Definition
Start from value term
This equation shows the total value of good i equals to the sum of its demand in all sector j, for private household, and for government.
It represents the demand of the same good for multiple purposes.
Since the market price is the same (all are 
), cancelling prices and we have the equation for quantity:
Equation above: from the regular mathematical format of GE closure (level, not percentage change)
Use total differentiation to starting converting level equation to percentage equation
Multiple quantity, divide quantities and multiply 100% for each component:
Note 
is the percentage change of QOi, or 
, so:
Multiply market price:
This is the linearization of market clearing condition.
Or, divide both side with 
:
SHR means value share.