Two kinds of equations
- Accounting relationship
- Behavior equations
GTAP model
Focus on government intervention and trade
Show value flow, not real flow (opposite direction)
Component of GTAP model framework
Simple example: one region closed economy
Regional household
- receive all income generated
- spent income on commodities, with C-D utility function [note how the C-D function is represented (as level / linearized form)]
Expenditure on:
- private household
- savings
- government
Constant share of regional income: expenditure share ratio = parameter in C-D function.
Firms have intermediate demand
VOAEndW: money flow to regional household. Value of output at agent price.
VDPA: money flow from household to producer, value of domestic private household purchase at agent price. CDE function (for commodity demand)
VDGA: value of domestic government purchase at agent price, Cobb-Douglas function
NETINV: investment is saving driven
Static model: investment do not affect capacity, affect total availability
Money flow from saving to producer, or "saving" purchase goods from producers
VDFA: value of domestic purchase at agent price. We assume constant return to scale. (so zero profit and can produce at any quantity)
Tax: private household, government and producer pay tax to regional household (can be interpret as "the economy")
All tax accrue to household
Income for the regional household:
Income = VOA + taxes - subsidies
Tax rate: T
PA = PM * T
agent price = market piece * Tax rate
Note: agent price refers to the agent we currently researched. Or the meaning of "agent" varies based on model setting
When sale side pays the tax (producer)
- T < 1, PA < PM: T is a tax
- T > 1, PA > PM: T is a subsidy
When purchase side pays the tax (consumer)
- T > 1, PA > PM: T is a tax
- T < 1, PA < PM: T is a subsidy
For a good, it reaches partial equilibrium when QO = Q, PS = PM (when there is no tax), so
VOM = PM* QO = PS*QO = VOA
(PS = PA here)
When there is a subsidy on output,
VOM = VOA + PTAX
VOA: Value of output at agent's price, value of output production
VOM: value of output at market price, value of consumption (including intermediate consumption and final consumption)
PTAX: Producer tax or subsidy.
My understanding:
When there is a subsidy, the supplier would supply more with the same price, so supply curve move rightward from S0 to S1.
VOM = PM1*QO1 (the Q on the right of QO, not shown on figure)
VOA = PS1*QO1
PTAX = (PM1 - PS1)*QO1 < 0, it is a "negative tax", or subsidy
So VOM = VOA + PTAX
Note: For PTAX, P refers to "producer", it is not a tax rate, but a value measurement.
Also, note PTAX here is a negative value (PS > PM) because it is a subsidy to the producer