A political economy of tax havens
Appendix 3.5: Worker's lobbying
4.2. The model
國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
45
has a similar economic logic as that in Coase (1960), in which the way to assign the property right only affects the wealth distribution but not the efficiency.
Our analysis also deals with the issue of the pollution spillover effect. While majority of the literature assumes fully transboundary pollution (i.e., pollutants cause the same damage in all other countries as well as the country that generates them), it is obvious that the damage of most kind of pollutants will diminish over distance (see, for example, Brooks and Sethi, 1997; Pesic et al., 2011). The magnitude of pollution spillover is relevant in trading decision-making because it captures the environmental costs of the permits that traded to the other country. Indeed, we release the assumption of fully transboundary pollution, and find that a lower spillover effect of transboundary pollution induces a higher after-trade emission level in both trading schemes. This result thus points out that the pollutant type of tradable permits could also influence the after-trade outcomes.
The rest of the chapter is organized as follows. In Section 4.2 we describe the model and compare the two different trading schemes. In Section 4.3 we compare the emission levels under different schemes and examine the effect of pollution spillover on the level of after-trade emissions. In Section 4.4 we demonstrate that the Nash-bargaining trading scheme is efficient, regardless of the bargaining power of each country. In Section 4.5 we reexamine our findings under a nonlinear damage function. The last section concludes the chapter.
4.2. The model
We consider an economy consisting of two countries labeled A and B. Each country contains one firm which generates polluting emissions ei, iA,B. Benefits of emissions, F ei( )i , satisfy the properties that F e( )0 and F e ( ) 0. We also assume that the two countries have the same benefit function, that is
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
46
( ) ( ) ( )
A B
F e F e F e . For analytical tractability, we consider a linear damage function of pollution.25 Let di denote the marginal damage of pollution in country i so that the total damage of pollution in country i is di(ei ei) , where ei is the emission generating in the neighboring country. Without loss of generality we assume
A B
d d . The parameter [0,1] describes the nature of transboundary pollution. A higher represents a higher spillover pollution effect. 0 represents the case of
"no transboundary pollution" and 1 represents the case of "fully transboundary pollution".
Without trading, each country maximizes its own welfare W with respect to the domestic emissions:
max ( ) ( )
i
i i i i i
e W F e d e e , (4.1)
The first-order condition of welfare maximization is:
( )i i
F e d . (4.2)
The above equation determines the emission level without trading, which is denoted by eic with the superscript c representing the closed economy.
Now we deal with the scenario with emission allowance trading. The timing of a trading scheme is as follows. In the first stage, two countries choose (or bargain to determine) the tradable emission allowances, denoted by i, iA,B. In the second stage, the firm in each country trades allowances in the international permit market and this pins down the equilibrium price for permits, denoted by p , which determines the after-trade level of emission.
We solve the model by backwards induction. In the second stage, given the permit price and each country's initial endowment, the firm in country i chooses emissions so as to
25 A similar specification could be found in, for example, Tahvonen (1994), Kennedy (1999) and Lai and Hu (2005). We will consider a nonlinear damage function of pollution in Section 4.5.
‧
The equilibrium conditions of profit maximization and market clearing are:
( )i 0
We see in (4.4) that because both countries face the same benefit function and permit price, the firm in each country will choose the same after-trade emission level, i.e.
A B
e e e. Moreover, as the permit price rises, emissions in both countries decline ( e/ p 1/F0). (4.5) is the market-clearing condition.
By differentiating (4.5) with i, we can obtain the effects of raising the tradable allowances on the equilibrium permit price and emissions, which are:
2 0,
From (4.7) we can see that if a country increases 1 unit of emission allowance, through the trade in the market, the allowance will be shared between both countries and thus only increase half unit of final emission in the host country. We now deal with the first stage of the trading scheme. Two possible schemes are considered in this chapter. The first is the non-cooperative trading scheme, and the second is the bargaining trade scheme. In what follows we treat them in turn.
4.2.1. Non-cooperative trading scheme
Under the non-cooperative trading scheme, each country chooses the tradable allowances independently to maximize its own social welfare. The objective function of country i is:
‧
By utilizing (4.4) and (4.7), the first-order condition for the problem can be written as:
( ) (1 ) 0
By summing (4.9) for both countries, we can obtain the equilibrium price for permits under the non-cooperative trading scheme:
(1 )( )
4
n dA dB
p
, (4.10)
where the superscript n denotes the non-cooperative trading scheme. Next, inserting (4.10) into (4.9) gives:
Thus we have the following result:
Proposition 4.1. Under the non-cooperative trading scheme, the low-damage country is a permit seller and the high-damage country is a permit-buyer.
Proposition 4.1 is consistent with the findings in Helm (2003). The intuition is quite straightforward. By purchasing the emission permit, the high-damage country can enjoy the benefit of emission with the cost of market price which is lower than the domestically high damage of pollution. On the other hand, the low-damage country can also take advantage of its low marginal damage of pollution by selling the emission permit.
4.2.2. Nash-bargaining trading scheme
In the bargaining scheme, countries do not choose allowances separately. Instead, they jointly determine their permit allowances via a Nash bargaining process. If two
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
49
countries fail to reach an agreement, then each one obtains a utility of i, iA B, , which are termed as the disagreement point or the breakdown of cooperation. In this chapter we treat i as exogenous. We also assume there exist a mutually beneficial agreement. That is, there exists an allocation of allowances such that Ui ( )i i,
, iA B.
Let denote the share of the welfare of country A in negotiation (so the remaining fraction 1 goes to the welfare of country B). The parameter can also be thought of as an indicator of country A’s bargaining power. Accordingly, two countries desire to maximize the joint welfare to determine the tradable permit allowances:
1
{max, } ( ) ( )
A B
A A B B
U U
. (4.13)
An interesting issue here is to examine whether the high-damage country is still the permit buyer under a Nash-bargaining trading scheme. To see this, let us consider a polar case where the high-damage country has all the bargaining power ( 1) and can dominate in the bargaining process. This case can be thought of as the case in which country A alone chooses A and B to maximize its own social welfare.
We show in the Appendix 4.1 that the equilibrium allowances would be A 0 and
B 0
, which turns the high-damage country A a permit seller. This result shall be of little surprise because if one country has every power to determine the allowances, there is no reason it should assign any to the counterparty. We establish the following proposition.
Proposition 4.2. Under the Nash-bargaining trading scheme, the high-damage country may be a permit seller if its bargaining power is sufficiently large.
‧
conditions for the maximization of the social welfare:1 1
Suppose that both countries have a positive bargaining power ((0,1)), from (4.14) and (4.15) we can obtain the equilibrium permit price
(1 )( )
2
b dA dB
p (4.16)
where the superscript b denotes the Nash-bargaining trading scheme.