Input versus emission taxes: environmental taxes in a mass balance and transaction costs perspective.

I. INTRODUCTION

Economists have traditionally argued for taxes or tradeable permits as superior to other pollution control instruments because they lead to an efficient allocation of control responsibility. For the past decades, most developments in the theory have focused on expanding this insight to real world applications where the ideal preconditions underpinning the standard model do not hold. Most attention has been paid to the assumptions concerning the economy, that is, the economic agents and/or the economic system in which these agents operate.(1) Less concern is normally paid to the characteristics of the physical world in which the operations take place.

There is a tendency among economists to describe the economy as distinctly demarcated from the physical world surrounding it and to largely disregard processes linking inputs and outputs across the analytically constructed boundaries. This is confirmed by the division between resource and environmental economics, concerned with problems related to inputs and "outputs," respectively. More specifically, resource economics focuses on questions related to the optimal paths of resource extraction, while environmental economics highlights the regulation of emissions considered to be by-products of production or consumption.(2)

Environmental economics may gain from a stronger focus on the interface between the economy and the biophysical systems it interacts with, recognizing that the economy is an open and integrated part of the biosphere (Folke 1991; Perrings 1987; Ruth 1993). As such, the economy must follow the law of conservation of mass. Further, while most matter will enter the economy at rather few and fairly easily demarcated points, it will tend to be degraded or lost to the environment continuously throughout all production and consumption processes. Inputs and emissions are thus related. Since it must be more costly to undertake regulation on dispersed emissions rather than well-demarcated inputs into the economy, it may be that an input-oriented environmental regime - at least under an important set of circumstances - is more efficient than an emission-oriented one. The aim of this paper is to explore this intuition.

Understanding emissions as more or less accidental by-products of production supports implicitly a piecemeal strategy. As was emphasized long ago by Solow (1971), such a strategy increases the danger of just moving the pollution problem from one medium to another, from an observed to an as-yet-unobserved point in space or time.

The analysis performed here is undertaken on the basis of the standard economic model for internalizing externalities. It is reorganized to explicitly take account of the flow of matter through the economy. The concept of transaction costs is introduced into the model, accounting for important relationships among matter dispersion, losses to the environment, and the costs of internalizing the externalities thereof. Characteristics of the material dispersion process highly influence the efficiency of different policy instruments, and the standard conclusion favoring taxes/tradeable quotas on final emissions seems efficient only for a subset of real-world problems. This leads to a discussion of the efficiency of different measures in cases with different material flow characteristics. The paper closes with a comparison of input taxes to output taxes or a deposit/refund system, other proposed alternatives to emission taxes.

II. THE STANDARD EXTERNALITY MODEL

Let us start by looking at the properties of the standard Pigovian model for analyzing Pareto-optimal strategies in cases with externalities. This model has been formalized and thoroughly discussed by several authors, with Baumol and Oates (1975/1988) as the standard exposition. They formulate a model where the utility for one consumer is maximized under the constraint that all other consumers are left no worse off:

Model I:

Max [U.sup.1] ([x.sub.11], . . ., [x.sub.n1], Z) [1]

subject to

[U.sup.c] ([x.sub.ic], . . ., [x.sub.nc], Z) [greater than or equal to] [U.sup.*c] (c = 2, . . ., m) [2]

[f.sup.a] ([y.sub.1a], . . ., [y.sub.na], [z.sub.a]) [less than or equal to] 0 (a = 1, . . ., d) [3]

[summation of] [x.sub.ic] where c = 1 to m - [summation of] [y.sub.ia] [less than or equal to] [k.sub.i] where i = 1 to d (i = 1, . . ., n) [4]

[x.sub.ic] [greater than or equal to] 0, [z.sub.a] [greater than or equal to] 0, Z [greater than or equal to] 0 [5]

where functions 1-3 are concave and twice differentiable. [U.sup.c]([center dot]) is the utility function of individual c, [U.sup.*c] is initial utility level, while [x.sub.ic] is the amount of good (resource) i consumed by the same individual. Z = [[Sigma].sub.a][Z.sub.a] is total emissions for the whole economy. Observe that, in this model, only firms, not consumers emit. Firm (a)'s production set is [f.sup.a], [y.sub.ia] is the amount of good (resource) i produced ([y.sub.ia] [greater than] 0) or used ([y.sub.ia] [less than] 0) by firm (a), [z.sub.a] is the emission of an externality-causing substance made by the same firm, and [k.sub.i] the available amount of resource i. One simplification is done compared to Baumol and Oates. Emissions only affect consumers.(3)

The standard first-order conditions for an interior solution are as we know:

[[Lambda].sub.c] [Delta][U.sup.c]/[Delta][x.sub.ic] - [[Omega].sub.i] = 0 ([for every] i, c) ([[Lambda].sub.1] = 1) [6]

-[[Mu].sub.a] [Delta][f.sup.a]/[Delta][y.sub.ia] + [[Omega].sub.i] = 0 ([for every] i, a) [7]

[summation of] [[Lambda].sub.c] where c = 1 to m [Delta][U.sup.c]/[Delta]Z [Delta]Z/[Delta][z.sub.a] - [[Mu].sub.a] [Delta][f.sup.a]/[Delta][z.sub.a] = 0 ([for every] a) [8]

where [[Lambda].sub.c] is the Lagrangian multiplier for the constraint on consumer c's utility, [[Mu].sub.a] the multiplier for the technology constraint (firm a) and [[Omega].sub.i] is the multiplier for the resource constraint. Equation [8] is the important one here, showing that for a social optimum the firm should emit pollutants to the point where the marginal benefit from doing so equals the sum of marginal disutilities for the consumers. In a competitive market this is, following Baumol and Oates (1975/1988), obtained by imposing taxes

[t.sub.a] = - [summation of] [[Lambda].sub.c] [Delta][U.sup.c]/[Delta]Z [Delta]Z/[Delta][z.sub.a] ([for every] a) [9]

on the emission [z.sub.a] from firm (a).(4)

There are …