## Sabtu, 10 Januari 2009

### Structure of Global Trade Analysis Project

Behavioral Equations

1. FIRM BEHAVIOR
This explanation about firm behavior will be derived from the technology tree. This kind of production structure is a convenient way of representing separable, constant return-to-scale technologies.

ava(j,s) qva(js
qf(i,j,s) af(i,j,s)
Land Labor Capital
qfe(i,j,s) afe (i,j,s)

Domestic Foreign
qfd(i,j,s) qfm(I,j,s)
qxs(i,r,s)
Leontief
CES
CES
CES

the primary factors of production are Labor,Capital, however in agriculture a third input, land enters the production factors. Their quantities are denoted as QFE(i,j,s) or in thr percentage change form qfe(i,j,s). Firm will purchase also intermediate goods which is supplied domestically qfd(i,j,s) and some are imported. Qfm(i,j,s). In case of imports, those will be sourced from particular exporters qxs(i,r,s). The manner in which the firm combines individual inputs to produce its output, QO(i,s) depends largely on the assumption of separability in production (i.e. assume that the firms choose their optimal mix of primary factors independently of the prices of intermediate input). By this type of separability, a restriction will be imposed that elasticity substitution (ES) between those primary factors on the one hand and and intermediate inputs on the other hand is equal.

Behavioral equation:
Composite Import Nest
pim(i,s)=∑MSHRS(i,k,s)*pms(i,k,s)
while
qxs=(i,r,s) =qim(i,s)-σM(i)*[pms(i,r,s)-pim(i,s)]

MSHRS (i,k,s) is the share of import of i from region k to region s
pim(i,s) is price of composite imports for i in region s
pms is individual market price.

Behavioral equation for Producers
Composite Intermediate Nest
Pf(i,j,r)=FMSHR(i,j,r)*pfm(i,j,r)+[1-FMSHR(i,j,r)]*pfd(i,j,r)
qfm(i,j,s)=qf(i,j,s)-σD(i)*[pfm(i,j,s)-pf(i,j,s)]
qfd(i,j,s)=qf(i,j,s)-σD(i)*[pfd(i,j,s)-pf(i,j,s)

FMSHR (i,j,r) is the share of import in firms for tradable commodities (i) in sector j in region r.

Pva(j,r)=∑SVA(k,j,r)*[pfe(k,j,r)-afe(k,j,r)]
qfe(i,j,r)+afe(i,j,r)=qva(j,r)-σVA(j)*[pfe(i,j,r)-afe(i,j,r)-pva(j,r)

pva is price of composite value added
qfe is conditional demands for endowment commodities
SVA is the share of endowment commodities (i) in sector j in region r
pfe is price variable
afe(i,j,r) is the rate of primary factor-augmenting technical change.

Total Output Nest:
qva(j,r)+ava(j,r)=qo(j,r)-ao(j,r)
af(i,j,r)+af(i,j,r)=qo(j,r)-ao(j,r)

Zero Profit:
VOA(j,r)*[ps(j,r)+ao(j,r)]= ∑VFA(i,j,r)*[pfe(i,j,r)-afe(i,j,r)-ava(j,r)]+∑VFA(i,j,r)*[pf(i,j,r)-af(i,j,r)+VOA(j,r)*profitslack(j,r)

While
The way to obtain CES-derived demand equation. Consider the CES is defined as the percentage change in the ratio of the two cost minimizing demand :
σ= (Q1/Q2)/(P1/P2)

expressing equation in a percentage change form :
(q1-q2)=σ(p1-p2) (equation 1)

use the fact that firms’pay factors their marginal value product, will give relationship between inputs and outputs:
q=θ1q1+(1-θ1)q1
θ is the cost share of input1 while (1-θ1) is the cost share of input 2, then
q2=(q-θ1q1)/(1-θ1)

which may substitute to equation 1 to yield :
q1=σ(p2-p1)+[q-θ1q1]/(1-θ1)

simplified to yield :
q1=(1-θ1)σ(p2-p1)+q (equation 2)

the percentage change in composite price
p=θ1p1+(1-θ1)p2
solving for p2 as a function of p1 and p then substituting this to equation 2 to obtain

q1=(1-θ1)σ{[p-θ1p1]/(1-θ1)-p1}+q

then simplified to get derived demand equation for the first input in this CES composite

q1=σ (p-p1)+q

2. HOUSEHOLD BEHAVIOUR
Regional household behavior is governed by an aggregate of utility function
over composite private consumption, composite government purchases,and saving. The behavioral equations for regional household are provided below: .

Aggregate utility:
INCOME(r)*u (r) = PRIVEXP*up(r)+GOVEXP(r)*[ug(r)-pop(r)]+SAVE(r)*[qsave(r)-pop(r)]

qsave is quantity of saving
ug is government’s composite

Regional saving:
qsave(r)=y(r)-psave+saveslack (r)

Government purchases:
ug(r)=y(r)-pgov(r)+govslack(r)

Demand for composite goods:
pgov(r)=∑VGA(i,r)/GOVEXP(r)*pg(i,r)
qg(i,r)=ug(r)-[pg(i,r)-pgov(r)
pgov is an aggregate price index of all government purchases
qg is demand for composite goods

pg(i,s)=GMSHR(i,s)*pgm(i,s)+[1-GMSHR (i,s)*pgd(i,s)

3. GLOBAL TRANSPORTATION
Global activities such as Internasional transport services are needed to be required in GTAP model in order to intermediate between supply and demand. To simplified just combine these services into a single composite international transport good, the value of which is :
VT=QT*PT

QT is the amount of homogenous product
Equilibrium in the global transport services market requires:

QT=∑ ∑ ∑ QTS(i,r,s)