Prices or Quantities Can Dominate Banking and Borrowing*

• Published date: 01 April 2020
• Date: 01 April 2020
• DOI: http://doi.org/10.1111/sjoe.12351
• Author: Martin L. Weitzman

Scand. J. of Economics 122(2), 437–463, 2020

DOI: 10.1111/sjoe.12351

Prices or Quantities Can Dominate Banking

and Borrowing*

Martin L. Weitzman†

Harvard University,Cambridge, MA 02138, USA

Abstract

The possibility of intertemporal banking and borrowing of tradable permits is often viewed as

tilting the various policy debates about optimal pollution control instruments towards favoring

such time-flexible quantities. This paper showsthat this view can be misleading, at least for the

simplest dynamic extension of the original “prices versus quantities” information structure. The

model of this paper allows firms to know and act upon the realization of uncertain future costs

two full periods ahead of the regulators. Forany given circumstance, the paper shows that either

a fixed price or a fixed quantity is superior in expected welfare to time-flexible banking and

borrowing. Furthermore, the standard original formula for the comparative advantage of prices

over quantities contains sufficient information to completely characterize the regulatory role of

intertemporal banking and borrowing. The logic and implications of these results are analyzed

and discussed.

Keywords: Banking and borrowing; climate change; pollution; prices; prices versus quantities;

quantities; regulatory instruments

JEL classification:Q50; Q51; Q52; Q54; Q58

I. Introduction

Choosing the best instrument for controlling pollution has been a long-

standing central issue in environmental economics. This paper is primarily

concerned with the theory of environmental policy in terms of the basic

theoretical foundations of the instrument choice issue among the three

alternatives of fixed prices, fixed quantities, and time-flexible quantities

from intertemporal banking and borrowing.1

*I am indebted to the following people for their helpful and constructive comments (without

implicating them in errors, omissions, or interpretations): Reyer Gerlagh, Kenneth Gillingham,

Ben Groom, Garth Heutel, Ryan Kellogg, Frank Krysiak, Derek Lemoine, Jing Li, Jussi

Lintunen, Ian MacKenzie, Gilbert Metcalf, Guy Meunier, Ian Parry, Cedric Philibert, Simon

Quemin, Philippe Quirion, Mar Reguant, TillRequate, Richard Revesz, Andrew Schein, Richard

Schmalansee, Joseph Shapiro, Robert Stavins, Jean Tirole,Yi-Ming Wei, and three anonymous

referees.

†Marty Weitzmanpassed away after the final version of this manuscript was accepted. Marty was

a deeply original thinker who will be greatly missed by the profession.

1I sprinkle in some comments on “practicality” throughout the paper, but the main focus is on

the pure economics of instrument choice. Thus, the broader dimensions of real-world political,

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The editors of The Scandinavian Journal of Economics 2019.

438 Prices or quantities can dominate banking and borrowing

Pollution is a negative externality. Pigou (1920) introduced and

subsequently popularized the central concept of placing a price charge on

pollution (now called a “Pigouvian tax”) as an efficient way to correct

a pollution externality. This Pigouvian-tax approach dominated economic

thinking about the pollution externality problem for about the next half-

century.

Dales (1968) introduced the idea of creating property rights in the

form of tradable pollution permits (also called “allowances”) as an efficient

alternative to a Pigouvian tax. Montgomery (1972) proved rigorously the

formal equivalence between a price on pollution emissions and a dual

quantity representing the total allotment of tradable permits. Henceforth, it

became widely accepted that there is a fundamental isomorphism between

a Pigouvian tax on pollution and the total quantity of allotted caps in a

cap-and-trade system that ends up with all permits trading at the same

competitive equilibrium market price as the Pigouvian tax. For every given

Pigouvian tax, there is a total quantity of tradable permits allotted whose

competitive equilibrium market price equals the Pigouvian tax. And for

every given total quantity of tradable permits allotted, there is a competitive

equilibrium market price that would yield the same result if it were imposed

as a Pigouvian tax. Thus far, all of the analysis took place in a deterministic

context where everything was known with certainty.

Weitzman (1974) showed that with uncertainty in cost and benefit

functions there is no longer an isomorphism between price and quantity

instruments. The key distinction under uncertainty is that setting a fixed

price stabilizes marginal cost while leaving the total quantity variable,

whereas setting a fixed total quantity of tradable permits stabilizes

the total quantity while leaving the price (or marginal cost) variable.

The question then becomes, Which instrument is better under which

circumstances?

In his paper “Prices vs. Quantities” (Weitzman, 1974), Weitzman derived

a relatively simple formula for the “comparative advantage of prices over

quantities”, denoted in the paper as Δ. The sign of Δdepends on the

relative slopes of the marginal abatement-cost curve and the marginal

abatement-benefit curve. The sign of Δis positive (prices are favored over

quantities) when the marginal benefit curve is flatter than the marginal cost

curve. Conversely, the sign of Δis negative (quantities are preferred over

ideological,legal, social, historical, administrative, motivational, informational, timing, lobbying,

monitoring and enforcing considerations, or any other issues that are not purely economic, are

beyond the scope of this paper.For a balanced and overarching discussion of both theoretical and

practical issues involved in choosing between carbon taxesand a cap-and-trade system, see the

review article of Goulder and Schein (2013) and the many references cited therein.

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The editors of The Scandinavian Journal of Economics 2019.