II-D
II. General equilibrium
approaches—theory
A. Ana lytical tools : produce rs, consumers, markets and trade
B. Geo metric models of trade and env ironment
- What are we measuring? Environmental and welfare outcomes
C. Comparative static result s and standa rd theo rems
D. Simpl e models of trade and environmental policy
(OEE Ch. 2.3 – 2.4)
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II-D
Trade and environment policies
• Analytically, we want to be able to identify
socially optimal policies in economies with
environmental problems
• The following model does so for an
economy with initial distortions due to trade
policy and pollution
• What are the optimal trade and
environmental policies in such an economy?
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II-D
-- Ima gin e a small open econo my in which n goods are produced using m
factors.
-- Produc tion of each good also gene rates poll ution or an ana logous bad. -- Vectors p, q, c, y and z, each of leng th n, deno te world and domestic
prices, consu mption o f marketed comm oditi es, domestic supply, and
poll ution respectively.
-- Factor endow ments are given by a vec tor v, with leng th m.
-- World prices are determi ned outside the model by the small coun try
assumption, and do me stic prices are related to them by q = p + t, whe re t
is a vec tor of tariffs or expo rt taxes.
-- Firms are also sub ject to poll ution taxe s at rates given by the n-vec tor s.
-- Choo se the first good to be numéraire, so
p = (1, p2, …, pn) and q = (1+t1, p2+t2, …, pn+tn).
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II-D
-- A representative con sumer ha s a utili ty func tion u(c, z), wit h uc > 0 and
uz < 0; by assumption, this func tion is strictly qua siconcave in c.
-- Agg rega te expend it ure is deno ted by the cond iti ona l expend it ure
func tion e(q, z,u)  minq' c | u, whe re a prim e denotes the transpo se of a
vec tor.
-- The expend it ure func tion is non-de creasing and concave in q, and nondecreasing in z and u.
-- Partial derivatives of the expend it ure func tion w it h respect to the i’th
price give commodit y de ma nds by con sumers. Thus the v ector c of
domestic consumer demand s ha s ele ments
ci  e(q, z,u) qi  0 .
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II-D
-- Agg rega te income is given by a revenue or GN P func tion
g(q,s,v)  maxq' y  s'z | v.
-- Partial derivatives of this func tion wit h respect to prices give domestic
output suppli es y, a vec tor wit h elements yi  g(q, s,v) qi  0 .
-- Derivatives wit h respect to env ironmental taxe s give the qu antiti es of
poll ution e mitt ed, i.e. zi   g(q, s,v) si  0 .
-- The revenue fun ction is convex in (q, s) and concav e in v.
-- Net imports, m, are the excess of domestic dema nds over supp li es, or
for sector i, mi = ci – yi; by definition, mi < 0 if a good is a net expo rt.
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II-D
Assume that tariff and tax revenues a re rebated to consu mers in lump-sum
form. Equili brium i s described by the agg rega te budge t constraint (2.1),
the market-clearing cond it ion for net imports (2.2), and the production of
poll ution (2.3):
e(q, z,u)  g(q,s,v)  s'z  t' m
(2.1)
m  eq (q, z,u)  gq (q,s,v)
(2.2)
z  gs
(2.3)
These equa tions can be so lved as a system f or the three endogenou s
variables: agg rega te welf are, ne t imports, and the quan tit y of pollution
produced .
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II-D
First-best policies address distortions at source
-- The welf are effect of small change s in tariff s and poll ution taxes is
obtained by totall y d iff erentiating (2.1), assumi ng wo rld prices to be fixed
so that dq = dt. Th is yields:
eudu = – (ez– s)'dz + t'dm,
(2.4)
whe re eu is the inve rse of the marginal utilit y of inco me, so the left-hand
side of (2.4) is a mon ey metric of welfare change .
-- Interpretation o f (2.4): t he fir st-best strategy for a socia l planne r is to set
env ir onmental taxes equa l to marginal da mage s, i.e. s = ez, and to pursue
free trade, i. e. t = 0.
-- Any o ther policy must be associated with lower welfare
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II-D
Second-best solutions depend on c hoosing the appropriate policy mix
-- Solve the model in terms of poli cy instruments. Fir st find the change in
poll ution by total differentiation o f (2.3):
dz = – (gsqdt + gssds),
(2.5)
and , from ( 2.2), find the change in net imports:
dm = Hqqdt + eqzdz + equdu – gqsds,
(2.6)
whe re Hqq = (eqq – gqq), is positi ve semidefinit e.
-- Combining (2.5) and (2.6) in (2.4) yields an exp ression for welf are
chang e in terms only o f change s in the poli cy instrume nts t and s:
eudu   zg sq  t' H qq dt   z g ss  t'gqs ds ,
(2.7)
whe re  = (1 – t'm) > 0 is the tariff m ulti pli er, and z = (es' – t'eqz – s')
captures the exce ss of po ll ution costs over env ironme ntal tax revenues .
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II-D
Understandin g economic and environmental policy choices from (2 .7)
eudu   zg sq  t' H qq dt   z g ss  t'gqs ds ,
(2.7)
whe re  > 0 is the tariff multi pli er, and z = (es' – t'eqz – s') captures the
exc ess of poll ution co sts ove r env ir onmental tax revenue s.
1. Poli cies interact. For example, the welfare cost of a tariff ha s a direct
effect through mis all ocation o f consu mer exp enditures and p roduc tive
resources, and an indir ect effect through incen tives to poll ute.
2. No sing le poli cy change must increase welfare. E.g. l et ds = 0, dt > 0.
Welf are ma y rise or fall , depend ing on whe ther the tariff protects clean or
dir ty indus tries (compositi on e ffects).
3. A positive tarif f on clean sectors may b e optim al (trade polic y a s
env ir onmental poli cy).
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II-D
Insights -- summary
1. In general equilibrium, there are both direct and
indirect effects to be accounted for.
2. Trade and environmental policies may interact.
•
A tariff has direct welfare effects, and indirect effects
through pollution.
3. No single policy change will necessarily
improve welfare.
•
•
(Theory of the second best)
Thus trade restrictions may serve as instruments of
environmental policy.
4. Free trade is not the same as laisser-faire.
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II-D
Some complications…
• Distribution of income: what if pollution taxes
have greatest impact on the poorest?
• Non-traded goods and endogenous factor supplies
• There may be env. irreversibilities.
• Property rights/open access to natural resources, or
free disposal of pollutants.
• Spatial variation may be important.
* More detailed models are more complex!
– Preceding results form a ‘benchmark’ when models
cannot easily be solved for analytical results.
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II-D
GE insights for environmental
analysis
• In open economies, factor and product markets
link all sectors.
– Indirect as well as direct effects of policies, price
shocks, etc., must be measured.
• When people derive utility from the environment,
‘true’ welfare is hard to measure.
– Most people are willing to accept some degree of
environmental damage in return for economic growth.
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