GTAP Models: Sets and Variables

Sets
NSAV_COMM	Non-Savings Commodities (NS)
TRAD_COMM	Traded Commodities (TC)
DEMD_COMM	Demanded Commodities (DC)
PROD_COMM	Produced Commodities (PC)
ENDW_COMM	Endowment Commodities (EC)
ENDWS_COMM	Sluggish Endowment Commodities (ECS)
ENDWM_COMM	Mobile Endowment Commodities (ECM)
CGDS_COMM	Capital Goods Commodities ("cgds")
ENDWC_COMM	Capital Endowment Commodity ("capital")

Subsets
PROD_COMM	in NSAV_COMM
DEMD_COMM	in NSAV_COMM
CGDS_COMM	in NSAV_COMM
ENDW_COMM	in DEMD_COMM
TRAD_COMM	in DEMD_COMM
TRAD_COMM	in PROD_COMM
CGDS_COMM	in PROD_COMM
ENDWS_COMM	in ENDW_COMM
ENDWM_COMM	in ENDW_COMM
ENDWC_COMM	in NSAV_COMM
ENDWC_COMM	in ENDW_COMM

Example: The 3x3 (3 regions x 3 sectors) economy
REG	= {usa, eu, row}
NSAV_COMM	= {land, labor, capital, food, manufacturing, services, capital goods}
TRAD_COMM	= {food, manufacturing, services}
DEMD_COMM	= {land, labor, capital, food, manufacturing, services}
PROD_COMM	= {food, manufacturing, services, capital goods}
ENDW_COMM	= {land, labor, capital}
ENDWS_COMM	= {land, capital}
ENDWM_COMM	= {labor}
CGDS_COMM	= {capital goods}
ENDWC_COMM	= {capital}

Value flows evaluated at agents' prices
EVOA_ir value of endowment commodity i output or supplied, in region r, evaluated at agent's prices *EVOA_i,r = PS_i,r QO_i,r** with i = ENDW_COMM and r = REG EVFA_ijr value of purchases of demanded commodity i by firms in sector j, in region r, evaluated at agent's prices *EVFA_ijr = PFE_ijr QFE_ijr** i = TRAD_COMM; j = ENDW_COMM; r = REG VDFA_ijrvalue of purchases of domestic tradeable commodity i by firms in sector j of region r evaluated at agents' prices *VDFA_ijr = PFD_ijr QFD_ijr** i = TRAD_COMM; j = ENDW_COMM; r = REG VIFA_ijrvalue of purchases of imported tradeable commodity i by firms in sector j of region r evaluated at agents' prices *VIFA_ijr = PFM_ijr QFM_ijr** i = TRAD_COMM; j = ENDW_COMM; r = REG VDPA_ir value of expenditure on domestic tradable commodity i, by private household in region r evaluated at agent's prices *VDPA_ir = PPD_ir QPD_ir** i = TRAD_COMM; r = REG VIPA_irvalue of expenditure on imported tradeable commodity i by firms in sector j of region r evaluated at agents' prices *VIPA_ir = PPM_ir QPM_ir** i = TRAD_COMM; r = REG VDGA_i value of government's expenditure on domestic tradable commodity i, in region r, evaluated at agent's prices *VDGA_ir = PGD_ir QGD_ir** i = TRAD_COMM; r = REG VIGA_i value of government's expenditure on imported tradable commodity i, in region r, evaluated at agent's prices *VIGA_ir = PGM_ir QGM_ir** i = TRAD_COMM; r = REG SAVE_r value of (net) savings in region r *SAVE_r = PSAVE_r QSAVE_r** r = REG VKB_r value of beginning-of-period capital stock in region r *VKB_r = PCGDS_r KB_r** r = REG VDEP_r value of capital depreciation expenditure in region r *VDEP_r = PCGDS_r KB_r** r = REG

Value flows evaluated at agents' prices

EVOA_ir value of endowment commodity i output or supplied, in region r, evaluated at agent's prices

EVOA_i,r = PS_i,r * QO_i,r with i = ENDW_COMM and r = REG

EVFA_ijr value of purchases of demanded commodity i by firms in sector j, in region r, evaluated at agent's prices

EVFA_ijr = PFE_ijr * QFE_ijr i = TRAD_COMM; j = ENDW_COMM; r = REG

VDFA_ijrvalue of purchases of domestic tradeable commodity i by firms in sector j of region r evaluated at agents' prices

VDFA_ijr = PFD_ijr * QFD_ijr i = TRAD_COMM; j = ENDW_COMM; r = REG

VIFA_ijrvalue of purchases of imported tradeable commodity i by firms in sector j of region r evaluated at agents' prices

VIFA_ijr = PFM_ijr * QFM_ijr i = TRAD_COMM; j = ENDW_COMM; r = REG

VDPA_ir value of expenditure on domestic tradable commodity i, by private household in region r evaluated at agent's prices

VDPA_ir = PPD_ir * QPD_ir i = TRAD_COMM; r = REG

VIPA_irvalue of expenditure on imported tradeable commodity i by firms in sector j of region r evaluated at agents' prices

VIPA_ir = PPM_ir * QPM_ir i = TRAD_COMM; r = REG

VDGA_i value of government's expenditure on domestic tradable commodity i, in region r, evaluated at agent's prices

VDGA_ir = PGD_ir * QGD_ir i = TRAD_COMM; r = REG

VIGA_i value of government's expenditure on imported tradable commodity i, in region r, evaluated at agent's prices

VIGA_ir = PGM_ir * QGM_ir i = TRAD_COMM; r = REG

SAVE_r value of (net) savings in region r

SAVE_r = PSAVE_r * QSAVE_r r = REG

VKB_r value of beginning-of-period capital stock in region r

VKB_r = PCGDS_r * KB_r r = REG

VDEP_r value of capital depreciation expenditure in region r

VDEP_r = PCGDS_r * KB_r r = REG

Value flows evaluated at market prices
VFM_ijr value of purchases of endowment commodity i by firms in sector j in region r, evaluated at market prices *VFM_ijr = PM_ir QFE_ijr** i = ENDWM_COMM; j = PROD_COMM; r = REG *VFM_ijr = PMES_ijr QFE_ijr** i = ENDWS_COMM; j = PROD_COMM; r = REG VDFM_ijr value of purchases of domestic tradable commodity i by firms in sector j in region r, evaluated at market prices *VDFM_ijr = PM_ir QFD_ijr** i = TRAD_COMM; j = PROD_COMM VIFM_ijr value of purchases of imported tradable commodity i by firms in sector j in region r, evaluated at market prices *VIFM_ijr = PIM_ir QFM_ijr** i = TRAD_COMM; j = PROD_COMM; r = REG VDPM_ir value of private household's purchases of domestic tradable commodity i in region r, evaluated at market prices *VDPM_ir = PM_ir QPD_ir** i = TRAD_COMM; r = REG VIPM_ir value of private household's purchases of imported tradable commodity i in region r, evaluated at market prices *VIPM_ir = PIM_ir QPM_ir** i = TRAD_COMM; r = REG VDGM_ir value of government's expenditure on domestic tradable commodity i, in region r, evaluated at market prices *VDGM_ir = PM_ir QGD_ir** i = TRAD_COMM; r = REG VIGM_ir value of government's expenditure on imported tradable commodity i, in region r, evaluated at market prices *VIGM_ir = PIM_ir QGM_ir** i = TRAD_COMM; r = REG VXMD_irs value of exports of tradable commodity i from source r to destination s, evaluated at (exporter's) market prices *VXMD_irs = PM_ir QXS_irs** i = TRAD_COMM; r = REG; s= REG VIMS_irs value of imports of tradable commodity i from source r to destination s, evaluated at (importer's) market prices *VIMS_irs = PMS_ir QXS_irs** i = TRAD_COMM; r = REG; s = REG VST_ir value of sales of tradable commodity i to the international transport sector in region r, evaluated at market prices *VST_ir = PM_ir QST_ir** i = MARG_COMM; r = REG

Value flows evaluated at market prices

VFM_ijr value of purchases of endowment commodity i by firms in sector j in region r, evaluated at market prices

VFM_ijr = PM_ir * QFE_ijr i = ENDWM_COMM; j = PROD_COMM; r = REG

VFM_ijr = PMES_ijr * QFE_ijr i = ENDWS_COMM; j = PROD_COMM; r = REG

VDFM_ijr value of purchases of domestic tradable commodity i by firms in sector j in region r, evaluated at market prices

VDFM_ijr = PM_ir * QFD_ijr i = TRAD_COMM; j = PROD_COMM

VIFM_ijr value of purchases of imported tradable commodity i by firms in sector j in region r, evaluated at market prices

VIFM_ijr = PIM_ir * QFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG

VDPM_ir value of private household's purchases of domestic tradable commodity i in region r, evaluated at market prices

VDPM_ir = PM_ir * QPD_ir i = TRAD_COMM; r = REG

VIPM_ir value of private household's purchases of imported tradable commodity i in region r, evaluated at market prices

VIPM_ir = PIM_ir * QPM_ir i = TRAD_COMM; r = REG

VDGM_ir value of government's expenditure on domestic tradable commodity i, in region r, evaluated at market prices

VDGM_ir = PM_ir * QGD_ir i = TRAD_COMM; r = REG

VIGM_ir value of government's expenditure on imported tradable commodity i, in region r, evaluated at market prices

VIGM_ir = PIM_ir * QGM_ir i = TRAD_COMM; r = REG

VXMD_irs value of exports of tradable commodity i from source r to destination s, evaluated at (exporter's) market prices

VXMD_irs = PM_ir * QXS_irs i = TRAD_COMM; r = REG; s= REG

VIMS_irs value of imports of tradable commodity i from source r to destination s, evaluated at (importer's) market prices

VIMS_irs = PMS_ir * QXS_irs i = TRAD_COMM; r = REG; s = REG

VST_ir value of sales of tradable commodity i to the international transport sector in region r, evaluated at market prices

VST_ir = PM_ir * QST_ir i = MARG_COMM; r = REG

Value flows evaluated at world prices
VXWD_irs value of exports of tradable commodity i from source r to destination s, evaluated at world (fob) prices *VXWD_irs = PFOB_irs QXS_irs** i = TRAD_COMM; r = REG; s = REG VIWS_irs value of imports of tradable commodity i from source r to destination s, evaluated at world (cif) prices *VIWS_irs = PCIF_irs QXS_irs** i = TRAD_COMM; r = REG; s = REG

Value flows evaluated at world prices

VXWD_irs value of exports of tradable commodity i from source r to destination s, evaluated at world (fob) prices

VXWD_irs = PFOB_irs * QXS_irs i = TRAD_COMM; r = REG; s = REG

VIWS_irs value of imports of tradable commodity i from source r to destination s, evaluated at world (cif) prices

VIWS_irs = PCIF_irs * QXS_irs i = TRAD_COMM; r = REG; s = REG

Technology Parameters
ESUBVA_j with j = PROD_COMM substitution parameter between primary factors in the CES value-added nest of the nested CES production function of sector j of all regions (i.e. elasticity of substitution between primary production factors; for example, in a situation where land doesn't play a role in production, hence labor and capital are the only primary factors, this parameter indicates how sensitive is the K/L ratio to a 1 percent change in the wage/rental ratio) ESUBD_i with i = TRAD_COMM substitution parameter between domestic and composite imported commodities in the Armington utility/production structure of agent/sector i in all regions ESUBM_i with i = TRAD_COMM substitution parameter among imported commodities from different sources in the Armington utility/production structure of agent/sector i in all regions.

Technology Parameters

ESUBVA_j with j = PROD_COMM

substitution parameter between primary factors in the CES value-added nest of the nested CES production function of sector j of all regions

(i.e. elasticity of substitution between primary production factors; for example, in a situation where land doesn't play a role in production, hence labor and capital are the only primary factors, this parameter indicates how sensitive is the K/L ratio to a 1 percent change in the wage/rental ratio)

ESUBD_i with i = TRAD_COMM substitution parameter between domestic and composite imported commodities in the Armington utility/production structure of agent/sector i in all regions

ESUBM_i with i = TRAD_COMM

substitution parameter among imported commodities from different sources in the Armington utility/production structure of agent/sector i in all regions.

CDE Preference Parameters and Associated Elasticities
SUBPAR_ir with i = TRAD_COMM; r = REG substitution parameter for tradable commodity i in the CDE minimum expenditure function of region r INCPAR_ir with i = TRAD_COMM; r = REG expansion parameter for tradable commodity i in the CDE minimum expenditure function of region r. ALPHA_ir 1 - sub. parameter in the CDE minimum expenditure function ALPHA_ir = 1 - SUBPAR_ir i = TRAD_COMM; r = REG APE_ikr Allen partial elst.of sub between composite i and k in r *APE_ikr = ALPHA_ir + ALPHA_kr- S_nCONSHR_nrALPHA_nr** i = k= n = TRAD_COMM; r = REG *APE_iir = 2.0ALPHA_ir - S_nCONSHR_nrALPHA_nr - ALPHA_ir / CONSHR_ir* EY_ir income elasticity of private household demand for i in r *EY_ir = (1/S_n CONSHR_nrINCPAR_nr) * (INCPAR_ir * (1.0 - ALPHA_ir) + S_nCONSHR_nrINCPAR_nrALPHA_nr) + (ALPHA_ir - S_nCONSHR_nrALPHA_nr)* i = n = TRAD_COMM; r = REG EP_ikr uncompensated cross-price elasticity private household demand for i wrt k in r *EP_ikr = (APE_ikr - EY_ir)CONSHR_kr** i = k = TRAD_COMM; r = REG

CDE Preference Parameters and Associated Elasticities

SUBPAR_ir with i = TRAD_COMM; r = REG

substitution parameter for tradable commodity i in the CDE minimum expenditure function of region r

INCPAR_ir with i = TRAD_COMM; r = REG

expansion parameter for tradable commodity i in the CDE minimum expenditure function of region r.

ALPHA_ir 1 - sub. parameter in the CDE minimum expenditure function

ALPHA_ir = 1 - SUBPAR_ir i = TRAD_COMM; r = REG

APE_ikr Allen partial elst.of sub between composite i and k in r

APE_ikr = ALPHA_ir + ALPHA_kr- S_nCONSHR_nr*ALPHA_nr i = k= n = TRAD_COMM; r = REG

APE_iir = 2.0*ALPHA_ir - S_nCONSHR_nr*ALPHA_nr - ALPHA_ir / CONSHR_ir

EY_ir income elasticity of private household demand for i in r

EY_ir = (1/S_n CONSHR_nr*INCPAR_nr) * (INCPAR_ir * (1.0 - ALPHA_ir) + S_nCONSHR_nr*INCPAR_nr*ALPHA_nr) + (ALPHA_ir - S_nCONSHR_nr*ALPHA_nr)

i = n = TRAD_COMM; r = REG

EP_ikr uncompensated cross-price elasticity private household demand for i wrt k in r

EP_ikr = (APE_ikr - EY_ir)*CONSHR_kr i = k = TRAD_COMM; r = REG

Mobility Parameter
ETRAE_i with i = ENDW_COMM transformation parameter between uses for a sluggish primary factor i in the one level CET production function (i.e. this parameter indicates how easy/difficult it is to transfer a sluggish factor (say, capital) from one sector to another; the closer is ETRAE to zero, the more immobile is the factor between alternative uses) RORFLEX_r with r = REG flexibility of expected net rate of return on capital stock in region r with respect to investment (if a region's capital stock increases by 1%, then it is expected that the net rate of return on capital will decline by RORFLEX%) RORDELTA binary coefficient that determines the mechanism of allocating investment across regions (when RORDELTA=1, investment is allocated across regions to equate the change in the expected rates of return, rore(r), when RORDELTA=0, investment is allocated across regions to maintain the existing composition of capital stocks).

Mobility Parameter

ETRAE_i with i = ENDW_COMM

transformation parameter between uses for a sluggish primary factor i in the one level CET production function

(i.e. this parameter indicates how easy/difficult it is to transfer a sluggish factor (say, capital) from one sector to another; the closer is ETRAE to zero, the more immobile is the factor between alternative uses)

RORFLEX_r with r = REG flexibility of expected net rate of return on capital stock in region r with respect to investment (if a region's capital stock increases by 1%, then it is expected that the net rate of return on capital will decline by RORFLEX%)

RORDELTA

binary coefficient that determines the mechanism of allocating investment across regions (when RORDELTA=1, investment is allocated across regions to equate the change in the expected rates of return, rore(r), when RORDELTA=0, investment is allocated across regions to maintain the existing composition of capital stocks).

Value Flows
VOA_ir value of non-saving commodity i output or supplied in region r evaluated at agents' prices VOA_ir = EVOA_ir i = ENDW_COMM; r = REG VOA_ir = S_jVFA_jir i = PROD_COMM; j = DEMD_COMM; r = REG VFA_ijr value of purchases of demanded commodity i by firms in sector j of regin r evaluated at agents' prices VFA_ijr = EVFA_ijr i = ENDW_COMM; j = PROD_COMM; r = REG VFA_ijr = VDFA_ijr + VIFA_ijr i =TRAD_COMM; j = PROD_COMM; r = REG VOM_ir value of non-saving commodity i output or supplied in region r evaluated at market prices VOM_ir = S_jVFM_ijr i = ENDW_COMM;j = PROD_COMM; r = REG VOM_ir = VDM_ir + VST_ir + S_sVXMD_irs i = MARG_COMM; r = REG; s = REG VOM_ir = VDM_ir + S_sVXMD_irs i = NMRG_COMM; r = REG; s = REG VOM_ir = VOA_ir i = CGDS_COMM; r = REG VDM_ir value of domestic sales of tradable commodity i in region r evaluated at market prices VDM_ir = VDPM_ir + VDGM_ir + S_jVDFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG VIM_ir value of aggregate imports of tradable commodity i in region r evaluated at market prices VIM_ir = VIPM_ir + VIGM_ir + S_jVIFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG VPA_ir value of private household expenditure on tradable commodity i in region r evaluated at agents' prices VPA_ir = VDPA_ir + VIPA_ir i = TRAD_COMM; r = REG PRIVEXP_r total consumption expenditure by private household in regin r PRIVEXP_r = S_iVPA_ir i = TRAD_COMM VGA_ir value of government expenditure on tradable commodity i in region r evaluated at agents' prices VGA_ir = VDGA_ir + VIGA_ir i = TRAD_COMM; r = REG GOVEXP_r total consumption expenditure by government in region r GOVEXP_r = S_iVGA_ir i = TRAD_COMM; r = REG INCOME_r total expenditure equals net income in region r INCOME_r = PRIVEXP_r + GOVEXP_r + SAVE_r r = REG REGINV_r gross investment in region r that equals value of output of "capital goods" sector REGINV_r = S_kVOA_kr k = CGDS_COMM NETINV_r net investment in region r NETINV_r = S_kVOA_kr - VDEP_r k = CGDS_COMM GLOBINV global net investment GLOBINV = S_rNETINV = S_rSAVE_r r = REG INVKERATIO_r ratio of gross investment to end-of-period capital stock in region r INVKERATIO_r = REGINV_r / (VKB_r + NETINV_r) r = REG GRNETRATIO_r ratio of gross to net rate of return on capital in regin r (VOA_capital,r is gross return to capital) GRNETRATIO_r = S_kVOA_kr / (S_kVOA_kr - VDEP_r) with k = ENDWC_COMM; r = REG GDP_r gross domestic product in region r (trade is valued at worl prices) GDP_r = S_iVPA_ir + S_iVGA_ir + S_kVOA_kr + S_iS_sVXWD_irs+ S_mVST_ms - S_iS_sVIWS_irs i = TRAD_COMM; k = CGDS_COMM; r = REG; s = REG VT international margin suply VT = S_iS_rVST_ir i = TRAD_COMM; r = REG VXW_ir value of exports of tradable commodity i from source r evaluated at world (fob) prices VXW_ir = S_sVXWD_irs+VST_ir i = MARG_COMM; r = REG VXW_ir = S_sVXWD_irs i = NMRG_COMM; r = REG VXWREGION_r value of exports from source r evaluated at world (fob) prices VXWREGION_r = S_iVXW_ir i = TRAD_COMM; r = REG VXWCOMMOD_i value of exports of tradable commodity i evaluated at world (fob) prices VXWCOMMOD_i= S_rVXW_ir i = TRAD_COMM; r = REG VIW_ir value of imports of tradable commodity i into region r evaluated at world (cif) prices VIW_ir= S_sVIWS_isr i = TRAD_COMM; r = REG; s = REG VIWREGION_r value of imports into region r evaluated at world (cif) prices VIWREGION_r = S_iVIW_ir i = TRAD_COMM; r = REG VIWCOMMOD_i value of imports of tradable commodity i evaluated at world (cif) prices VIWCOMMOD_i= S_rVIW_ir i = TRAD_COMM; r = REG VXWLD value of worldwide commodity exports evaluated at world (fob) prices VXWLD= S_rVXWREGION_r r = REG PW_PM_ir ratio of world (fob) to domestic market prices for tradable commodity i in region PW_PM_ir = S_sVXWD_irs / S_sVXMD_irs i = TRAD_COMM; r = REG; s = REG VOW_ir value of output of tradable commodity i in region r, evaluated at world (fob) prices *VOW_ir = VDM_ir PW_PM_ir + S_sVXWD_irs + VST_ir** i = MARG_COMM; r = REG; s = REG *VOW_ir = VDM_ir PW_PM_ir + S_sVXWD_irs** i = NMRG_COMM; r = REG; s = REG VWOW_i value of world supply of tradable commodity i evaluated at world (fob) prices VWOW_i = S_rVOW_iri = TRAD_COMM; r = REG VTMFSD_mirs int'l margin usage, by margin, freight, source, and destination m = MARG_COMM;i = TRAD_COMM; r = REG; s = REG VTFSD_irs aggregate value of svces in the shipment of i from r to s VTFSD_irs = S_mVTMFSD_mirs In a balanced data base VIWS_irs = VXWD_irs + VTFSD_irs i = TRAD_COMM; m = MARG_COMM; r = REG; s = REG VTMPROV_m international margin services provision VTMPROV_m = S_rVST_mr m = MARG_COMM; r = REG VTRPROV_r international margin supply, by region VTRPROV_r = S_mVST_mr m = MARG_COMM; r = REG VTMUSE_m international margin services usage, by type VTMUSE_m = S_iS_rS_sVTMFSD_mirs m = MARG_COMM; i = TRAD_COMM; r = s = REG In a balanced data base, VTMPROV = VTMUSE VTMUSESHR_mirs share of i,r,s usage in global demand for m VTMUSESHR_mirs = VTFSD_irs / VT m = MARG_COMM; i = TRAD_COMM; r = s = REG if VTMUSE_m <> 0.0 then VTMUSESHR_mirs = VTMFSD_mirs / VTMUSE_m VTSUPPSHR_mr share of region r in global supply of margin m VTSUPPSHR_mr = VTRPROV_r / VT if VTMPROV_m <> 0.0 then VTSUPPSHR_mr = VST_mr / VTMPROV_m m = MARG_COMM; r = REG VTUSE international margin services usage; VTUSE=S_mS_iS_rS_sVTMFSD_mirs m = MARG_COMM; i = TRAD_COMM; r = s = REG VWOU_i value of world output of i at user prices VWOU_i = S_s[(VPA_is + VGA_is) + S_jVFA_ijs] s = REG; j = PROD_COMM VENDWREG_r value of primary factors, at mkt prices, by region VENDWREG_r = S_i VOM_ir i = ENDOW_COMM; r = REG VENDWWLD value of primary factors, at mkt prices, worldwide VENDWWLD = S_r VENDWREG_r r = REG VPAEV_ir private household expend. on i in r valued at agent's prices, for EV calculation VPAEV_ir = qpev_ir i = TRAD_COMM, r = REG VPAREGEV_r private consumption expenditure in region r, for EV calculation VPAREGEV_r = S_iVPAEV_ir i = TRAD_COMM, r = REG YG_r regional government consumption expenditure, in region r r = REG

Value Flows

VOA_ir value of non-saving commodity i output or supplied in region r evaluated at agents' prices

VOA_ir = EVOA_ir i = ENDW_COMM; r = REG

VOA_ir = S_jVFA_jir i = PROD_COMM; j = DEMD_COMM; r = REG

VFA_ijr value of purchases of demanded commodity i by firms in sector j of regin r evaluated at agents' prices

VFA_ijr = EVFA_ijr i = ENDW_COMM; j = PROD_COMM; r = REG

VFA_ijr = VDFA_ijr + VIFA_ijr i =TRAD_COMM; j = PROD_COMM; r = REG

VOM_ir value of non-saving commodity i output or supplied in region r evaluated at market prices

VOM_ir = S_jVFM_ijr        i = ENDW_COMM;j = PROD_COMM; r = REG

VOM_ir = VDM_ir + VST_ir + S_sVXMD_irs        i = MARG_COMM; r = REG; s = REG

VOM_ir = VDM_ir + S_sVXMD_irs        i = NMRG_COMM; r = REG; s = REG

VOM_ir = VOA_ir        i = CGDS_COMM; r = REG

VDM_ir value of domestic sales of tradable commodity i in region r evaluated at market prices

VDM_ir = VDPM_ir + VDGM_ir + S_jVDFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG

VIM_ir value of aggregate imports of tradable commodity i in region r evaluated at market prices

VIM_ir = VIPM_ir + VIGM_ir + S_jVIFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG

VPA_ir value of private household expenditure on tradable commodity i in region r evaluated at agents' prices

VPA_ir = VDPA_ir + VIPA_ir i = TRAD_COMM; r = REG

PRIVEXP_r total consumption expenditure by private household in regin r

PRIVEXP_r = S_iVPA_ir i = TRAD_COMM

VGA_ir value of government expenditure on tradable commodity i in region r evaluated at agents' prices

VGA_ir = VDGA_ir + VIGA_ir i = TRAD_COMM; r = REG

GOVEXP_r total consumption expenditure by government in region r

GOVEXP_r = S_iVGA_ir i = TRAD_COMM; r = REG

INCOME_r total expenditure equals net income in region r

INCOME_r = PRIVEXP_r + GOVEXP_r + SAVE_r r = REG

REGINV_r gross investment in region r that equals value of output of "capital goods" sector

REGINV_r = S_kVOA_kr k = CGDS_COMM

NETINV_r net investment in region r

NETINV_r = S_kVOA_kr - VDEP_r k = CGDS_COMM

GLOBINV global net investment

GLOBINV = S_rNETINV = S_rSAVE_r r = REG

INVKERATIO_r ratio of gross investment to end-of-period capital stock in region r

INVKERATIO_r = REGINV_r / (VKB_r + NETINV_r) r = REG

GRNETRATIO_r ratio of gross to net rate of return on capital in regin r (VOA_capital,r is gross return to capital)

GRNETRATIO_r = S_kVOA_kr / (S_kVOA_kr - VDEP_r) with k = ENDWC_COMM; r = REG

GDP_r gross domestic product in region r (trade is valued at worl prices)

GDP_r = S_iVPA_ir + S_iVGA_ir + S_kVOA_kr + S_iS_sVXWD_irs+ S_mVST_ms - S_iS_sVIWS_irs i = TRAD_COMM; k = CGDS_COMM; r = REG; s = REG

VT international margin suply

VT = S_iS_rVST_ir i = TRAD_COMM; r = REG

VXW_ir value of exports of tradable commodity i from source r evaluated at world (fob) prices

VXW_ir = S_sVXWD_irs+VST_ir i = MARG_COMM; r = REG

VXW_ir = S_sVXWD_irs i = NMRG_COMM; r = REG

VXWREGION_r value of exports from source r evaluated at world (fob) prices

VXWREGION_r = S_iVXW_ir i = TRAD_COMM; r = REG

VXWCOMMOD_i value of exports of tradable commodity i evaluated at world (fob) prices

VXWCOMMOD_i= S_rVXW_ir i = TRAD_COMM; r = REG

VIW_ir value of imports of tradable commodity i into region r evaluated at world (cif) prices

VIW_ir= S_sVIWS_isr i = TRAD_COMM; r = REG; s = REG

VIWREGION_r value of imports into region r evaluated at world (cif) prices

VIWREGION_r = S_iVIW_ir i = TRAD_COMM; r = REG

VIWCOMMOD_i value of imports of tradable commodity i evaluated at world (cif) prices

VIWCOMMOD_i= S_rVIW_ir i = TRAD_COMM; r = REG

VXWLD value of worldwide commodity exports evaluated at world (fob) prices

VXWLD= S_rVXWREGION_r r = REG

PW_PM_ir ratio of world (fob) to domestic market prices for tradable commodity i in region

PW_PM_ir = S_sVXWD_irs / S_sVXMD_irs i = TRAD_COMM; r = REG; s = REG

VOW_ir value of output of tradable commodity i in region r, evaluated at world (fob) prices

VOW_ir = VDM_ir * PW_PM_ir + S_sVXWD_irs + VST_ir i = MARG_COMM; r = REG; s = REG

VOW_ir = VDM_ir * PW_PM_ir + S_sVXWD_irs i = NMRG_COMM; r = REG; s = REG

VWOW_i value of world supply of tradable commodity i evaluated at world (fob) prices

VWOW_i = S_rVOW_iri = TRAD_COMM; r = REG

VTMFSD_mirs int'l margin usage, by margin, freight, source, and destination

m = MARG_COMM;i = TRAD_COMM; r = REG; s = REG

VTFSD_irs aggregate value of svces in the shipment of i from r to s

VTFSD_irs = S_mVTMFSD_mirs

In a balanced data base VIWS_irs = VXWD_irs + VTFSD_irs

i = TRAD_COMM; m = MARG_COMM; r = REG; s = REG

VTMPROV_m international margin services provision

VTMPROV_m = S_rVST_mr m = MARG_COMM; r = REG

VTRPROV_r international margin supply, by region

VTRPROV_r = S_mVST_mr m = MARG_COMM; r = REG

VTMUSE_m international margin services usage, by type

VTMUSE_m = S_iS_rS_sVTMFSD_mirs m = MARG_COMM; i = TRAD_COMM; r = s = REG

In a balanced data base, VTMPROV = VTMUSE

VTMUSESHR_mirs share of i,r,s usage in global demand for m

VTMUSESHR_mirs = VTFSD_irs / VT m = MARG_COMM; i = TRAD_COMM; r = s = REG

if VTMUSE_m <> 0.0 then VTMUSESHR_mirs = VTMFSD_mirs / VTMUSE_m

VTSUPPSHR_mr share of region r in global supply of margin m

VTSUPPSHR_mr = VTRPROV_r / VT if VTMPROV_m <> 0.0 then VTSUPPSHR_mr = VST_mr / VTMPROV_m

m = MARG_COMM; r = REG

VTUSE international margin services usage;

VTUSE=S_mS_iS_rS_sVTMFSD_mirs m = MARG_COMM; i = TRAD_COMM; r = s = REG

VWOU_i value of world output of i at user prices

VWOU_i = S_s[(VPA_is + VGA_is) + S_jVFA_ijs]

s = REG; j = PROD_COMM

VENDWREG_r value of primary factors, at mkt prices, by region

VENDWREG_r = S_i VOM_ir i = ENDOW_COMM; r = REG

VENDWWLD value of primary factors, at mkt prices, worldwide

VENDWWLD = S_r VENDWREG_r r = REG

VPAEV_ir private household expend. on i in r valued at agent's prices, for EV calculation

VPAEV_ir = qpev_ir i = TRAD_COMM, r = REG

VPAREGEV_r private consumption expenditure in region r, for EV calculation

VPAREGEV_r = S_iVPAEV_ir i = TRAD_COMM, r = REG

YG_r regional government consumption expenditure, in region r r = REG

Shares
SHRDFM_ijr share of domestic sales of tradable commodity i used by firms in sector j of regin r evaluated at market prices SHRFM_ijr = VDFM_ijr / VDM_ir i = TRAD_COMM; j = PROD_COMM; r = REG SHRDPM_i share of domestic sales of commodity i used by private household in region r evaluated at market prices SHRDPM_ir = VDPM_ir / VDM_ir i = TRAD_COMM; r = REG SHRDGM_i share of domestic sales of commodity i used by the government in region r evaluated at market prices SHRDGM_ir = VDGM_ir / VDM_ir i = TRAD_COMM; r = REG SHRIFM_ijr share of aggregate imports of tradable commodity i used by firms in sector j of regin r evaluated at market prices SHRIFM_ijr = VIFM_ijr / VIM_ir i = TRAD_COMM; j = PROD_COMM; r = REG SHRIPM_ir share of aggregate imports of commodity i used by private household in region r evaluated at market prices SHRIPM_ir = VIPM_ir / VIM_ir i = TRAD_COMM; r = REG SHRIGM_ir share of aggregate imports of commodity i used by the government in region r evaluated at market prices SHRIGM_ir = VIGM_ir / VIM_ir i = TRAD_COMM; r = REG FMSHR_ijr share of imports in the composite for tradable commodity i used by firms in sector j of region r evaluated at agents' prices FMSHR_ijr = VIFA_ijr / VFA_ijr i = TRAD_COMM; j = PROD_COMM; r = REG PMSHR_ir share of imports in the composite for tradable commodity i used by private household in region r evaluated at agents' prices PMSHR_ir = VIPA_ir / VPA_ir i = TRAD_COMM; r = REG GMSHR_ir share of impotrs in the composite for tradable commodity i used by the government in region r evaluated at agents' prices GMSHR_ir = VIGA_ir / VGA_ir i = TRAD_COMM; r = REG CONSHR_ir budget share of the composite for tradable i in total private household expenditure in regin r evaluated at agents' prices CONSHR_ir = VPA_ir / PRIVEXP_r i = TRAD_COMM; r = REG MSHRS_irs market share of source r in the aggregate imports of tradable commodity i in region s evaluated at market prices MSHRS_irs = VIMS_irs / S_rVIMS_irs i = TRAD_COMM; r = s = REG SVA_ijr share of endowment commodity i in value-added of sector j of region r evaluated at agents' prices SVA_ijr= VFA_ijr / S_kVFA_kjr i = ENDW_COMM; j = PROD_COMM; k = ENDW_COMM; r = REG REVSHR_ijr share of endowment commodity i used by fiorms in sector j of regin r evaluated at market prices REVSHR_ijr= VFM_ijr / S_kVFM_kjr i = ENDW_COMM; j = PROD_COMM; k = PROD_COMM; r = REG FOBSHR_irs share of fob price in the cif price for tradable commodity i exported from source r to destination s FOBSHR_irs= VXWD_irs / VIWSCOST_irs i = TRAD_COMM; r = s = REG XSHRPRIV_r private expenditure share in regional income XSHRPRIV_r = PRIVEXP_r/INCOME_r r = REG XSHRGOV_r government expenditure share in regional income XSHRGOV_r = GOVEXP_r/INCOME_r r = REG XSHRSAVE_r saving share in regional income XSHRSAVE_r = SAVE_r/INCOME_r r = REG SHRDM_ir share of domestic sales of i in r i = TRAD_COMM; r = REG SHRDM_ir = VDM_ir / VOM_ir SHRST_mr share of sales of m to global transport services in r m = MARG_COMM; r = REG SHRST_mr = VST_mr / VOM_mr SHRXMD_irs share of export sales of i to s in r i = TRAD_COMM; r = s = REG SHRXMD_irs = VXMD_irs / VOM_ir i = TRAD_COMM; r = s = REG SHREM_ijr share of mobile endowments i used by sector j at mkt prices SHREM_ijr = VFM_ijr / VOM_ir i = ENDWM_COMM; j = PROD_COMM; r = REG TRNSHR_irs share of transport price in the cif price for tradable commodity i exported from source r to destination s TRSHR_irs= VTFSD_irs / VIWSCOST_irs i = TRAD_COMM; r = s = REG XWCONSHR_ir expansion-parameter-weighted consumption share *XWCONSHR_ir = CONSHR_irINCPAR_ir/UELASPRIV_r** i = TRAD_COMM; r = REG XSHRPRIVEV_r private expenditure share in regional income, for EV calculation r = REG XSHRPRIVEV_r = PRIVEXPEV_r/INCOMEEV_r r = REG XSHRGOVEV_r government expenditure share in regional income, for EV calculation r = REG XSHRGOVEV_r = GOVEXPEV_r/INCOMEEV_r r = REG XSHRSAVEEV_r saving share in regional income, for EV calculation r = REG XSHRSAVEEV_r = SAVEEV_r/INCOMEEV_r r = REG XWCONSHREV_ir expansion-parameter-weighted consumption share, for EV calculation *XWCONSHREV_ir = CONSHREV_irINCPAR_ir/UELASPRIVEV_r** i = TRAD_COMM, r = REG CONSHREV_ir share of private household consn devoted to good i in r, for EV calculation CONSHREV_ir = VPAEV_ir/VPAREGEV_r STC_ijr share of i in total costs of j in r STC_ijr = VFA_ijr / S_k VFA_kjr i = k = DEMD_COMM; j = PROD_COMM; r = REG

SHRDFM_ijr share of domestic sales of tradable commodity i used by firms in sector j of regin r evaluated at market prices

SHRFM_ijr = VDFM_ijr / VDM_ir i = TRAD_COMM; j = PROD_COMM; r = REG

SHRDPM_i share of domestic sales of commodity i used by private household in region r evaluated at market prices

SHRDPM_ir = VDPM_ir / VDM_ir i = TRAD_COMM; r = REG

SHRDGM_i share of domestic sales of commodity i used by the government in region r evaluated at market prices

SHRDGM_ir = VDGM_ir / VDM_ir i = TRAD_COMM; r = REG

SHRIFM_ijr share of aggregate imports of tradable commodity i used by firms in sector j of regin r evaluated at market prices

SHRIFM_ijr = VIFM_ijr / VIM_ir i = TRAD_COMM; j = PROD_COMM; r = REG

SHRIPM_ir share of aggregate imports of commodity i used by private household in region r evaluated at market prices

SHRIPM_ir = VIPM_ir / VIM_ir i = TRAD_COMM; r = REG

SHRIGM_ir share of aggregate imports of commodity i used by the government in region r evaluated at market prices

SHRIGM_ir = VIGM_ir / VIM_ir i = TRAD_COMM; r = REG

FMSHR_ijr share of imports in the composite for tradable commodity i used by firms in sector j of region r evaluated at agents' prices

FMSHR_ijr = VIFA_ijr / VFA_ijr i = TRAD_COMM; j = PROD_COMM; r = REG

PMSHR_ir share of imports in the composite for tradable commodity i used by private household in region r evaluated at agents' prices

PMSHR_ir = VIPA_ir / VPA_ir i = TRAD_COMM; r = REG

GMSHR_ir share of impotrs in the composite for tradable commodity i used by the government in region r evaluated at agents' prices

GMSHR_ir = VIGA_ir / VGA_ir i = TRAD_COMM; r = REG

CONSHR_ir budget share of the composite for tradable i in total private household expenditure in regin r evaluated at agents' prices

CONSHR_ir = VPA_ir / PRIVEXP_r i = TRAD_COMM; r = REG

MSHRS_irs market share of source r in the aggregate imports of tradable commodity i in region s evaluated at market prices

MSHRS_irs = VIMS_irs / S_rVIMS_irs i = TRAD_COMM; r = s = REG

SVA_ijr share of endowment commodity i in value-added of sector j of region r evaluated at agents' prices

SVA_ijr= VFA_ijr / S_kVFA_kjr i = ENDW_COMM; j = PROD_COMM; k = ENDW_COMM; r = REG

REVSHR_ijr share of endowment commodity i used by fiorms in sector j of regin r evaluated at market prices

REVSHR_ijr= VFM_ijr / S_kVFM_kjr i = ENDW_COMM; j = PROD_COMM; k = PROD_COMM; r = REG

FOBSHR_irs share of fob price in the cif price for tradable commodity i exported from source r to destination s

FOBSHR_irs= VXWD_irs / VIWSCOST_irs i = TRAD_COMM; r = s = REG

XSHRPRIV_r private expenditure share in regional income

XSHRPRIV_r = PRIVEXP_r/INCOME_r r = REG

XSHRGOV_r government expenditure share in regional income

XSHRGOV_r = GOVEXP_r/INCOME_r r = REG

XSHRSAVE_r saving share in regional income

XSHRSAVE_r = SAVE_r/INCOME_r r = REG

SHRDM_ir share of domestic sales of i in r i = TRAD_COMM; r = REG

SHRDM_ir = VDM_ir / VOM_ir

SHRST_mr share of sales of m to global transport services in r m = MARG_COMM; r = REG

SHRST_mr = VST_mr / VOM_mr

SHRXMD_irs share of export sales of i to s in r i = TRAD_COMM; r = s = REG

SHRXMD_irs = VXMD_irs / VOM_ir i = TRAD_COMM; r = s = REG

SHREM_ijr share of mobile endowments i used by sector j at mkt prices

SHREM_ijr = VFM_ijr / VOM_ir i = ENDWM_COMM; j = PROD_COMM; r = REG

TRNSHR_irs share of transport price in the cif price for tradable commodity i exported from source r to destination s

TRSHR_irs= VTFSD_irs / VIWSCOST_irs

i = TRAD_COMM; r = s = REG

XWCONSHR_ir expansion-parameter-weighted consumption share

XWCONSHR_ir = CONSHR_ir*INCPAR_ir/UELASPRIV_r i = TRAD_COMM; r = REG

XSHRPRIVEV_r private expenditure share in regional income, for EV calculation        r = REG

XSHRPRIVEV_r = PRIVEXPEV_r/INCOMEEV_r        r = REG

XSHRGOVEV_r government expenditure share in regional income, for EV calculation        r = REG

XSHRGOVEV_r = GOVEXPEV_r/INCOMEEV_r        r = REG

XSHRSAVEEV_r saving share in regional income, for EV calculation        r = REG

XSHRSAVEEV_r = SAVEEV_r/INCOMEEV_r        r = REG

XWCONSHREV_ir expansion-parameter-weighted consumption share, for EV calculation

XWCONSHREV_ir = CONSHREV_ir*INCPAR_ir/UELASPRIVEV_r i = TRAD_COMM, r = REG

CONSHREV_ir share of private household consn devoted to good i in r, for EV calculation

CONSHREV_ir = VPAEV_ir/VPAREGEV_r

STC_ijr share of i in total costs of j in r

STC_ijr = VFA_ijr / S_k VFA_kjr i = k = DEMD_COMM; j = PROD_COMM; r = REG

Quantity Variables
QO_ir quantity of non-saving commodity i output or supplied in region r i = NSAV_COMM r = REG QOES_ijr quantity of sluggish endowment i supplied to sector j firm of region r i = ENDWS_COMM; j = PROD_COMM; r = REG QDS_ir quantity of domestic sales of tradable commodity i in region r i = TRAD_COMM; r = REG QXS_irs quantity of exports of tradable commodity i from source r to destination s i = TRAD_COMM; r = s = REG QST_ir quantity of sales of marginal commodity i to the international transport sector in region r i = MARG_COMM; r = REG QFE_ijr quantity of endowment i demanded by sector j firm in region r i = ENDW_COMM; j = PROD_COMM; r = REG QVA_jr quantity index of land-labor-capital composite (value-added) in sector j firm in region r j = PROD_COMM; r = REG QF_ijr quantity of composite tradable commodity i demanded by sector j firm in region r i = TRAD_COMM; j = PROD_COMM; r = REG QFD_ijr quantity of domestic tradable i demanded by sector j firm in region r i = TRAD_COMM; j = PROD_COMM; r = REG QFM_ijr quantity of imported tradable i demanded by sector j firm in region r i = TRAD_COMM; j = PROD_COMM; r = REG QP_ir quantity of composite tradable i demanded by private household in region r i = TRAD_COMM; r = REG QPD_ir quantity of domestic tradable i demanded by private household in region r i = TRAD_COMM; r = REG QPM_ir quantity of imported tradable i demanded by private household in region r i = TRAD_COMM; r = REG QG_ir quantity of composite tradable commodity i demanded by government household in region r i = TRAD_COMM; r = REG QGD_ir quantity of domestic tradable commodity i demanded by government household in region r i = TRAD_COMM; r = REG QGM_ir quantity of imported tradable commodity i demanded by government household in region r i = TRAD_COMM; r = REG QIM_ir quantity of aggregate imports of tradable commodity i demanded by region r using market prices as weights i = TRAD_COMM; r = REG QIW_ir quantity of aggregate imports of tradable commodity i demanded by region r using cif prices as weights i = TRAD_COMM; r = REG QXW_ir quantity of aggregate exports of tradable commodity i supplied from region r using fob prices as weights i = TRAD_COMM; r = REG QIWREG_rvolume of merchandise imports demanded by region r r = REG QXWREG_rvolume of merchandise exports supplied by region r r = REG QIWCOM_ivolume of global merchandise imports of tradable commodity i i = TRAD_COMM; r = REG QXWCOM_ivolume of global merchandise exports of tradable commodity i i = TRAD_COMM; r = REG QXWWLDvolume of world trade QOW_iquantity index for world supply of tradable commodity i i = TRAD_COMM EXPAND_ir Change in investment levels relative to endowment stock i = ENDWC_COMM; r = REG QOWU_irquantity index for world supply of good i at user prices i = TRAD_COMM; r = REG QTMFSD_mirs international usage margin m on i from r to s m = MARG_COMM; i = TRAD_COMM; r = s = REG QTM_m global margin usage m = MARG_COMM QCGDS_r quantity of capital goods sector supplied in region r r = REG QSAVE_r quantity of savings demanded in region r r = REG GLOBALCGDS quantity of global supply of capital for net investment KSVCES_r quantity of capital services in region r r = REG KB_r quantity of beginning-of-period capital stock in region r r = REG KE_r quantity of end-of-period capital stock in region r r = REG QGDP_r quantity index for GDP in region r r = REG WALRAS_DEM quantity demanded in the omitted market - equals global demand for savings WALRAS_SUP quantity supplied in the omitted market - equals global supply of new capital goods composite POP_r population in region r r = REG COMPVALAD_ir composition of value added for good i and region r i = TRAD_COMM; r = REG

Quantity Variables

QO_ir quantity of non-saving commodity i output or supplied in region r

i = NSAV_COMM    r = REG

QOES_ijr quantity of sluggish endowment i supplied to sector j firm of region r

i = ENDWS_COMM; j = PROD_COMM; r = REG

QDS_ir quantity of domestic sales of tradable commodity i in region r

i = TRAD_COMM; r = REG

QXS_irs quantity of exports of tradable commodity i from source r to destination s

i = TRAD_COMM; r = s = REG

QST_ir quantity of sales of marginal commodity i to the international transport sector in region r

i = MARG_COMM; r = REG

QFE_ijr quantity of endowment i demanded by sector j firm in region r

i = ENDW_COMM; j = PROD_COMM; r = REG

QVA_jr quantity index of land-labor-capital composite (value-added) in sector j firm in region r

j = PROD_COMM; r = REG

QF_ijr quantity of composite tradable commodity i demanded by sector j firm in region r

i = TRAD_COMM; j = PROD_COMM; r = REG

QFD_ijr quantity of domestic tradable i demanded by sector j firm in region r

i = TRAD_COMM; j = PROD_COMM; r = REG

QFM_ijr quantity of imported tradable i demanded by sector j firm in region r

i = TRAD_COMM; j = PROD_COMM; r = REG

QP_ir quantity of composite tradable i demanded by private household in region r

i = TRAD_COMM; r = REG

QPD_ir quantity of domestic tradable i demanded by private household in region r

i = TRAD_COMM; r = REG

QPM_ir quantity of imported tradable i demanded by private household in region r

i = TRAD_COMM; r = REG

QG_ir quantity of composite tradable commodity i demanded by government household in region r

i = TRAD_COMM; r = REG

QGD_ir quantity of domestic tradable commodity i demanded by government household in region r

i = TRAD_COMM; r = REG

QGM_ir quantity of imported tradable commodity i demanded by government household in region r

i = TRAD_COMM; r = REG

QIM_ir quantity of aggregate imports of tradable commodity i demanded by region r using market prices as weights

i = TRAD_COMM; r = REG

QIW_ir quantity of aggregate imports of tradable commodity i demanded by region r using cif prices as weights

i = TRAD_COMM; r = REG

QXW_ir quantity of aggregate exports of tradable commodity i supplied from region r using fob prices as weights

i = TRAD_COMM; r = REG

QIWREG_rvolume of merchandise imports demanded by region r

r = REG

QXWREG_rvolume of merchandise exports supplied by region r

r = REG

QIWCOM_ivolume of global merchandise imports of tradable commodity i

i = TRAD_COMM; r = REG

QXWCOM_ivolume of global merchandise exports of tradable commodity i

i = TRAD_COMM; r = REG

QXWWLDvolume of world trade

QOW_iquantity index for world supply of tradable commodity i

i = TRAD_COMM

EXPAND_ir Change in investment levels relative to endowment stock

i = ENDWC_COMM; r = REG

QOWU_irquantity index for world supply of good i at user prices        i = TRAD_COMM; r = REG

QTMFSD_mirs international usage margin m on i from r to s        m = MARG_COMM; i = TRAD_COMM; r = s = REG

QTM_m global margin usage        m = MARG_COMM

QCGDS_r quantity of capital goods sector supplied in region r        r = REG

QSAVE_r quantity of savings demanded in region r        r = REG

GLOBALCGDS quantity of global supply of capital for net investment

KSVCES_r quantity of capital services in region r        r = REG

KB_r quantity of beginning-of-period capital stock in region r        r = REG

KE_r quantity of end-of-period capital stock in region r        r = REG

QGDP_r quantity index for GDP in region r        r = REG

WALRAS_DEM quantity demanded in the omitted market - equals global demand for savings

WALRAS_SUP quantity supplied in the omitted market - equals global supply of new capital goods composite

POP_r population in region r        r = REG

COMPVALAD_ir composition of value added for good i and region r i = TRAD_COMM; r = REG

Price Variables
PM_ir market price of non-saving commodity i in region r i = NSAV_COMM; r = REG PMES_ijr market price for sluggish endowment i supplied to firm j in region r i = ENDWS_COMM; j = PROD_COMM; r = REG PS_ir supply price of non-saving commodity i in region r i = NSAV_COMM; r = REG PFE_ijr demand price for endowment i by firms in sector j of region r i = ENDW_COMM; j = PROD_COMM; r = REG PVA_jr price of value-added in sector j j = PROD_COMM; r = REG PF_ijr demand price for composite tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG PFD_ijr demand price for domestic tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG PFM_ijr demand price for imported tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG PP_ir private household's demand price for composite tradable i in region r i = TRAD_COMM; r = REG PPD_ir private household's demand price for domestic tradable i in region r i = TRAD_COMM; r = REG PPM_ir private household's demand price for imported tradable i in region r i = TRAD_COMM; r = REG PG_ir government household's demand price for composite tradable i in region r i = TRAD_COMM; r = REG PGD_ir government household's demand price for domestic tradable i in region r i = TRAD_COMM; r = REG PGM_ir government household's demand price for imported tradable i in region r i = TRAD_COMM; r = REG PSAVE_r price of savings in region r r = REG PCGDS_r price of investment good in region r - equals PS(cgds,r) r = REG PGDP_r price index for GDP in region r r = REG PPRIV_r price index for private household expenditure in region r r = REG PGOV_r price index for government household expenditure in region r r = REG PFOB_irs world fob price of tradable commodity i exported from source r to destination s (prior to including transport margins) i = TRAD_COMM; r = s = REG PCIF_irs world cif price of tradable commodity i imported from source r to destination s ) after including transport margins) i = TRAD_COMM; r = s = REG PMS_irs market price by source of tradable commodity i imported from source r to destination s i = TRAD_COMM; r = s = REG PIM_ir market price of aggregate imports of tradable commodity i in region r i = TRAD_COMM; r = REG PIW_ir world price of aggregate imports of tradable commodity i in region r i = TRAD_COMM; r = REG PXW_ir price index for aggregate exports of tradable commodity i from region r i = TRAD_COMM; r = REG PIWREG_r price index of merchandise imports in region r r = REG PXWREG_r price index of merchandise exports from region r r = REG PIWCOM_i price index of global merchandise imports of tradable commodity i i = TRAD_COMM PXWCOM_i price index of global merchandise exports of tradable commodity i i = TRAD_COMM PXWWLD price index of world trade PR_ir ratio of domestic market price to market price of imports for tradable commodity i in region r i = TRAD_COMM; r = REG PW_i world price index for total supply of tradable commodity i in region r i = TRAD_COMM PSW_r price index received for tradable commodities produced in region r including sales of net investment to the global bank r = REG PDW_r price index paid for tradable commodities used in region r including purchases of savings from the global bank r = REG TOT_r terms of trade for region r r = REG PT_m price of margin services supplied m = MARG_COMM PCGDSWLD world average price of capital goods (net investment weights) PWU_i world price index for total good i supplies at user prices i = TRAD_COMM PTRANS_irs cost index for international transport of i from r to s i = TRAD_COMM; r = s = REG RENTAL_r rental rate on capital stock in regin r - equals PS(CGDS,r) r = REG RORC_r current net rate of return on capital stock in region r r = REG RORE_r expected net rate of return on capital stock in region r r = REG RORG global net rate of return on capital stock P_r price index for disposition of income by regional household PFACTREAL_ir ratio of return to primary factor i to cpi in r i = ENDOW_COMM; r = REG PFACTOR_r market price index of primary factors, by region PFACTWLDworld price index of primary factors

Price Variables

PM_ir market price of non-saving commodity i in region r

i = NSAV_COMM; r = REG

PMES_ijr market price for sluggish endowment i supplied to firm j in region r

i = ENDWS_COMM; j = PROD_COMM; r = REG

PS_ir supply price of non-saving commodity i in region r

i = NSAV_COMM; r = REG

PFE_ijr demand price for endowment i by firms in sector j of region r

i = ENDW_COMM; j = PROD_COMM; r = REG

PVA_jr price of value-added in sector j

j = PROD_COMM; r = REG

PF_ijr demand price for composite tradable i by firms in sector j of region r

i = TRAD_COMM; j = PROD_COMM; r = REG

PFD_ijr demand price for domestic tradable i by firms in sector j of region r

i = TRAD_COMM; j = PROD_COMM; r = REG

PFM_ijr demand price for imported tradable i by firms in sector j of region r

i = TRAD_COMM; j = PROD_COMM; r = REG

PP_ir private household's demand price for composite tradable i in region r

i = TRAD_COMM; r = REG

PPD_ir private household's demand price for domestic tradable i in region r

i = TRAD_COMM; r = REG

PPM_ir private household's demand price for imported tradable i in region r

i = TRAD_COMM; r = REG

PG_ir government household's demand price for composite tradable i in region r

i = TRAD_COMM; r = REG

PGD_ir government household's demand price for domestic tradable i in region r

i = TRAD_COMM; r = REG

PGM_ir government household's demand price for imported tradable i in region r

i = TRAD_COMM; r = REG

PSAVE_r price of savings in region r

r = REG

PCGDS_r price of investment good in region r - equals PS(cgds,r)

r = REG

PGDP_r price index for GDP in region r

r = REG

PPRIV_r price index for private household expenditure in region r

r = REG

PGOV_r price index for government household expenditure in region r

r = REG

PFOB_irs world fob price of tradable commodity i exported from source r to destination s (prior to including transport margins)

i = TRAD_COMM; r = s = REG

PCIF_irs world cif price of tradable commodity i imported from source r to destination s ) after including transport margins)

i = TRAD_COMM; r = s = REG

PMS_irs market price by source of tradable commodity i imported from source r to destination s

i = TRAD_COMM; r = s = REG

PIM_ir market price of aggregate imports of tradable commodity i in region r

i = TRAD_COMM; r = REG

PIW_ir world price of aggregate imports of tradable commodity i in region r

i = TRAD_COMM; r = REG

PXW_ir price index for aggregate exports of tradable commodity i from region r

i = TRAD_COMM; r = REG

PIWREG_r price index of merchandise imports in region r

r = REG

PXWREG_r price index of merchandise exports from region r

r = REG

PIWCOM_i price index of global merchandise imports of tradable commodity i

i = TRAD_COMM

PXWCOM_i price index of global merchandise exports of tradable commodity i

i = TRAD_COMM

PXWWLD price index of world trade

PR_ir ratio of domestic market price to market price of imports for tradable commodity i in region r

i = TRAD_COMM; r = REG

PW_i world price index for total supply of tradable commodity i in region r

i = TRAD_COMM

PSW_r price index received for tradable commodities produced in region r including sales of net investment to the global bank

r = REG

PDW_r price index paid for tradable commodities used in region r including purchases of savings from the global bank

r = REG

TOT_r terms of trade for region r

r = REG

PT_m price of margin services supplied

m = MARG_COMM

PCGDSWLD world average price of capital goods (net investment weights)

PWU_i world price index for total good i supplies at user prices

i = TRAD_COMM

PTRANS_irs cost index for international transport of i from r to s

i = TRAD_COMM; r = s = REG

RENTAL_r rental rate on capital stock in regin r - equals PS(CGDS,r)

r = REG

RORC_r current net rate of return on capital stock in region r

r = REG

RORE_r expected net rate of return on capital stock in region r

r = REG

RORG global net rate of return on capital stock

P_r price index for disposition of income by regional household

PFACTREAL_ir ratio of return to primary factor i to cpi in r

i = ENDOW_COMM; r = REG

PFACTOR_r market price index of primary factors, by region

PFACTWLDworld price index of primary factors

Technical Change Variables
AO_ir output augmenting technical change in sector j of region r j = PROD_COMM; r = REG AFE_ijr primary factor i augmenting technical change in sector j of region r i = ENDW_COMM; j = PROD_COMM; r = REG AF_ijr intermediate input i augmenting technical change in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG AVA_jr value-added augmenting technical change in sector j of region r j = PROD_COMM; r = REG AMS_irs import i from region r augmenting tech change in region s i = TRAD_COMM, r = s = REG AOSEC_j output tech change of sector j, worldwide j = PROD_COMM AOREG_r output tech change in region r r = REG AOALL_jr output augmenting technical change in sector j of r j = PROD_COMM; r = REG ESUBT_j elasticity of substitution among composite intermediate inputs in production j = PROD_COMM AFCOM_i intermediate tech change of input i, worldwide i = TRAD_COMM AFSEC_j intermediate tech change of sector j, worldwide j = PROD_COMM AFREG_r intermediate tech change in region r r = REG AFALL_ijr intermediate input i augmenting tech change by j in r i = TRAD_COMM,j = PROD_COMM; r = REG AFECOM_i factor input tech change of input i, worldwide i = ENDW_COMM AFESEC_j factor input tech change of sector j, worldwide j = PROD_COMM AFEREG_r factor input tech change in region r r = REG AFEALL_ijr primary factor i augmenting tech change sector j in r i = ENDW_COMM; j = PROD_COMM; r = REG AMS_irs reduction in effective price associated with delivery of i from r to s i = TRAD_COMM; r = REG; s = REG ATMFSD_mirs tech change in m's shipping of i from region r to s m = MARG_COMM; i = TRAD_COMM; r = s = REG ATM_m tech change in mode m, worldwide; m = TRAD_COMM ATF_i tech change shipping of i, worldwide i = TRAD_COMM ATS_r tech change shipping from region r r = REG ATD_s tech change shipping to s s = REG ATALL_mirs tech change in m's shipping of i from region r to s m = MARG_COMM; i = TRAD_COMM; r = REG; s = REG AU_r input-neutral shift in utility function r = REG

Technical Change Variables

AO_ir output augmenting technical change in sector j of region r

j = PROD_COMM; r = REG

AFE_ijr primary factor i augmenting technical change in sector j of region r

i = ENDW_COMM; j = PROD_COMM; r = REG

AF_ijr intermediate input i augmenting technical change in sector j of region r

i = TRAD_COMM; j = PROD_COMM; r = REG

AVA_jr value-added augmenting technical change in sector j of region r

j = PROD_COMM; r = REG

AMS_irs import i from region r augmenting tech change in region s

i = TRAD_COMM, r = s = REG

AOSEC_j output tech change of sector j, worldwide

j = PROD_COMM

AOREG_r output tech change in region r

r = REG

AOALL_jr output augmenting technical change in sector j of r

j = PROD_COMM; r = REG

ESUBT_j elasticity of substitution among composite intermediate inputs in production

j = PROD_COMM

AFCOM_i intermediate tech change of input i, worldwide

i = TRAD_COMM

AFSEC_j intermediate tech change of sector j, worldwide

j = PROD_COMM

AFREG_r intermediate tech change in region r

r = REG

AFALL_ijr intermediate input i augmenting tech change by j in r

i = TRAD_COMM,j = PROD_COMM; r = REG

AFECOM_i factor input tech change of input i, worldwide

i = ENDW_COMM

AFESEC_j factor input tech change of sector j, worldwide

j = PROD_COMM

AFEREG_r factor input tech change in region r

r = REG

AFEALL_ijr primary factor i augmenting tech change sector j in r

i = ENDW_COMM; j = PROD_COMM; r = REG

AMS_irs reduction in effective price associated with delivery of i from r to s

i = TRAD_COMM; r = REG; s = REG

ATMFSD_mirs tech change in m's shipping of i from region r to s

m = MARG_COMM; i = TRAD_COMM; r = s = REG

ATM_m tech change in mode m, worldwide;

m = TRAD_COMM

ATF_i tech change shipping of i, worldwide

i = TRAD_COMM

ATS_r tech change shipping from region r

r = REG

ATD_s tech change shipping to s

s = REG

ATALL_mirs tech change in m's shipping of i from region r to s

m = MARG_COMM; i = TRAD_COMM; r = REG; s = REG

AU_r input-neutral shift in utility function

r = REG

Policy Variables
TO_ir power of the tax on output (or income) of non-savings commodity i in region r i = NSAV_COMM; r = REG TF_ijr power of the tax on endowment commodity i demanded by sector j of regin r i = ENDW_COMM; j = PROD_COMM; r = REG TFD_ijr power of the tax on domestic tradable commodity i demanded by sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG TFM_ijr power of the tax on imported tradable commodity i demanded by sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG TPD_ir power of the tax on domestic tradable commodity i purchased by private household in region r i = TRAD_COMM; r = REG TPM_ir power of the tax on imported tradable commodity i purchased by private household in region r i = TRAD_COMM; r = REG TGD_ir power of the tax on domestic tradable commodity i purchased by government household in region r i = TRAD_COMM; r = REG TGM_ir power of the tax on imported tradable commodity i purchased by government household in region r i = TRAD_COMM; r = REG TXS_irs power of the tax on exports of tradable commodity i from source r to destination r (levied in region r) i = TRAD_COMM; r = s = REG TMS_irs power of the tax on imports of tradable commodity i from source r to destination s (levied in region s) i = TRAD_COMM; r = s = REG TX_ir power of the variable export tax on exports of tradable commodity from region r - destination generic i = TRAD_COMM; r = REG TM_ir power of the variable import tax (levy) on imports of tradable commodity i in region s - source generic i = TRAD_COMM; r = REG TP_r region-wide shock to tax on purchases by private household in region r r = REG ATPM_ir actual tax on imported traded commodity i purchased by private households in region r i = TRAD_COMM; r = REG ATPD_ir actual tax on domestic traded commodity i purchased by private households in region r i = TRAD_COMM; r = REG DGTAX_ir tax on government consumption of domestic good i in region r r = REG IGTAX_ir tax on government consumption of imported good i in region r r = REG TGC_r government consumption tax payments in r TGC_r = S_iDGTAX_ir + IGTAX_ir i = TRAD_COMM; r = REG DPTAX_ir tax on private consumption of domestic good i in region r DPTAX_ir = VDPA_ir - VDPM_ir i = TRAD_COMM; r = REG IPTAX_ir tax on private consumption of imported good i in region r IPTAX_ir = VIPA_ir - VIPM_ir i = TRAD_COMM; r = REG TPCr private consumption tax payments in r TPC_r = S_iDPTAX_ir + IPTAX_ir i = TRAD_COMM; r = REG DFTAX_ijr tax on use of domestic intermediate good i by j in r DFTAX_ijr = VDFA_ijr - VDFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG IFTAX_ijrtax on use of imported intermediate good i by j in r IFTAX_ijr = VIFA_ijr - VIFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG TIU_r firms' tax payments on intermediate goods usage in r TIU_r = S_jS_i(DFTAX_ijr + IFTAX_ijr) i = TRAD_COMM; j = PROD_COMM; r = REG ETAX_ijr tax on use of endowment good i by industry j in region r ETAX_ijr = VFA_ijr - VFM_ijr i = ENDW_COMM; j = PROD_COMM; r = REG TFU_r firms' tax payments on primary factor usage in r TFU_r = S_iS_jETAX_ijr i = ENDW_COMM; j = PROD_COMM; r = REG PTAX_ir output tax on good i in region r PTAX_ir = VOM_ir - VOA_ir i = NSAV_COMM; r = REG TOUT_r production tax payments in r TOUT_r = S_iPTAX_ir i = PROD_COMM; r = REG XTAXD_irstax on exports of good i from source r to destination s XTAXD_irs = VXWD_irs - VXMD_irs i = TRAD_COMM; r = s = REG TEX_r export tax payments in r TEXr = S_iS_sXTAXD_irs i = TRAD_COMM; r = s = REG MTAX_irs tax on imports of good i from source r in destination s MTAX_irs = VIMS_irs - VIWS_irs i = TRAD_COMM; r = s = REG TIM_r import tax payments in r TIM_r = S_iS_sMTAX_isr i = TRAD_COMM; r = s = REG TOTTAX_r Total tax receipts in r TOTTAX_r = TPC_r + TGC_r + TIU_r + TFU_r + TOUT_r + TEX_r + TIM_r + TINC_r r = REG TGCR_r change in ratio of government consumption tax to INCOME in region r r = REG TPCR_r change in ratio of private consumption tax to INCOME in region r r = REG TIUR_r change in ratio of tax on intermediate usage to INCOME in region r r = REG TFUR_r change in ratio of tax on primary factor usage to INCOME in region r r = REG TOUTR_r change in ratio of output tax to INCOME in region r nbsp; r = REG TEXPR_r change in ratio of export tax to INCOME in region r r = REG TIMPR_r change in ratio of import tax to INCOME in region r r = REG TINC_r income tax payments in r TINC_r = S_iPTAX_ir i = ENDOW_COMM; r = REG TINCR_r change in ratio of income tax to INCOME in region r r = REG DTAXR_r change in ratio of taxes to INCOME in r r = REG

Policy Variables

TO_ir power of the tax on output (or income) of non-savings commodity i in region r

i = NSAV_COMM; r = REG

TF_ijr power of the tax on endowment commodity i demanded by sector j of regin r

i = ENDW_COMM; j = PROD_COMM; r = REG

TFD_ijr power of the tax on domestic tradable commodity i demanded by sector j of region r

i = TRAD_COMM; j = PROD_COMM; r = REG

TFM_ijr power of the tax on imported tradable commodity i demanded by sector j of region r

i = TRAD_COMM; j = PROD_COMM; r = REG

TPD_ir power of the tax on domestic tradable commodity i purchased by private household in region r

i = TRAD_COMM; r = REG

TPM_ir power of the tax on imported tradable commodity i purchased by private household in region r

i = TRAD_COMM; r = REG

TGD_ir power of the tax on domestic tradable commodity i purchased by government household in region r

i = TRAD_COMM; r = REG

TGM_ir power of the tax on imported tradable commodity i purchased by government household in region r

i = TRAD_COMM; r = REG

TXS_irs power of the tax on exports of tradable commodity i from source r to destination r (levied in region r)

i = TRAD_COMM; r = s = REG

TMS_irs power of the tax on imports of tradable commodity i from source r to destination s (levied in region s)

i = TRAD_COMM; r = s = REG

TX_ir power of the variable export tax on exports of tradable commodity from region r - destination generic

i = TRAD_COMM; r = REG

TM_ir power of the variable import tax (levy) on imports of tradable commodity i in region s - source generic

i = TRAD_COMM; r = REG

TP_r region-wide shock to tax on purchases by private household in region r

r = REG

ATPM_ir actual tax on imported traded commodity i purchased by private households in region r

i = TRAD_COMM; r = REG

ATPD_ir actual tax on domestic traded commodity i purchased by private households in region r

i = TRAD_COMM; r = REG

DGTAX_ir tax on government consumption of domestic good i in region r

r = REG

IGTAX_ir tax on government consumption of imported good i in region r

r = REG

TGC_r government consumption tax payments in r

TGC_r = S_iDGTAX_ir + IGTAX_ir i = TRAD_COMM; r = REG

DPTAX_ir tax on private consumption of domestic good i in region r

DPTAX_ir = VDPA_ir - VDPM_ir i = TRAD_COMM; r = REG

IPTAX_ir tax on private consumption of imported good i in region r

IPTAX_ir = VIPA_ir - VIPM_ir i = TRAD_COMM; r = REG

TPCr private consumption tax payments in r

TPC_r = S_iDPTAX_ir + IPTAX_ir i = TRAD_COMM; r = REG

DFTAX_ijr tax on use of domestic intermediate good i by j in r

DFTAX_ijr = VDFA_ijr - VDFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG

IFTAX_ijrtax on use of imported intermediate good i by j in r

IFTAX_ijr = VIFA_ijr - VIFM_ijr i = TRAD_COMM; j = PROD_COMM; r = REG

TIU_r firms' tax payments on intermediate goods usage in r

TIU_r = S_jS_i(DFTAX_ijr + IFTAX_ijr) i = TRAD_COMM; j = PROD_COMM; r = REG

ETAX_ijr tax on use of endowment good i by industry j in region r

ETAX_ijr = VFA_ijr - VFM_ijr i = ENDW_COMM; j = PROD_COMM; r = REG

TFU_r firms' tax payments on primary factor usage in r

TFU_r = S_iS_jETAX_ijr i = ENDW_COMM; j = PROD_COMM; r = REG

PTAX_ir output tax on good i in region r

PTAX_ir = VOM_ir - VOA_ir i = NSAV_COMM; r = REG

TOUT_r production tax payments in r

TOUT_r = S_iPTAX_ir i = PROD_COMM; r = REG

XTAXD_irstax on exports of good i from source r to destination s

XTAXD_irs = VXWD_irs - VXMD_irs i = TRAD_COMM; r = s = REG

TEX_r export tax payments in r

TEXr = S_iS_sXTAXD_irs i = TRAD_COMM; r = s = REG

MTAX_irs tax on imports of good i from source r in destination s

MTAX_irs = VIMS_irs - VIWS_irs i = TRAD_COMM; r = s = REG

TIM_r import tax payments in r

TIM_r = S_iS_sMTAX_isr i = TRAD_COMM; r = s = REG

TOTTAX_r Total tax receipts in r

TOTTAX_r = TPC_r + TGC_r + TIU_r + TFU_r + TOUT_r + TEX_r + TIM_r + TINC_r r = REG

TGCR_r change in ratio of government consumption tax to INCOME in region r        r = REG

TPCR_r change in ratio of private consumption tax to INCOME in region r        r = REG

TIUR_r change in ratio of tax on intermediate usage to INCOME in region r        r = REG

TFUR_r change in ratio of tax on primary factor usage to INCOME in region r        r = REG

TOUTR_r change in ratio of output tax to INCOME in region r nbsp;      r = REG

TEXPR_r change in ratio of export tax to INCOME in region r        r = REG

TIMPR_r change in ratio of import tax to INCOME in region r        r = REG

TINC_r income tax payments in r

TINC_r = S_iPTAX_ir i = ENDOW_COMM; r = REG

TINCR_r change in ratio of income tax to INCOME in region r r = REG

DTAXR_r change in ratio of taxes to INCOME in r r = REG

Regional Household Preference Parameters and Shifters
DPARPRIV_r private consumption distribution parameter *DPARPRIV_r = UELASPRIV_rXSHRPRIV_r/UTILELAS_r** r = REG DPARGOV_r government consumption distribution parameter DPARGOV_r = XSHRGOV_r/UTILELAS_r r = REG DPARSAVE_r saving distribution parameter DPARSAVE_r = XSHRSAVE_r/UTILELAS_r r = REG DPARSUM_r sum of distribution parameters r = REG dpav_r change in average distribution parameter r = REG dpsum_r change in sum of the distribution parameters r = REG dppriv_r change in private consumption distribution parameter r = REG dpgov_r change in government consumption distribution parameter r = REG dpsave_r change in saving distribution parameter r = REG

Regional Household Preference Parameters and Shifters

DPARPRIV_r private consumption distribution parameter

DPARPRIV_r = UELASPRIV_r*XSHRPRIV_r/UTILELAS_r r = REG

DPARGOV_r government consumption distribution parameter

DPARGOV_r = XSHRGOV_r/UTILELAS_r r = REG

DPARSAVE_r saving distribution parameter

DPARSAVE_r = XSHRSAVE_r/UTILELAS_r r = REG

DPARSUM_r sum of distribution parameters        r = REG

dpav_r change in average distribution parameter        r = REG

dpsum_r change in sum of the distribution parameters        r = REG

dppriv_r change in private consumption distribution parameter        r = REG

dpgov_r change in government consumption distribution parameter        r = REG

dpsave_r change in saving distribution parameter        r = REG

Slack Variables
profitslack_jc slack variable in the ZEROPROFITS equation (this is exogenous as long as output level, QO(j), is determined endogenously) j = PROD_COMM; r = REG cgdslack_r slack variable in the CAPGOODS equation (this is exogenous as long as output level of new capital goods, QO("cgds"), is determined endogenously r = REG endwslack_ir slack variable in the MKTCLENDWM and ENDW_SUPPLY equations (this is exogenous as long as primary factor rental rates, PMi and PMESij are determined endogenously) i = ENDWS_COMM; r = REG tradslack_ir slack variable in the MKTCLTRD equation (this is exogenous as long as market price of tradable, PMi, is determined endogenously) i = TRAD_COMM; r = REG incomeslack_r slack variable in the INCOME equation (this is exogenous as long as income, Y, is determined endogenously) r = REG psaveslack_r slack variable in the SAVINGS equation (this is exogenous as long as level of savings, QSAVE, is determined endogenously) r = REG walraslack slack variable in the WALRAS equation (this is endogenous as long as price of savings, PSAVE, is determined exogenously which is the case in a standard GE closure. When any one of the GE links is broken, this is swapped with PSAVE, the numeraire price, thereby forcing global savings to equal global investment). incomeslack_r slack variable in the expression for regional income r = REG

Slack Variables

profitslack_jc slack variable in the ZEROPROFITS equation (this is exogenous as long as output level, QO(j), is determined endogenously)

j = PROD_COMM; r = REG

cgdslack_r slack variable in the CAPGOODS equation (this is exogenous as long as output level of new capital goods, QO("cgds"), is determined endogenously

r = REG

endwslack_ir slack variable in the MKTCLENDWM and ENDW_SUPPLY equations (this is exogenous as long as primary factor rental rates, PMi and PMESij are determined endogenously)

i = ENDWS_COMM; r = REG

tradslack_ir slack variable in the MKTCLTRD equation (this is exogenous as long as market price of tradable, PMi, is determined endogenously)

i = TRAD_COMM; r = REG

incomeslack_r slack variable in the INCOME equation (this is exogenous as long as income, Y, is determined endogenously)

r = REG

psaveslack_r slack variable in the SAVINGS equation (this is exogenous as long as level of savings, QSAVE, is determined endogenously)

r = REG

walraslack slack variable in the WALRAS equation (this is endogenous as long as price of savings, PSAVE, is determined exogenously which is the case in a standard GE closure. When any one of the GE links is broken, this is swapped with PSAVE, the numeraire price, thereby forcing global savings to equal global investment).

incomeslack_r slack variable in the expression for regional income r = REG

Value and Income Variables
vxwfob_ir percentage change in value of exports of tradable commodity i from source region r using fob weights (is identical to the linearized form of VXW_ir) i = TRAD_COMM; r = REG vxwreg_r percentage change in value of merchandise exports from region r using fob weights (is identical to the linearized form of VXWREGION_r) r = REG vxwcom_i percentage change in value of global merchandise exports of tradable commodity i using fob weights (is identical to the linearized form of VXWCOMMOD_i) i = TRAD_COMM viwcif_ir percentage change in value of imports of tradable commodity i into region r using fob weights (is identical to the linearized form of VIW_ir) i = TRAD_COMM; r = REG viwreg_r percentage change in value of merchandise imports into region r using cif weights (is identical to the linearized form of VIWREGION_ir) r = REG viwcom_i percentage change in value of global merchandise imports of tradable commodity i using fob weights (is identical to the linearized form of VIWCOMMOD_i) i = TRAD_COMM vxwwld percentage change in value of worlwide commodity exports using fob weights (is identical to the linearized form of VXWLD) valuew_i percentage change in value of global supply of tradable commodity i using fob weights (is identical to the linearized form of VWOW_i) i = TRAD_COMM valuewu_i value of world supply of good i at user prices i = TRAD_COMM vgdp_r percentage change in value of GDP in region r (is identical to the linearized form of GDP_r) r = REG y_r percentage change in regional household income (is identical to the linearized form of INCOME) r = REG yp_r percentage change in private household expenditure (is identical to the linearized form of PRIVEXP). r = REG FY_r primary factor income in r net of depreciation FY_r = S_iVOM_ir - VDEP_r i = ENDW_COMM; r = REG fincome_r pc change in factor income variable in r net of depreciation r = REG

Value and Income Variables

vxwfob_ir percentage change in value of exports of tradable commodity i from source region r using fob weights (is identical to the linearized form of VXW_ir)

i = TRAD_COMM; r = REG

vxwreg_r percentage change in value of merchandise exports from region r using fob weights (is identical to the linearized form of VXWREGION_r)

r = REG

vxwcom_i percentage change in value of global merchandise exports of tradable commodity i using fob weights (is identical to the linearized form of VXWCOMMOD_i)

i = TRAD_COMM

viwcif_ir percentage change in value of imports of tradable commodity i into region r using fob weights (is identical to the linearized form of VIW_ir)

i = TRAD_COMM; r = REG

viwreg_r percentage change in value of merchandise imports into region r using cif weights (is identical to the linearized form of VIWREGION_ir)

r = REG

viwcom_i percentage change in value of global merchandise imports of tradable commodity i using fob weights (is identical to the linearized form of VIWCOMMOD_i)

i = TRAD_COMM

vxwwld percentage change in value of worlwide commodity exports using fob weights (is identical to the linearized form of VXWLD)

valuew_i percentage change in value of global supply of tradable commodity i using fob weights (is identical to the linearized form of VWOW_i)

i = TRAD_COMM

valuewu_i value of world supply of good i at user prices

i = TRAD_COMM

vgdp_r percentage change in value of GDP in region r (is identical to the linearized form of GDP_r)

r = REG

y_r percentage change in regional household income (is identical to the linearized form of INCOME)

r = REG

yp_r percentage change in private household expenditure (is identical to the linearized form of PRIVEXP).

r = REG

FY_r primary factor income in r net of depreciation

FY_r = S_iVOM_ir - VDEP_r i = ENDW_COMM; r = REG

fincome_r pc change in factor income variable in r net of depreciation r = REG

Utility Variables
U_r per capita utility from aggregate household expenditure in region r r = REG UP_r per capita utility from private household expenditure in region r r = REG UG_r aggregate utility from government household expenditure in region r r = REG UTILELAS_r elasticity of cost of utility wrt utility *UTILELAS_r = (UELASPRIV_rXSHRPRIV_r + XSHRGOV_r + XSHRSAVE_r)/DPARSUM*_r r = REG* uelas_r pc change in elasticity of cost of utility wrt utility r = REG uepriv_r pc change in utility elasticity of private cons expenditure r = REG uelasev_r pc change in elasticity of cost of utility wrt utility, for EV calculation r = REG ueprivev_r pc change in utility elasticity of private cons expenditure, for EV calculation r = REG

Utility Variables

U_r per capita utility from aggregate household expenditure in region r      r = REG

UP_r per capita utility from private household expenditure in region r      r = REG

UG_r aggregate utility from government household expenditure in region r      r = REG

UTILELAS_r elasticity of cost of utility wrt utility

UTILELAS_r = (UELASPRIV_r*XSHRPRIV_r + XSHRGOV_r + XSHRSAVE_r)/DPARSUM_r r = REG

uelas_r pc change in elasticity of cost of utility wrt utility      r = REG

uepriv_r pc change in utility elasticity of private cons expenditure      r = REG

uelasev_r pc change in elasticity of cost of utility wrt utility, for EV calculation      r = REG

ueprivev_r pc change in utility elasticity of private cons expenditure, for EV calculation      r = REG

Welfare Variables
EV_r equivalent variation, in $ US million (positive figure indicates welfare improvement) r = REG WEV equivalent variation, in $ US million, for the world (positive figure indicates welfare improvement) ugev_r per capita utility from gov't expend., for EV calculation r = REG upev_r per capita utility from private expend., for EV calculation r = REG qsaveev_r total quantity of savings demanded, for EV calculation r = REG ypev_r private consumption expenditure, in region r, for EV calculation r = REG ygev_r government consumption expenditure, in region r, for EV calculation r = REG qpev_ir private household demand for commodity i in region r, for EV calculation i = TRAD_COMM, r = REG yev_r regional household income, in region r, for EV calculation ysaveev_r NET savings expenditure, for EV calculation dpavev_r average distribution parameter shift, for EV calculation r = REG

Welfare Variables

EV_r equivalent variation, in $ US million (positive figure indicates welfare improvement)      r = REG

WEV equivalent variation, in $ US million, for the world (positive figure indicates welfare improvement)

ugev_r per capita utility from gov't expend., for EV calculation      r = REG

upev_r per capita utility from private expend., for EV calculation      r = REG

qsaveev_r total quantity of savings demanded, for EV calculation      r = REG

ypev_r private consumption expenditure, in region r, for EV calculation      r = REG

ygev_r government consumption expenditure, in region r, for EV calculation      r = REG

qpev_ir private household demand for commodity i in region r, for EV calculation      i = TRAD_COMM, r = REG

yev_r regional household income, in region r, for EV calculation

ysaveev_r NET savings expenditure, for EV calculation

dpavev_r average distribution parameter shift, for EV calculation      r = REG

Trade Balance Variables
DTBAL_r change in trade balance of region r , in US$ million (positive figure indicates increases in exports exceeds increases in imports) r = REG DTBALi_ir change in trade balance for tradable commodity i in region r , in US$ million (positive figure indicates increases in exports exceeds increases in imports) i = TRAD_COMM; r = REG

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GTAP Models

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GTAP Models: Sets and Variables