The Second Welfare Theorem in Economies with Non‐Walrasian Markets

• DOI: http://doi.org/10.1111/jpet.12128
• Author: NICHOLAS ZIROS,LEONIDAS C. KOUTSOUGERAS
• Date: 01 June 2015
• Published date: 01 June 2015

THE SECOND WELFARE THEOREM IN ECONOMIES WITH

NON-WALRASIAN MARKETS

LEONIDAS C. KOUTSOUGERAS

University of Manchester

NICHOLAS ZIROS

University of Cyprus

Abstract

The standard version of the second welfare theorem

assumes that market operations produce Walrasian out-

comes. Therefore, if there are individuals who can manipu-

late prices, the conclusion of the second welfare theorem

is questionable. In this paper, we address the decentral-

ization of a Pareto-optimal allocation, when markets are

non-Walrasian. Our objective in this paper is to develop a

game which can implement Pareto-optimal allocations as

Nash equilibria of strategic exchange in markets. In this

way, we develop a version of the second welfare theorem

for economies where markets are strategic.

1. Introduction

The second welfare theorem, namely that with appropriate wealth transfers

any chosen Pareto-optimal allocation can be obtained as Walrasian equilib-

rium, is central in modern welfare economics. Since the early attempts of

its articulation this theorem has been the subject of quite extensive discus-

sions in the literature, which have brought to light various interpretations,

implications, extensions, and limitations. Besides its use as a basic tool in the

political economy debate, where it was viewed by a number of authors as

the theoretical foundation of socialist organization of an economy through

Leonidas C. Koutsougeras, University of Manchester, Oxford Road, Manchester M13 9PL,

UK (leonidas@manchester.ac.uk). Nicholas Ziros, Department of Economics, University

of Cyprus, P.O.Box 20537, 1678 Nicosia, Cyprus (n.ziros@ucy.ac.cy).

Received June 13, 2014; Accepted July 16, 2014.

C2014 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 17 (3), 2015, pp. 415–432.

415

416 Journal of Public Economic Theory

markets,1this theorem had a profound influence on the development of

public economics. Since its early use (albeit not in its current form) by

Hotelling (1938) on issues of taxation it has been used in issues of optimal

taxation, the development of methods of cost-benefit analysis, the justifica-

tion of marginal cost pricing by publicly owned firms, and so on.2

Whatever the interpretation of the second welfare theorem, its central

message, which is accepted by its supporters and critics alike, is that issues of

efficiency can be effectively separated from issues of distribution: whatever

the equity objectives of the center, those can be implemented by a suitable

distribution of wealth and the operation of markets. The essential feature

of this theorem is that Pareto-optimal allocations can be obtained as out-

comes of market transactions. One of the qualifications of the theorem is

that market interactions produce Walrasian outcomes. In other words there

is a “price taking” hypothesis invoked about market functioning. Anderson

(1988) points out that “the above story assumes that the operations of the

market produce Walrasian equilibria as outcomes; this may not be the case

if there are large agents, who have incentives not to act as price-takers.” The

same observation is made by Mas-Colell, Whinston, and Green (1995), who

state that “the first observation to make is that a planning authority wishing

to implement a particular Pareto-optimal allocation must be able to ensure

that the supporting prices will be taken as given by consumers and firms.” In

other words, if there are individuals who can manipulate prices, the conclu-

sion of the second welfare theorem is questionable. This is the issue that

we wish to tackle in this paper. In particular, we wish to address the fol-

lowing questions: in an environment where individuals are strategic rather

than price takers in markets, is it possible to decentralize Pareto-optimal out-

comes, i.e., implement Pareto-optimal allocations as equilibrium outcomes

of market interactions? And if so how?

We believe that the development of a version of the second welfare

theorem in a strategic context is very important because that theorem has

been key in the development of principles in public economics, welfare

economics, and political economy where it has been used extensively, so

it would be quite interesting to evaluate which of those, if any, carry over

to the strategic context. For instance, the work of Lange (1942) exposed

the relationship of Pareto-optimality and social welfare maximization, which

uncovered a far-reaching interpretation of market prices as “marginal social

valuation” of commodities, which in turn has deeply influenced public eco-

nomics. We believe therefore that it is very important to investigate whether

or not non-Walrasian market clearing prices can be given such an analogous

1There is an extensive literature on this subject starting with Lange and Taylor (1939) all

the way up to Stiglitz (1994). It would be impossible to list here this extensive literature

but the interested reader can find a comprehensive listing in the last reference.

2See Mirrlees (1997) and the references thereafter.