A3 Wealth Differentials
A3.1 The Neutrality Result
Pollution due to growth may harm the environment. Thus, abatement activities are important in order to attain welfare-enhancing growth. A natural conjecture is that growth normally enhances welfare, especially for the poor agent since she or he significantly evaluates growth. As already suggested, some economists, many of whom are associated with international organizations, advocate an international lump sum income transfer to developing countries in order to help them stimulate pollution abatement activities that improve the global environment.
However, as implied by the neutrality theorem of public goods (see Sect. 6 of the main text of this chapter), the effect of lump sum inter-agent income transfers on aggregate emissions is zero at best when optimizing abatement behavior is determined as an interior solution. This is because a reallocation of the agents’ aggregate income has a neutral effect in determining the Nash equilibrium pollution level when all countries are rich enough to emit the equilibrium level of pollution. If we assume that all agents attain their respective internal solutions at the Nash equilibrium and, consequently, the set of contributors to the abatement activities is fixed, wealth differentials with the same aggregate wealth do not matter at all. This is a well-known neutrality theorem, as explained in Sect. 6 of this chapter.
Some countries with a small amount of wealth, though, choose not to contribute to the abatement because the Nash equilibrium quantity of pollutants remaining in the environment achieved by others (a_) is larger than their individually desirable level of total abatement (A), particularly with regard to poor agents. Such agents do not contribute to the abatement at all since the marginal utility of private consumption is strictly greater than the marginal utility of abatement in terms of consumption. In such an instance, changes in wealth differentials due to economic growth or redistribution have real effects; namely, a plausible conjecture is that a transfer from the rich to the poor is desirable since the poor significantly evaluate an increase in income. However, we now show that this conjecture is not necessarily valid.
Suppose the world consists of two types of n +1 country: n identical poor countries 1, 2, ..., n, and one rich country n+1. Thus,
w1 = ... = wn = wL < wn+1 = wH. Subscripts L and H denote the poor and rich respectively. Country L does not abate at the corner solution: aL = 0. Suppose income is redistributed from country H to country L, so that wH declines and wL rises but total income nwL + wH does not change. Since the redistribution occurs after production activities are over, the initial pollutant Z does not change either.
Because the income of country H, wH, decreases from the income effect, yH and A decrease; hence, UH and aH also decrease. After receiving an income transfer, if country L still faces the corner solution, an increase in wL results in the same increase in yL without raising aL. From this direct effect of redistribution, UL increases. Thus, a decrease in wealth differentials normally benefits the poor country and harms the rich country. At the same time, a decrease in aH means a deterioration of environmental quality, A; namely, overall environmental quality deteriorates. This harms country L to some extent. If the abatement activity of country H is very efficient or the number of poor countries (n) is large, the negative spillovers of a reduction of country H’s abatement are large; thus, the poor country could also lose.