Definition
The equation gives the change of income = change of each component that forms income.
d Income = d (factor revenue) + d (tax revenue)
INCOME * y
= sum{i,ENDW_COMM, VOA(i) * [ps(i) + qo(i)]}
- VDEP * [pcgds + kb]
+ sum{i,NSAV_COMM, VOM(i) * [pm(i) + qo(i)]
- VOA(i) * [ps(i) + qo(i)]}
+ sum{j,PROD_COMM, sum{i,ENDWM_COMM, VFA(i,j) * [pfe(i,j) + qfe(i,j)]
- VFM(i,j) * [pm(i) + qfe(i,j)]}}
+ sum{j,PROD_COMM, sum{i,ENDWS_COMM, VFA(i,j) * [pfe(i,j) + qfe(i,j)]
- VFM(i,j) * [pmes(i,j) + qfe(i,j)]}}
+ sum{j,PROD_COMM, sum{i,TRAD_COMM, VFA(i,j) * [pf(i,j) + qf(i,j)]
- VFM(i,j) * [pm(i) + qf(i,j)]}}
+ sum{i,TRAD_COMM, VPA(i) * [pp(i) + qp(i)] - VPM(i) * [pm(i) + qp(i)]}+ sum{i,TRAD_COMM, VGA(i) * [pg(i) + qg(i)] - VGM(i) * [pm(i) + qg(i)]}
+ INCOME * incomeslack ;
Note:
- INCOME * y is actually dINCOME. This is because y = dIINCOME / INCOME * 100. Since there are 100 on both sides of the long equation, they are cancelled out.
- In the first part, VOA(i) * [ps(i) + qo(i)]} is the change of income from supplying endowment factors to producers (supplier) as input
- d VOA = d(PS*QO) = dPS * QO + PS * dQO = PS * ps * QO + PS * qo * QO = PS * QO (ps + qo) = VOA (ps + qo)
- Highlighted parts refers to the change of revenue from tax revenue change (see price linkage) over all sectors
Note
Recall definition of sets used in GTAP.