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  • Taxes vs. Quotasor Taxes vs. Upper Bounds?

    Nicholas Brozovíc,∗

    David L. Sunding, and David Zilberman†

    November 2, 2004

    Abstract

    We compare taxes and quotas where a regulator and a non-strategic firm have asymmetric information about a pollution-producing activity. In previ- ous studies, optimal quotas are generally assumed to bind with probability one. We analyze the conditions under which a quota that bindswith prob- ability less than one is optimal. A quota that may be slack canbe targeted towards some firms whilst allowing others to operate unconstrained. Failure to consider optimal quotas that may be slack overestimates the advantage of taxes over quotas, even in situations where the marginal benefit function is much steeper than the marginal cost function.

    Keywords: Pollution control; Taxes and quotas; Asymmetric informa- tion

    JEL classification:D81; H23; L51

    ∗Corresponding author; University of Illinois at Urbana-Champaign, Department of Agricul- tural and Consumer Economics, 307 Mumford Hall, Urbana, IL 61801; emailnbroz@uiuc.edu; tel 217-333 6194; fax 217-333 2312

    †Both at University of California at Berkeley, Department ofAgricultural and Resource Eco- nomics, 207 Giannini Hall, Berkeley, CA 94720

  • 1 Introduction

    Many pollution problems are characterized by uncertainty on the part of the regu-

    lator. This may be because polluting firms have better information than regulators

    on their emissions or abatement costs, so that there is asymmetric information.

    Alternatively, the damages caused by pollution and the pollution process itself

    may be subject to uncertainty. Price instruments and quantity instruments are

    commonly used to control pollution. With a price instrumentthe regulator uses a

    tax, on pollution or on a suitable proxy, and firms equate the marginal benefits of

    their productive activity to this tax. Under a tax with asymmetric information, the

    aggregate level of output is uncertain. Conversely, with a quantity instrument and

    asymmetric information, the regulator uses a quota to obtain a certain aggregate

    level of output; the marginal benefits of productive activity are uncertain.

    If the regulator is able to use contingent regulations that differentiate each

    type of firm or possible state of nature, first-best taxes and quotas have identical

    welfare outcomes. If there is asymmetric information and first-best regulation

    is not feasible, the welfare effects of taxes and quotas willvary. An extensive

    literature in the tradition of Weitzman [11] considers the choice between taxes

    and quotas under asymmetric information (e.g. Roberts and Spence [9]; Laffont

    [5]; Malcomson [6]; Nichols [7]; Kolstad [4]; Stavins [10];Hoel and Karp [2]).

    These papers assume, implicitly or explicitly, that quantity regulation involves

    the dictation of a specific level of activity that is strictlyadhered to. The chosen

    quota will thus influence the decisions of the regulated group in all states of na-

    ture, and binds with probability one. However, quotas oftenimply an upper bound

    on regulated activities, because quota recipients have theoption of not taking full

    advantage of their allocation. Hence, the assumption that optimal quotas bind with

    probability one is unduly restrictive. Indeed, in practicemost quantity regulations

    are implemented as upper bounds: for example, environmental regulators are gen-

    1

  • erally unconcerned if a firm emits less pollution than it is legally entitled to, and

    there is no penalty for driving below the speed limit on a highway. Moreover,

    if an industry is very heterogeneous in terms of either its productive or polluting

    capacities, it is unlikely that firm response to a uniform quota will be identical

    in all possible states of nature. This paper analyzes the implications of allowing

    regulated groups to treat quotas as upper bounds – that is to say, allowing quotas

    to be slack with positive probability.

    We are aware of only a few previous studies that consider the possibility that

    quotas may not bind with probability one. Hochman and Zilberman [1] compare

    the welfare impacts of taxes and quotas using fixed proportions production and

    pollution functions. Because of this functional form, firm adjustment to regula-

    tion only occurs at the extensive margin, and individual production units cannot

    adjust at the intensive margin in response to regulation. Thus, under each kind of

    regulation, firms either continue to operate at full capacity, or shut down. Wu and

    Babcock [12] consider firm adjustment at both intensive and extensive margins

    for the problem of second-best regulation under heterogeneity. Although they do

    recognize the possibility that quotas may not bind with probability one, they do

    not analyze either the potential optimality or the implications of this. Karp and

    Costello [3], using a dynamic model with asymmetric information, show that a

    regulator may use a slack quota to gain information with which to better target fu-

    ture quotas. However, in their model, the optimal one-period quota still binds with

    probability one, and use of a slack quota leads to loss of surplus in that period.

    Finally, in a numerical simulation of alternative policiesto mitigate global climate

    change, Pizer [8] shows that for realistic cost and benefit parameters, second-best

    quotas do not bind in all cases. For the particular application he considers, Pizer

    calculates that a failure to account correctly for slack quotas overestimates by a

    factor of five the advantage of taxes over quotas, yielding anestimated gain of $10

    2

  • billion in 2010, rather than the correct figure of $2.2 billion.

    Our objective is to compare taxes and quotas in a static framework when the

    regulator may use a quota that is slack with positive probability. Setting a quota

    that may be slack allows targeting of the regulation on a subset of possible firms.

    Firms that are targeted in this way will operate closer to thesocial first-best level

    of production. Conversely, firms for which the quota is slackwill operate uncon-

    strained and will be producing further from the social first-best level. There are

    thus two opposite effects from allowing a quota to be slack: firm targeting leads

    to an increase in net surplus, whereas unconstrained firm operation leads to a de-

    crease in net surplus. In order to allow comparison with existing work, we derive

    analytical results using the same assumptions about functional forms as previous

    literature. We derive conditions under which an optimal quota may be slack, and

    compare taxes and quotas under these conditions. We show that if there is enough

    heterogenity in the regulated industry, the optimal quota must be slack with posi-

    tive probability. Moreover, our analysis suggests that previous studies have over-

    estimated the relative advantage of taxes over quotas. The ability to use a quota

    that may be slack means that quotas are preferred to taxes over a wide range of

    parameter values where previous studies would indicate theopposite result.

    2 The model

    We begin by describing the functional forms and informationasymmetry used in

    the general model. We then present optimality conditions for second-best regula-

    tion with taxes and quotas.

    3

  • 2.1 Elements of the model

    We assume a representative firm which has a production technology and a pollu-

    tion technology. The production technology captures the quasi-rents of a given

    level of production activity by the firm. The pollution technology captures the ex-

    ternality costs of the firm’s activity. We assume that the production and pollution

    technologies are independent attributes of the representative firm.

    The regulator has full information about the firm’s pollution technology, but

    is uncertain of the firm’s production technology.1 For simplicity, we assume that

    there are two possible production technologies, low-productivity (L) and high-

    productivity (H). The representative firm is anL-type with probabilityθ and an

    H-type with probability1−θ. Our major results hold for continuous distributions

    of production technology, but the proofs are more difficult to interpret.

    The firm uses a scalar input,xi, in the production of a numeraire good, where

    i ∈ {L, H} and denotes whether the firm is anL-type or anH-type. Its quasi-

    rents net of input prices are given by the production function fi(xi). Additionally,

    we assume thatfi(xi) ≥ 0, f ′i(xi) > 0, f ′′ i (xi) < 0, fi(0) = 0, and thatf

    ′ L(xi) ≤

    f ′H(xi) for all positive values ofxi.

    Input use by each firm causes a negative externality. The damage caused by

    using xi units of input is given by the functiong(xi), where we assume that

    g(xi) ≥ (0), g′(xi) > 0, g′′(xi) > 0, and g(0) = 0. We also assume that

    f ′L(0) > g ′(0), so that it is socially desirable for the firm to continue to oper-

    ate at some positive level even if it is a low-productivity type. This assumption

    implies that the representative firm will never shut down as aresult of regulation,

    and adjustment will take place at the i

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