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Each consumer maximizes utility, treating pollution as given. For simplicity, we assume preferences over consumption goods are homothetic and the marginal disutility of pollution is constant. The indirect utility function of a typical consumer is given by
where G is national income (so G/N is per capita income), p is a price index, u is increasing and concave, and 5 is the marginal disutility of pollution. Note that pollution is harmful to consumers and is treated as a pure public bad (all consumers experience the same level of pollution).
It is convenient to define real per capita income as



Pollution policy is determined by the government, and will vary with economic conditions. We model the policy process very simply by assuming the government sets a pollution tax, and that the level of the tax is an increasing function of the optimal tax. This allows for the possibility that government behavior varies across countries (perhaps depending on country characteristics and political systems), but also allows pollution policy to respond endogenously to changing economic conditions.
Since all consumers are identical, the optimal pollution tax maximizes the sum of utilities:
where ф = p(p)/u’, and ф: > 0 since u is concave. 5f[p,I] can be interpreted as marginal damage per person, and hence (2.13) is just the standard Samuelson rule. The pollution tax is the sum of marginal damages across all individuals and is increasing in real income because environmental quality is a normal good.
The actual pollution tax t is assumed to be an increasing function T of the optimal tax
where T’ > 0, T(t*) < t*, and we assume STt* < 1. T depends on variables (suppressed here) that reflect the responsiveness of the government to the efficient policy. If policy is always optimal, then the elasticity of T with respect to the optimal tax, ST t* = 1.
The equilibrium level of pollution can now be determined by substituting (2.14) and (2.6) into (2.3), and then using the market clearing conditions (2.7) – (2.10) to determine output levels.

Scale, technique and composition effects

Because the relationship between economic activity and environmental quality is complex, it is useful to begin by decomposing the total effect of a change in pollution into scale, composition, and technique effects. To investigate further, define the scale of economic activity S as the value of the economy’s gross output at world prices: