1. Environmental Taxes and Wage Setting Structure
Juan Carlos Bárcena-Ruiz, María Begoña Garzón
Universidad del País Vasco

2. Introduction
The link between environmental regulation, the labor market and international trade is widely acknowledged.
Although the number of papers analyzing this issue is growing there is still much work to do.
One issue that remains to be studied is whether environmental regulations set by governments under free trade are affected by the way in which workers are organized for wage bargaining.
This is an important issue since the organizational structure of both domestic and foreign workers affects production costs and, thus, the market share of firms → it affects the environmental pollution caused by firms and the environmental taxes set by governments.
Governments should take into account the way in which workers are organized for wage bargaining when setting their environmental taxes.

3. The literature on wage bargaining has focused mainly on two structures:
1. Each firm negotiates with an independent union at firm level (decentralization).
2. Each firm bargains with an industry-wide union (centralization).
This literature does not take into account that firms pollute the environment.
On the other hand, the literature on the environment does not consider that workers can adopt different organizational structures to set wages.
We analyze in this paper the choice of environmental taxes by governments when there is a unionized labor force in each country which can set up a centralized or a decentralized organizational structure to set wages.

4. The model Single market comprising two countries: A, B.
In each country there are two firms: 1, 2; homogeneous product.
The world inverse demand function for the product is linear.
The only factor used in the production process is labor. Firm ki hires Lki workers with a uniform wage rate wki.
The technology used by the firms exhibits constant returns to scale: qki= Lki.
Monopoly-union model: the unions set the wage while the firms choose the employment level once the wage is set by unions.
Organizational structures to set wages:
Centralized wage setting: there is an industry-wide union that sets the wages of both firms. The utility function of the industry-wide union in country k is: Uk(wk1, wk2, Lk1, Lk2) = wk1Lk1+wk2Lk2.
Decentralized wage setting: there is an independent union at each firm. The utility function of the union at firm ki is: Uki (wki, Lki) = wki Lki.

5. There is a pollutant associated with the production of the good
There is a pollutant associated with the production of the good. Each unit of the good produced causes one unit of pollution.
Producers have technology available for abating this pollutant. If firm ki chooses output level qki and pollution abatement level aki, pollutant emissions by this firm are: qki – aki.
The total cost of pollution abatement at firm ki is: CAki = aki2/2.
To abate an additional unit of emissions has a bigger cost than that of the preceding unit abated.
Each government has the environmental tax per unit of pollutant emitted, tk, as a decision variable.
The profit of firm ki is: pki = p qki – wkiLki – tk (qki – aki) – aki2/2

6. Parameter g measures the valuation of the environment by government k.
Total taxes collected by each government: Tk = tk(qk1–ak1+qk2–ak2).
The producer surplus in country k, is: PSk = pk1+pk2.
Local environmental damage: the emission of pollutant by firm ki affects only the country in which the firm is located.
Quadratic functional form to measure the environmental damage generated in country k by the production process: EDk = g (qk1–ak1+qk2–ak2)2/2
An additional unit of emissions generates more damage than the previous one.
Parameter g measures the valuation of the environment by government k.
Social welfare considered by government k :
Wk = CSk + PSk + Tk + Uk – EDk .

7. Given that there are two countries and that workers can be organized in independent unions at firm level or in an industry-wide union in each country, there are three cases :
decentralized wage setting in both countries (denoted by DD),
centralized wage setting in both countries (denoted by CC),
centralized wage setting in one country and decentralized in the other (denoted by CD and DC, respectively).
We propose a three stage game with the following timing:
1st stage: the governments set their environmental taxes.
2nd stage: unions set wages in the two countries.
3rd stage: firms choose their output and pollution abatement levels.
We solve the game by backward induction from the last stage of the game to obtain a subgame Perfect Nash Equilibrium.

8. qki = Lki = (a – 3tk + 2tl – 4wki + wkj + wli + wlj),
Results
Third stage of the game: qki, aki / max pki
Solving the first order conditions for profit maximization we obtain the equilibrium output, employment and abatement levels of the firms, as a function of environmental taxes and wage rates:
qki = Lki = (a – 3tk + 2tl – 4wki + wkj + wli + wlj),
aki = tk .
The result of this stage of the game is identical independently of the wage setting structure considered.

9. Second stage of the game: w / max U. There are three cases:
Decentralized wage setting in both countries (DD)
Independent union at each firm in the two countries. The union at firm ki sets the wage wki / max Uki. Solving: wki=(9 a – 17tk + 8tl)/45.
Centralized wage setting in the two countries (CC)
There is in an industry-wide union in each country. Union k sets wages wk1 and wk2 that maximize union rents, Uk. Solving: wki=(4 a – 7tk + 3tl)/16.
Centralized wage setting in country k and decentralized in country l (CD)
Union k sets wages wk1 and wk2 that maximize union rents, Uk. Union li sets wage wli that maximizes union rents, Uli. Solving: wki=(9 a – 17tk + 8tl)/38, wli=(4 a – 7tl+ 3tk)/19.
First stage: t / max W. Solving this problem in the three cases considered above we obtain the equilibrium output, profits, taxes and abatement levels and welfare.

10. Next we compare the results obtained in the different cases.
Wages: wCC> wCD> wDC> wDD (domestic country, foreign country)
Although the environmental tax set by government k affects wages, the wage paid in country k depends mainly on the organizational structure adopted by workers → is greater under centralization than under decentralization, independently of the structure set by workers in the other country since, in the first case, the workers internalize the effect that the wage set in one firm has on the incomes of the workers of the other firm.
Output/Employment: qDC= LDC> qDD= LDD> qCC= LCC> qCD= LCD
Although the tax set by government k reduces the output/employment of the domestic firms, the output/employment of the firms depends mainly on the wage setting structure (wCC>wCD>wDC>wDD). The production/employment is greater under centralization than under decentralization since wages are lower in the first case.

11. (domestic country, foreign country)
Consumer Surplus: CSDD> CSDC= CSCD> CSCC
As the CS increases with the output of industry, the highest (lowest) CS is obtained when bargaining is decentralized (centralized) in both countries. The intermediate CS is obtained when bargaining is centralized in one country and decentralized in the other.
Unions’ Utility: UCC> max{UCD, UDC} >UDD
As usual in these models, the wage has a greater effect than the employment on the utility of unions  the highest (lowest) unions utility is obtained when bargaining is centralized (decentralized) in both countries. Intermediate unions utility levels are obtained when bargaining is centralized in one country and decentralized in the other.
Firms’ profits: pDC>pDD > pCC >pCD
The wages paid by the firms determine their market shares and profits.
Producer Surplus: PSDC>PSDD > PSCC >PSCD
This result is explained by the fact that: PSmn=2pmn.

12. In order to analyze how the organizational structure of workers affects environmental taxes, environmental damage and social welfare, for a given wage setting structure, we distinguish two strategic effects:
The rent capture effect (R.C.E.) encourages each government to reduce its tax to give domestic firms a competitive advantage over foreign firms. This reduction in the domestic tax raises exports of domestic firms and so permits the capture of rents from foreigners.
The pollution-shifting effect (P-S.E.) works in the opposite direction. Each government has the incentive to increase the tax to transfer production and its associated pollution to the other country.
For a given wage setting structure the R.C.E. is stronger than the P-S.E.  taxes are lower than is socially efficient.

13. When the workers can set up different organizational structures, an additional effect arises that influences the other two effects.
Decentralization weakens the R.C.E. compared with centralization.
Under decentralization the wage is lower and therefore domestic firms produce more than under centralization  the decentralized structure reduces the government’s incentive to decrease the tax to capture rents from abroad.
Decentralization reinforces the P-S.E. compared with centralization.
Under decentralization more production and pollution is transferred to the country than under centralization  the decentralized structure provides more incentives for each government to increase taxes and transfer pollution to the other country than the centralized structure.

14. (domestic country, foreign country)
Taxes: tDC > tDD > tCC > tCD
Decentralization weakens the R.C.E. and reinforces the P-S.E. compared with centralization. Besides, the R.C.E. has a greater effect on taxes than the P-S.E. → taxes are greater under decentralization than under centralization.
Total taxes collected by governments: TDC > TDD > TCC > TCD
Under decentralization there are greater production (and emissions) and taxes than under centralization → the total taxes collected by the governments are also greater.
Environmental Damage: EDDC> EDDD> EDCC> EDCD
ED in one country depends positively on the pollution emitted by the firms and that the emissions level is greater under a decentralized structure than under a centralized one → ED is greater in the first case.
For a given wage setting structure in one country, the damage in that country is greater if there is a centralized structure rather than a decentralized one in the other country because the centralized structure gives a strategic disadvantage to the firms located in the other country.

15. Comparing the different components of the social welfare funcion:
Social Welfare: WDC> WDD> WCC> WCD (domestic country, foreign country)
The environmental tax in a country is greater under a decentralized structure than under a centralized one (tDC>tDD>tCC>tCD) → the tax is nearer to socially efficient levels in the former case → in that country social welfare is greater under a decentralized structure than under a centralized one.
Comparing the different components of the social welfare funcion:
CSDD> CSDC= CSCD> CSCC
PSDC>PSDD > PSCC >PSCD
TDC > TDD > TCC > TCD
UCC> max{UCD, UDC} >UDD
EDDC> EDDD> EDCC> EDCD
the greater CS, PS and T obtained under a decentralized structure has a greater effect on social welfare than the lower U and greater ED.
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