ( d /ū ) 1 σ c σ c (22) p F f (1 + tf f )pf f pf f p F f = (1 + t F f ) pf f pc (1 + tc )p p c p c = (1 + t c ) p tlde agent agent p F f pc θ θj x p jā x j = c θ pa ā = c θ F f p F f āf f c a θ c p c d ē = p j ā x j l p lā x l + pa p a ā ā l p lā x l + pa p F f āf f p k F k āf k = p c d p j c d j j p p a p F f āx j ā āf f m ū t F f t C σ σ σc α x j α β f γ ā SAM Part 7 SAM SAM = {AGR, MAN, SER} f = {LAB, CAP } 9

10 4.3 1: SAM Harberger Conenton SAM SAM Harberger conenton Harberger conenton 1 1 SAM w w t L 3 w = (1 t L )w w 1 w calbraton_example.gms Part 5 ge_sample_dual.gms calbraton_example.gms * * set / agr, man, ser / 8 Part

11 4.3 f / lab, cap / ; * alas alas(,j), (,), (f,ff); dsplay, j, f; * * $ontext + + $offtext parameter alpha_x(j,) alpha_() beta_(f,) gamma() ; * * $ontext + (elastcty of substtuton, EOS) Cobb-Douglas Leontef + Part 5 $offtext parameter sg() EOS sg_() EOS sg_c EOS ; sg() = 0.5; sg_() = 0.5; sg_c = 0.5; dsplay sg, sg_, sg_c; ge_sample_dual.gms f ge_sample_dual.gms 3 ge_sample_dual.gms * * $ontext SAM $offtext table SAM SAM data (benchmark data) agr man ser lab cap hh agr man

12 4.3 ser lab cap hh ; set row / agr, man, ser, lab, cap, hh /; alas(col,row), (row, roww); SAM SAM table 1 SAM $ontext 0 $offtext parameters p0() p_a0() p_f0(f) ; y0() f0(f,) x0(j,) _a0() a_x0(j,) a_0() a_f0(f,) d0() m0 u0 c0() c_a0() e0 0 * Harberger conenton 1 p0() = 1; p_a0() = 1; p_f0(f) = 1; Harberger conenton Harberger conenton 1 * / 12

13 4.3 y0() = sum(col, SAM(col,)) / p0(); SAM 1 p0() p0() 1 * / x0(j,) = SAM(j,) / p0(j); SAM * / _a0() = sum(f, SAM(f,)) / p_a0(); * / f0(f,) = SAM(f,) / p_f0(f); / * / a_x0(j,) = x0(j,) / y0(); * / a_0() = _a0() / y0(); * / a_f0(f,) = f0(f,) / _a0(); * / d0() = SAM(,"hh") / p0(); 13

14 4.3 SAM * m0 = sum(f, SAM("hh",f)); SAM * u0 = m0; CGE % * c0() = p0(); * c_a0() = p_a0(); 1 1 * e0 = m0; * * alpha_x(j,) = (a_x0(j,))**(1/sg()) * p0(j) / c0(); 9 CGE % CGE 14

15 4.3 alpha_() = (a_0())**(1/sg()) * p_a0() / c0(); beta_(f,) = (a_f0(f,))**(1/sg_()) * p_f0(f) / c_a0(); gamma() = (d0()/u0)**(1/sg_c) * p0() * u0 / e0; opton alpha_x:8, alpha_:8, beta_:8, gamma:8; dsplay alpha_x, alpha_, beta_, gamma; (19) (22) opton alpha_x:8, alpha_:8, beta_:8, gamma:8; dsplay opton decmals = 8; * * arables c() c_a() y() _a() a_x(j,) x(j,) a_() a_f(f,) f(f,) e d() p() p_a() p_f(f) u m ; * * equatons e_c() e_c_a() e_y() e a() 15

16 4.3 ; e_a_x(j,) e_x(j,) e_a_() e_a_f(f,) e_f(f,) e_e e_d() e_p() e_p_a() e_p_f(f) e_u e_m (2) (17) * * $ontext $offtext * e_c().. c() =e= (sum(j, alpha_x(j,)**sg() * p(j)**(1-sg())) + alpha_()**sg() * p_a()**(1-sg()))**(1/(1-sg())); * e_c_a().. c_a() =e= (sum(f, beta_(f,)**sg_() * ((1+t_f(f,))*p_f(f))**(1-sg_())))**(1/(1-sg_())); * e_y().. c() - p() =e= 0; * e a().. c_a() - p_a() =e= 0; * e_a_x(j,).. a_x(j,) =e= (alpha_x(j,) * c()/p(j))**(sg()); * e_a_().. a_() =e= (alpha_() * c()/p_a())**(sg()); * e_a_f(f,).. a_f(f,) =e= (beta_(f,) * c_a() / ((1+t_f(f,))*p_f(f)))**(sg_()); * e_e.. e =e= u * (sum(, (gamma())**(sg_c) * ((1+t_c())*p())**(1-sg_c)))**(1/(1-sg_c)); * 16

17 4.3 e_d().. d() =e= u * (gamma()*(e/u)/((1+t_c())*p()))**(sg_c); * e_p().. y() =e= sum(j, a_x(,j)*y(j)) + d(); * e_p_a().. _a() =e= a_()*y(); * e_p_f(f).. _bar(f) =e= sum(, a_f(f,)*_a()); * e_u.. e - m =e= 0; * e_m.. m =e= sum(f, p_f(f)*_bar(f)) + sum(, t_c()*p()*d()) + sum((f,), t_f(f,)*p_f(f)*a_f(f,)*_a()); * e_x(j,).. x(j,) =e= a_x(j,) * y(); * e_f(f,).. f(f,) =e= a_f(f,) * _a(); (2) (17) * * $ontext $offtext c.l() = c0(); c_a.l() = c_a0(); y.l() = y0(); _a.l() = _a0(); a_x.l(j,) = a_x0(j,); a_.l() = a_0(); a_f.l(f,) = a_f0(f,); e.l = e0; d.l() = d0(); x.l(j,) = a_x0(j,) * y0(); f.l(f,) = a_f0(f,) * _a0(); p.l() = 1; p_a.l() = 1; p_f.l(f) = 1; u.l = u0; m.l = m0; ge_sample_dual.gms 17

18 4.3 * * $ontext MCP $offtext opton mcp = path; sole ge_sample_dual usng mcp; $ext VAR y LOWER LEVEL UPPER MARGINAL agr INF. man INF. ser INF. VAR _a LOWER LEVEL UPPER MARGINAL agr INF. man INF. ser INF. calbraton_example.lst y() _a() CGE sole $ext ge_sample_dual.gms ge_sample_dual.gms 18

19 5 Calbrated Share Form CES 4 CES CES calbrated share form 5.1 Calbrated Share Form CES 4 CES Calbrated share form CES Calbrated share form αj x α (19) (20) CES calbrated share form Calbrated share form calbrated share form CES y = f y (x 1,, x n, a ) = j αj(x x j ) σ 1 σ + α ( a ) σ 1 σ σ σ 1 α x j α (19) (20) y = j ] ] θj(ā x x j) 1 σ σ (x j ) σ 1 σ + θ (ā ) 1 σ σ ( a ) σ 1 σ σ σ 1 = j ( = 1 ȳ θ x j ( xj ) 1 σ σ ȳ ) 1 σ σ j θ x j (x j ) σ 1 σ ( xj x j + θ ( a ȳ ) 1 σ σ ( a ) σ 1 σ ) σ 1 ( ) σ 1 1 σ ( σ + θ a ȳ a ) σ 1 σ σ σ 1 σ σ 1 y = ȳ j θ x j ( xj x j ) σ 1 σ + θ ( a a ) σ 1 σ σ σ 1 calbrated share form CES 19

20 5.1 Calbrated Share Form CES a calbrated share form a = a f u = ū θ C θ F f ( f f ( d d ) σ ) σ 1 σ c 1 σ c σ σ 1 σ c σ c Calbrated share form calbrated share form c (p, p a ) = j (α x j) σ (p j ) 1 σ + (α ) σ (p a ) 1 σ 1 1 σ α x j α c (p, p a ) = j = j θ x j(ā x j) 1 σ σ ] σ (pj ) 1 σ + θ x j (āx j θ x j θ (ā ) 1 σ σ ] σ (p a ) 1 σ (ā ) 1 σ (p j ) 1 σ + θ θ (p a ) 1 σ ) 1 σ 1 1 σ 1 1 σ c = j p jā x j + pa ā θx j = p jā x j / c c (p, p a ) = j θ x j ( c c (p, p a p j ) = c j ) 1 σ ( ) 1 σ (p j ) 1 σ + θ c p a (p a θ x j ( pj p j ) 1 σ + θ ( p a p a ) 1 σ ) 1 σ calbrated share form c a ( p F ) = c a f θ F f p F f p F f ] 1 σ 1 1 σ 1 1 σ 1 1 σ p F = { p F 1,, p F m} = {(1 + t F 1)p F 1,, (1 + t F m)p F m} 20

21 5.1 Calbrated Share Form CES c a = f p F fā F f θ F f = p F fāf f c a e( p c, u) p c = { p c 1,, p c n} = {(1 + t c 1)p 1,, (1 + t c n)p n } γ (22) ] 1 e( p c, u) = u (γ ) σc ( p c ) 1 σc = u = u ē = p c d θ c = p c d /ē θ c ( d ū θ c ( d ūθ c e( p c, u) = u ē θ c ū ) 1 σc σ c ) 1 σ c p c p c 1 σ c σc ( p c calbrated share form ) 1 σc ( p c ) 1 σc ] 1 1 σ c ] 1 σ c] 1 1 σ c 1 1 σ c Calbrated share form calbrated share form α x ] σ a x j j = a = p j ] α σ p a l l (αl) x σ (p l ) 1 σ + (α ) σ (p a ) 1 σ (αl) x σ (p l ) 1 σ + (α ) σ (p a ) 1 σ ] σ 1 σ = ] σ 1 σ = α x j α ax j a x j = θx j (āx j ) 1 σ σ = ā x j α a = p j c σ = p jā x j ] σ ] σ pj c = ā x c / c j c p j p j / p j θ (ā ) 1 σ σ p a c ]σ = p a ā c 1 σ c (ā x j ) σ (ā a p j c σ ) 1 σ ]σ σ c p a α x j c p j ] σ ] α σ c p a 21

22 5.2 Calbrated Share Form = ā p a ī c c p a ] σ = ā c / c p a / p a ] σ a x j = ā x c / c j a = ā c / c p j / p j p a / p a calbrated share form calbrated share form a F f = ā F f d = u d ū (e/u)/(ē/ū) p c / p c ] σ c c a / c a p F f / p F f = d ū u ] σ ] σ ] 1 σ c e/ē p c / p c ] σ c ] σ 5.2 Calbrated Share Form Calbrated share form y = ȳ j θ x j ( xj x j ) σ 1 σ + θ ( a a ) σ 1 σ σ σ 1 (23) a = a f u = ū θ C θ F f ( f f ( d d ) σ ) σ 1 σ c 1 σ c σ σ 1 (24) σ c σ c 1 (25) Calbrated share form c (p, p a c a ) = c j ( p F ) = c a f θ x j θ F f e( p c, u) = u ē θ c ū ( pj p j p F f p c p c ) 1 σ + θ p F f ] 1 σ ( p a p a 1 1 σ ) 1 σ 1 1 σ (26) (27) ] 1 σ c] 1 1 σ c (28) Calbrated share form ] σ c / c (29) a x j = ā x j p j / p j c / c ] σ (30) a = ā p a / p a 22

23 5.3 Calbrated Share Form a F f = ā F f d = d ū u c a / c a p F f / p F f ] σ ] 1 σ c e/ē p c / p c ] σ c (31) (32) 5.3 Calbrated Share Form CES calbrated share form calbrated share form calbrated share form CGE calbrated share form CGE Thomas F. Rutherford Chrstoph Böhrnger calbrated share form calbrated share form calbrated share form calbrated share form MPS/GE (mathematcal programmng system for general equlbrum) MPS/GE Thomas F. Rutherford GAMS GAMS 10 MPS/GE calbrated share form calbrated share form MPS/GE MPS/GE 5.4 Calbrated Share Form calbrated_share_form.gms calbrated share form calbraton_example.gms parameter cost_y0() cost a0() cost_c0 ; 10 GAMS MPS/GE MPS/GE MCP PATH MCP MPS/GE 23

24 5.4 Calbrated Share Form cost_y0() = sum(j, p0(j)*x0(j,)) + p_a0()*_a0(); cost a0() = sum(f, p_f0(f)*f0(f,)); cost_c0 = sum(, p0()*d0()); dsplay cost_y0, cost a0, cost_c0; agent 0 parameter sh_x(j,) sh_() sh_f(f,) sh_c() ; sh_x(j,) = p0(j)*x0(j,) / cost_y0(); sh_() = p_a0()*_a0() / cost_y0(); sh_f(f,) = p_f0(f)*f0(f,) / cost a0(); sh_c() = p0()*d0() / cost_c0; dsplay sh_x, sh_, sh_f, sh_c; sh_x(j,) = p0(j)*x0(j,) / cost_y0(); j sh_() = p_a0()*_a0() / cost_y0(); sh_f(f,) = p_f0(f)*f0(f,) / cost a0(); f sh_c() = p0()*d0() / cost_c0; 24

25 5.4 Calbrated Share Form * * $ontext $offtext * e_c().. c() =e= c0() * (sum(j, sh_x(j,) * (p(j)/p0(j))**(1-sg())) + sh_() * (p_a()/p_a0())**(1-sg()))**(1/(1-sg())); * e_c_a().. c_a() =e= c_a0() * (sum(f, sh_f(f,) * (((1+t_f(f,))*p_f(f))/((1+t_f0(f,))*p_f0(f)))**(1-sg_())) )**(1/(1-sg_())); * e_a_x(j,).. a_x(j,) =e= a_x0(j,) * ((c() / c0()) / (p(j) / p0(j)))**sg(); * e_a_().. a_() =e= a_0() * ((c() / c0()) / (p_a() / p_a0()))**sg(); * e_a_f(f,).. a_f(f,) =e= a_f0(f,) * ((c_a() / c_a0()) / (((1+t_f(f,))*p_f(f)) / ((1+t_f0(f,))*p_f0(f))))**sg_(); * e_e.. e =e= u * (e0/u0) * (sum(, sh_c() * (((1+t_c())*p()) / ((1+t_c0())*p0()))**(1-sg_c)) )**(1/(1-sg_c)); * e_d().. d() =e= d0() * (u/u0)**(1-sg_c) * ((e/e0) / (((1+t_c())*p()) / ((1+t_c0())*p0())))**sg_c; calbraton_example.gms calbrated share form 25

26 5.5 Cobb-Douglas 5.2 (26) (32) calbraton_example.gms calbraton_example.gms CES calbrated share form 5.5 Cobb-Douglas CES calbrated share form Cobb-Douglas Cobb-Douglas calbrated share form Cobb-Douglas y = f y (x, a ) = ϕ (x j ) αx j ( a ) α a = f ( ) = ϕ ( f ) β f f j αx j + α = 1 f β f = 1 Cobb-Douglas u = ϕ u (d ) γ γ = 1 Part A-1 c (p, p a ) = 1 pj ϕ α j j p F f c a ( p F ) = 1 ϕ e( p c, u) = u p c ϕ u f βf ] γ c γ c ] αj ] p a α α ] β f (33) (34) (35) a x j = c (p, p a ) p j = a = c (p, p a ) p a = a F f = ca ( p F ) p F = f d = e( pc, u) p c α x j p j ] 1 ϕ l pl ] α 1 p a ϕ l ] β f 1 p F l p F f γ c = p c ϕ l ] u ϕ u j α x l pl β l α x l ] α x l ] α x l ] β F l p c ] γj j = γc e γ j p a αj p a α j ] α ] α = β f ca p F f p c = αx j c p j (36) = α c p a (37) (38) (39) 26

27 5.5 Cobb-Douglas Cobb-Douglas 1). αj x 2). ϕ αj x (36) (36) (39) α x j = p jā x j c Cobb-Douglas α x j j α = pa ā βf = c p F fāf f c a γ = p c d ē / ϕ = ȳ ( x j ) αx j ( a ) α / ϕ = a ( f ) β f / ϕ u = ū ( d ) γ (33) (35) f ϕ = 1 c pj ϕ = 1 c a ϕ u = ū ē j α j p F f f p c γ c β f ] αj p a α j ] γ c ] β f ] α Calbrated share form CES calbarated share form Calbrated share form y = ȳ j xj x j ] α x j a ] α 27

28 a = a u = ū f f f d d ] γ Calbrated share form c (p, p a ) = c j c a ( p F ) = c a e( p c, u) = u ē ū ] β f ] α x pj p j p F f f p F f p p ] γ ] α a p a j p a Calbrated share form CES ] β f (29) (32) calbrated_share_form_cd.gms calbraton_example_cd.gms Cobb-Douglas calbrated_share_form.gms calbraton_example.gms Ballard, Charles L., John B. Shoen, John Whalley, and Don Fullerton (1985) General Equlbrum Computatons of the Margnal Welfare Costs of Taxes n the Unted States, Amercan Economc Reew, Vol. 75, No. 1, pp Burnaux, Jean-marc, Jean Chateau, and Roman Dual (2008) The Economcs of Clmate Change Mtgaton: Polces and Optons for the Future. Hertel, Thomas W. (1999) Global Trade Analyss: Modelng and Applcatons, New York: Cambrdge Unersty Press, URL: Hertel, Thomas W., J. Mark Horrdge, and Ken R. Pearson (1992) A Reconclaton of the Lnearzaton and Leels Schools of AGE Modellng, Economc Modellng, Vol. 9, No. 4, pp , URL: Lofgren, Hans, Rebecca Lee Harrs, and Sherman Robnson (2002) A Standard Computable General Equlbrum (CGE) Model n GAMS. an der Mensbrugghe, Domnque (2005) LINKAGE Techncal Reference Document Verson 6.0, URL: LnkageTechncalReferenceDoc.pdf. 28

29 Paltse, 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. Robchaud, Véronque, André Lemeln, Hélèn Masonnae, and Vernard Decaluwé (2012) No PEP-1-1 A User Gude, URL: pep-standard-cge-models/. Shoen, John B. and John Whalley (1992) Applyng General Equlbrum, New York: Cambrdge Unersty Press. (1991) 6 : Harberger Conenton Harberger Conenton harberger_check.gms harberger_check_2.gms harberger_check.gms calbraton_example.gms harberger_check.gms bench ˆ 20% cap_up ˆ man ser 2 10% tax_c harberger_check.gms $macro calc_results(sc) \ results("u",sc) = u.l; \ results("y_agr",sc) = y.l("agr"); \ results("y_man",sc) = y.l("man"); \ results("y_ser",sc) = y.l("ser"); \ results("_y_agr",sc) = p.l("agr")*y.l("agr") / p.l("agr"); \ results("_y_man",sc) = p.l("man")*y.l("man") / p.l("agr"); \ results("_y_ser",sc) = p.l("ser")*y.l("ser") / p.l("agr"); \ results("d_agr",sc) = d.l("agr"); \ results("d_man",sc) = d.l("man"); \ results("d_ser",sc) = d.l("ser"); results("u",sc) results("y_agr",sc) 3 results("_y_agr",sc) AGR AGR 3 29

30 harberger_check.gms results 413 PARAMETER results bench cap_up tax_c u y_agr y_man y_ser _y_agr _y_man _y_ser d_agr d_man d_ser bench % 422 PARAMETER results_pc cap_up tax_c u y_agr y_man y_ser _y_agr _y_man _y_ser d_agr d_man d_ser harberger_check_2.gms Harberger Conenton * Harberger conenton p0() = 2; p_a0() = 0.5; p_f0(f) = 3; harberger_check_2.gms 418 PARAMETER results bench cap_up tax_c u y_agr

31 y_man y_ser _y_agr _y_man _y_ser d_agr d_man d_ser PARAMETER results_pc cap_up tax_c u y_agr y_man y_ser _y_agr _y_man _y_ser d_agr d_man d_ser results harberger_check.gms results_pc harberger_check.gms % 1 7 ˆ : ˆ : ˆ :