Price Linkage in GTAP

Review

Levels of price of value:

Multi-region model
- Price or value at world price
  - One-region model
    - Price or value at agent's price
    - Price or value at market price

output tax with level form:
TO = VOA / VOM = PS * QO / PM * QO = PS / PM

PS= PM * TO

PS: agent's price

with % change form (differential form):
to = ps - pm
ps = pm + to

Overview of value linkages

A more comprehensive figure showing GTAP value linkages:

Producer use endowment inputs, intermediate input and capital goods to produce tradable goods (VOA)
After collecting output tax, produced goods become market goods
After collecting consumption tax, market goods are consumed by producer (intermediate input), consumer, government
After collecting HTAX, revenue from endowment input become income of the economy
After taking away VDEP, economy's income are allocated to saving, private household and government
Tax happens at transaction (when goods enter or leave the market)
Note: this figure does not show where does tax revenue go.

Price linkage

Price linkage structure

PM: market price
- Producer for endowment input
  - TFE:
  - PFE:
- Producer for output
  - TO: output tax
  - PS: output price
- Prodcer for intermediate input
  - TF
  - PF
- Consumer for consumption
  - TP:
  - PP:
- Government for consumption
  - TG:
  - PG

Price linkage equations

SUPPLYPRICE: links pre- and post-tax supply price for all industries and for endowments
MPFACTPRICE: links market and firm demand price for mobile endowment commodities
SPFACTPRICE: links market and firm demand price for sluggish endowment commodities
DMNDPRICE: links market and firm demand price for tradable commodities
PHHPRICE: links market and private household demand price for tradable commodities
GHHPRICE: links market and government demand price for tradable commodities
PRICESAVE: equates price of saving to price of investment goods. Saving is the numeraire in the model, hence it is not taxed.

Change of tax revenue calculation

The change of revenue: dRevenue = d(VOM - VOA) = dVOM - dVOA = dPTAX

Recall: in Overview of the GTAP Framework
VOM = PM1*QO1
VOA = PS1*QO1
Tax revenue PTAX = (PM1 - PS1)*QO1 = VOM - VOA

Interpretation: tax revenue = tax rate (PM - PS) times quantity (QO).

So we have dRevenue is dPTAX = d(VOM - VOA) = dVOM - dVOA

Then consider dVOM:

dVOM = d(PM * QO)

= dPM * QO + PM * dQO
= pm / 100 * PM * QO + PM * qo * QO / 100

Note: it is because pm = dPM / PM * 100, or pm is PM's proportional change, in percentage form (for example, 0.25 => 25%, then pm = 25)

= PM * QO * (pm + qo) / 100
= VOM * (pm + qo) / 100

Note: this equation can be represented as
vom = dVOM / VOM * 100 = pm + qo, it is from linearized VOM = PM * QO → vom = pm + qo

Similarly, we have:
dVOA = VOA * (ps + qo) / 100

So we can drive the tax revenue change as:

dRevenue = d(VOM - VOA)

= dVOM - dVOA
= VOM * (pm + qo) / 100 - VOA * (ps + qo) / 100

If output tax rate TO changes, we have ps - pm = to

If TO does not change, change in price pm = ps; then the change of tax revenue is because of change in quantity of commodity transacted: qo

Change of income calculation

We use the equation of tax revenue change to calculate the change in income (in Regional income expression), which shows the change of total income comes from:

change in income from supplying endowment
change in income from collecting tax