Appendix 2. The Standard Trade Model

Composite government consumption

G=Ω^G YN i=1

g_i^θGi ; Ω^G >0; 0<θ^G_i <1

P^GG= XN

i=1

P_i^Xgi

gi

gj

= θ^G_i P_j^X

θ^G_j P_i^X; i, j = 1,2, .., N Government consumption price index

P^G = 1 Ω^G

YN i=1

µP_i^X θ^G_i

¶θ^G_j

;N = 10 Government consumption demand functions

gi =θ^G_i P^CG P_i^X Composite investment

I =Ω^I YN i=1

inv_i^θIi; Ω^I >0; 0 <θ^I_i <1

P^II = XN

i=1

P_i^Xinvi

invi

invj

= θ^I_iP_j^X

θ^I_jP_i^X; i, j = 1,2, .., N Investment price index

P^I = 1 Ω^I

YN i=1

µP_i^X θ^I_i

¶θ^I_j

;N = 10 Investment demand functions

invi =θ^I_iP^II P_i^X Leontief production function

Qi = min

½V Ai

a0,i

, qj,i

aj,i

, ....

¾

;i, j = 1,2, .., N Value-added production function

V Ai =Ai

"

αiLD

σi−1 σi

i + (1−αi)KD

σi−1 σi

i

#_σ^σi

i−1

; 0<αi <1;σi >0;σi 6= 1

P_i^{V A}V Ai =wLDi +rKDi

KDi

LDi

=

∙w r

(1−αi) αi

¸σi

Labour demand function

LDi = (Ai)^(σi−1)V Ai

µαiP_i^{V A} w

¶σi

Capital demand

KDi = (Ai)^(σi−1)V Ai

∙(1−αi)P_i^{V A} r

¸σi

Value-added price

P_i^{V A}= 1 Ai

£w^(1−σi)(αi)^σi+r^(1−σi)(1−αi)^σi¤₁₋¹_σ

i

CES Armington function

The equations below have been used in the calibration procedure in a general form;

more specifically, in the model the same equations apply to private consumption, government consumption, investment and intermediate inputs: therefore Xi has to be replaced byci, gi, invi and qj,i; Mi has to replaced bycmi, gmi, invmi and qmj,i; and cdi, gdi, invdi and qdj,i will replace Di, where the subscripts i and j indicate the production sector; functional parameters and prices are the same for all specific forms.

Xi =Φi

∙

εi(Mi)

γ_i−1

γ_i + (1−εi) (Di)

γ_i−1 γ_i

¸_γ^γi

i−1

Φi >0; 0<εi <1;γ_i >0;γ_i 6= 1; i= 1,2, ...,10

P_i^XXi =P_i^MMi+¡

1 +vat^D_i ¢ P_i^DDi

Di

Mi

=

∙ (1−εi)P_i^{M F} εi(1 +vat^D_i )P_i^D

¸γ_i

Imports demand function

Mi = (Φi)^(γi−1)Xi

µεiP_i^X P_i^M

¶γ_i

Domestic goods demand function

Di = (Φi)^(γi−1)Xi

∙ (1−εi)P_i^X (1 +vat^D_i )P_i^D

¸^γi

Composite CES Armington price

P_i^X = 1 Φi

n¡P_i^M¢(1−γ_i)

(εi)^γi+£¡

1 +vat^D_i ¢

P_i^D¤(1−γ_i)

(1−εi)^γio₁₋¹_γ

i

Cobb-Douglas total imports

The equations for total imports have been used in the calibration procedure in the general form described below; in the model, the same equations apply to private con-sumption, government concon-sumption, investment and intermediate inputs: therefore

Mi has to replaced by cmi, gmi, invmi and qmj,i; and M_i^j will be replaced by cm^j_i, gm^j_i, invm^j_i and qm^j_i,k, where i and k are production sector indeces and j is index indicating the foreign region; functional parameters and prices are the same for all specific forms.

Mi =Φ^M_i ¡

M_i^EU¢ε^EU_i ¡

M_i^RW¢ε^RW_i

Φ^M_i >0; 0<ε^EU_i ,ε^RW_i <1;ε^EU_i +ε^RW_i = 1; i= 1,2, .., N

P_i^MMi =P M_i^EUM_i^EU+P M_i^RWM_i^RW

M_i^EU

M_i^RW = ε^EU_i P M_i^RW ε^RW_i P M_i^EU Regional imports demand functions

M_i^j =ε^j_iP_i^MMi

P M_i^j ; i= 1,2, ..,10;j =EU, RW Import composite price

P_i^M = 1 Φ^M_i

µP M_i^EU ε^EU_i

¶ε^EU_i µ

P M_i^RW ε^RW_i

¶ε^RW_i

Import prices

P M_i^j =erP W Mi

¡1 +tm^j_i¢ ¡

1 +vat^M_i ¢

;j =EU, RW CET function

Qi =χ_i

∙ λi(Ei)

1+Ψi

Ψi + (1−λi) (Di)

1+Ψi

Ψi

¸_1+Ψ^Ψi

i

χ_i >0; 0<λi <1;Ψi >0; i= 1,2, ..., N

P_i^QQi =P_i^EEi+P_i^DDi

Di

Ei

=

∙ λiP_i^D (1−λi)P_i^E

¸Ψi

Export supply function

Ei = Qi

(χ_i)^(1+Ψi)³ P_i^Q´Ψi

µP_i^E λi

¶Ψi

Domestic good supply function

Di = Qi

(χ_i)^(1+Ψi)

³ P_i^Q

´Ψi

µ P_i^D 1−λi

¶^Ψi

Composite output price

P_i^Q= 1 χ_i

"¡

P_i^E¢(1+Ψi)

(λi)^Ψi +

¡P_i^D¢(1+Ψi)

(1−λi)^Ψi

#_1+Ψ¹

i

CET composite exports

Ei =χ^E_i

"

λ^EU_i ¡

E_i^EU¢^1+Ψ_ΨE^Ei

i +λ^RW_i ¡

E_i^RW¢^1+Ψ_ΨE^Ei i

#_1+Ψ^ΨEiE i

χ^E_i >0; 0<λ^EU_i ,λ^RW_i <1; λ^EU_i +λ^RW_i = 1; Ψ^E_i >0;i= 1,2, , .., N

P_i^EEi =P E_i^EUE_i^EU +P E_i^RWE_i^RW

E_i^EU E_i^RW =

µλ^RW_i P E_i^EU λ^EU_i P E_i^RW

¶^ΨEi

Exports supply functions

E_i^j = Ei

(P_i^E)^ΨEi (χ^E_i )(^1+ΨEi )

ÃP E_i^j λ^j_i

!Ψ_E

; i= 1,2, , .., N; j =EU, RW

Export composite price

P_i^E = 1 χ^E_i

"¡

P E_i^EU¢1+Ψ^E_i

(χ^E_i )^ΨEi +

¡P E_i^RW¢1+Ψ^E_i

(χ^D_i )^ΨEi

#_1+Ψ¹E i

Export prices

P E_i^j =erP W Ei; j =EU, RW Domestic goods VAT revenue

V AT^D = XN

i=1

vat^D_i P_i^DDi

Imported goods VAT revenue

V AT^M = XN

i=1

X

j=EU,RW

vat^M_i ¡

1 +tm^j_i¢

erP W_i^MM_i^j Imports tariffs revenue

T M = XN

i=1

X

j=EU,RW

tm^j_ierP W_i^MM_i^j Capital rent tax revenue

T K =t^KrK Income tax revenue

T Y =ti

£wL+¡

1−t^K¢

rK +T R+erF REM¤ Government budget

V AT^D+V AT^M +T Y +T K+T M +erF RG=T R+G

Labour market equilibrium

L= XN

i=1

LDi

Capital goods market equilibrium

K = XN

i=1

KDi

Domestic goods markets equilibrium

Xi = XN

j=1

qi,j +ci+invi+gi

External equilibrium XN

i=1

P W_i^MMi = XN

i=1

P W_i^EEi+F REM +F GR

2.B. Glossary

N: number of production sectors (N = 10) er: exchange rate (numeraire)

L: labour supply K: capital supply C: private consumption

P^C: private consumption price index Y D: personal disposable income

T R: government transfers to households F REM: foreign remittances to households t^Y: income tax rate

t^K: tax on capital income ρ: household’s discount rate δ: deprecation rate of capital

P_i^X: composite price of good i

ci: household’s consumption of good i

Ω^C: shift parameter in the Cobb-Douglas private consumption function

θ^C_i : goodi’s share parameter in the Cobb-Douglas private consumption function I: aggregate investment

P^I: price index of aggregate investment invi: sector i’s investment demand

Ω^I: shift parameter in the Cobb-Douglas investment function

θ^I_i: good i’s share parameter in the Cobb-Douglas investment function G: aggregate government consumption

P^G: price index of aggregate government consumption gi: government consumption of good i

Ω^G: shift parameter in the Cobb-Douglas government consumption function θ^G_i : goodi’s share parameter in the Cobb-Douglas government consumption func-tion

V Ai: sectori’s value-added production P_i^{V A}: sectori’s value-added price LDi: sectori’s demand for labour KDi: sectori’s demand for capital

Ai: shift parameter of the value-added production function in sectori σi: elasticity of substitution between primary inputs in sector i

αi: share parameter of labour used in the production of goodi w: nominal wage rate

r: nominal return to capital Qi: total output of sector i

P_i^Q: composite output price of sectori

qj,i: intermediate input produced by sector j used in the production of sector i a0,i: fixed coefficient of value-added output for sector i’s production

aj,i: fixed coefficient of intermediate input j in the production of good i Xi: total domestic absorption of sector i

Mi: total imports of sector i

cmi: private consumption demand for import good produced by sector i gmi: government consumption demand for import good produced by sector i invmi: investment demand for import good produced by sector i

qmj,i: imported intermediate input produced by sector j used in the production of sector i

Di: total domestic production of sector i

cdi: private consumption demand for domestic good produced by sectori gdi: government consumption demand for domestic good produced by sector i invdi: investment demand for domestic good produced by sector i

qdj,i: intermediate input produced domestically by sectorj used in the production of sector i

Φi: shift parameter in the CES Armington function of sector i

εi: imports share parameter in the CES Armington function of sectori

γ_i: sectori’s elasticity of substitution between imports and domestically-produced output

P_i^X: composite price of domestic absorption of sector i P_i^M: import price of sector i

P_i^D: price of sectori’s domestically-produced good vat^D_i : VAT rate on sector i’s domestically-produced good M_i^j: imports of sectori from region j

cm^j_i: private consumption of good i imported from region j gm^j_i: government consumption of good i imported from region j invm^j_i: investment demand for good iimported from region j

qm^j_i,k: intermediate input consumption of goodi used in the production of sector k and imported from regionj

P M_i^j: sectori’s price of imports from region j

Φ^M_i : shift parameter in the imports CES function of sector i

ε^j_i: region j’s share parameter in the imports CES function of sector i tm^j_i: import tax rate applying to sectori’s imports from region j vat^M_i : VAT rate on sector i’s imported goods

P W_i^M: sector i’s world price of imports Ei: total exports of sector i

P_i^E: export price of sector i

χ_i: shift parameter in the CET function of sector i λi: export share parameter of sector i

Ψi: elasticity of transformation between exports and domestically-sold output of sector i

E_i^j: total exports of sector i to region j

χ^E_i : shift parameter in the CET exports function of sector i λ^j_i: share parameter of exports to region j in sector i

Ψ^E_i : elasticity of transformation between exports to different regions of sector i P E_i^j: price of exports to regionj of sector i

P W_i^E: world price of exports of sector i V AT^D: domestic goods VAT revenue V AT^M: imported goods VAT revenue T M: aggregate import tariffs revenue T K: capital tax revenue

T Y: income tax revenue

F RG: foreign grants to the government

Im Dokument A Dynamic General Equilibrium Analysis of Jordan's Trade Liberalisation (Seite 83-94)