Free Trade and Strategic Environmental Policy

Huei-Chin Lin

National Dong-Hwa University

Introduction

Eco-dumping and free trade Rent-shifting effect, e.g. Brander and Spencer

(1985) Burden-shifting effect, or pollution-shifting effect,

e.g. Markusen et al.(1992) Terms of trade effect and general equilibrium eff

ect, e.g. Krutilla (1991), Rauscher (1994) Inferior factor effect, e.g. Greaker (2003) Bertrand vs. Cournot competition, e.g. Eaton an

d Grossman (1986), Barrett (1994)

The Model

Two-stage, two-country modelGovernment sets the emission tax in the

first stageFirms choose their output level in the

second stageFirms from different countries have

different abatement/transitional cost

Notation

θi is the marginal costs of abatement.ei = e(θi ) is the emission level per unit of outp

ut, , and suppose e' < 0, e" > 0.di = d( ) denotes damages from loc

al, global, and transboundary pollution, suppose d' > 0, d" > 0, n: # of firms in each country

jjj

N

j

ji yen 1

Notation (cont.)

]1,0[ji

denotes the share of country i’s total environmental damage caused by country j’s production.

11

N

i

ji : purely rivalry case (in externality)

NN

i

ji 1

: purely non-rivalry case

2nd Stage: Industry Equilibrium

A representative firm solves

iiiiiFii

Hii

yyyetyyXpyXpMax

Fi

Hi

)()(,

Fi

Hii yyy

Fii

Hiii ynynX

where

: total production in country i,

: total consumption in country i,

First order condition:

iiii et

ypp

2

1eti

2i

i

ii

yp

k

ep

Let |e'|= k = - e'.

The second-order condition

3p'+p"y < 0

Symmetry case:

Equilibrium output:

p

ptey

)(2

Learning-By-Doing Capability

Differentiate (4) with respect to y and k yields

)3(

)(2 2

ypp

kedkd

dk

dy dkd

ke

ii ii

If dθ/dk<0, and by definition e'= - k,then dy/dk > 0.

Learning-By-Doing Capability (cont.)

k = -e '=−(∂e/∂θ) can be treated as a “learning by doing” capability, it shows the effect of the abatement spending on the reduction of emission.

Suppose the size of k is affected by transitional costs of adopting /managing/developing abatement technology. The lower the transitional costs the higher the size of k.

m = ∂k/∂θ = −e" can be treated as “marginal learning by doing capability”.

∂k/∂θ< 0, which means “learning-by-doing” effect increases with a decreasing rate when firm increases its abatement experiences.

Learning-By-Doing Capability (cont.)

Hence, higher k means a more effective learning-by-doing capability.

dy/dk > 0, i.e., higher k induces higher y. Countries with lower transitional costs of adopting new abatement technology will have higher k, and consequently, it would be able to produce more output.

Learning-By-Doing Capability (cont.)

Differentiate equation (3) with respect to θi and ti yields

e

k

e

e

etet

e

dt

d

i

i

22

2

)(1> 0

1st stage: Efficient Emission Taxes

The joint welfare function is

DYte

YetYpYpXduupW

ii

iiiiii

X

][]2)([2

0

ii

X

i dYduupW 2

0)(

1st stage: Efficient Emission Taxes (cont.)

First-order condition:

i

i

i

j

i

i

i

i

i

i

i

dtd

iiijj

iii

dt

dY

jjjj

jii

dtdY

iijj

iii

dtd

idtdY

iidtdX

eYdd

edd

edd

Yp

)(

)(

)(

2

Symmetry case

The efficient tax is

eedp

kdt

ij

ii

ij

ii

])([2

])(1[

1st stage: Nash Equilibrium Taxes

Government chooses ti to maximize

iii

X

iiii dXYpXduupWi )()(])([

0

iiiiiiiiiii

X

i dYetYetYpYpXduupWi ][])([

0

1st stage: Nash Equilibrium Taxes (cont.)

First-order condition:

0)1(

])()[())((

21

etiiiiidt

dY

jj

ij i

dtdX

iiidtdX

dtdY

i

ii

j

i

i

i

i

i

i

Ykded

pXYpp

1st stage: Nash Equilibrium Taxes (cont.)

The symmetric Nash equilibrium tax is

Compared with the efficient tax

])[(

1

jjj

ijii

iii

edpe

kdt

eedp

kdt

ij

ii

ij

ii

])([2

])(1[

Nash Equilibrium Tax vs. Efficiency Tax under the symmetric case > 0 and

t(NE) > t*

< 0 and

t(NE) < t*

])([ deep jj

iiii kdi

jii 1

])([ deep jj

iiii kdi

jii 1

Conclusion

Higher technological capability (i.e. k) on abatement induces higher equilibrium output.

when emission taxes can yield more welfare benefit from reduced pollution damages than the welfare loss of profit reduction , if the country’s additional pollution caused by home production (i.e. ) is greater/less than the cost of domestic firms’ effort on abatement innovation (i.e. ), then government will have the incentive to set a low/high emission tax rate (lower/higher than the efficient level).

ij

ii

kd1

Conclusion (cont.)

when emission taxes yield less welfare benefit from reduced pollution damages than the welfare loss of profit reduction, if the country’s additional pollution caused by home production (i.e. ) is less than the cost of domestic firms’ effort on abatement innovation (i.e. ), then government will have the incentive to set a low emission tax rate (lower than the efficient level).

ij

ii

kd1

Conclusion (cont.)

And when the country’s additional pollution caused by home production is equal to the cost of domestic firms’ effort on abatement innovation, (i.e. ) Nash equilibrium emission tax is equal to the efficient tax level.

kdij

ii 1