This paper analyzes the definition of economic efficiency. The standard definition used in economic literature is the Pareto Optimum which is based in the space of individual utilities. This paper proposes new definitions based on alternative spaces. The paper also introduces a dominance criterion for efficiency over a set of social evaluation spaces.Efficiency, Social justice, Dominance

Paul Makdissi

English

Research Papers in Economics

 
 
 
CIRPÉE 
Centre interuniversitaire sur le risque, les politiques économiques et l’emploi 
 
 
 
 
 
Cahier de recherche/Working Paper 06-44 
 
 
 
 
 
 
On the Definition of Economic Efficiency 
 
 
 
Paul Makdissi 
 
 
 
 
 
 
 
 
Novembre/November 2006 
 
 
 
 
 
 
 
 
 
 
 
_______________________ 
Makdissi: Département d’économique, CIRPÉE and GRÉDI, Université de Sherbrooke, 2500, boulevard de 
l’Université, Sherbrooke, Québec, Canada J1K 2R1 
paul.makdissi@usherbrooke.ca 
 
 
 
I thank Claude Fluet and Daniel Parent for useful comments. 
 
 Abstract:  
This paper analyzes the definition of economic efficiency. The standard definition 
used in economic literature is the Pareto Optimum which is based in the space of 
individual utilities. This paper proposes new definitions basd on alternative spaces. 
The paper also introduces a dominance criterion for efficiency over a set of social 
evaluation spaces. 
  
Keywords: Efficiency, Social justice, Dominance 
 
JEL Classification: D63, H20 
 1 Introduction
In their ﬁrst introductory courses, economists learn that eﬃciency is
achieved when an economic allocation is Pareto optimal. In other words,
economic eﬃciency implies that it is impossible to increase one’s utility wi-
thout decreasing someone else’s utility. However, the normative concepts
underlying the deﬁnition of eﬃciency are far more complex than it seems.
Since Rawl’s Theory of Justice (Rawls, 1971), political philosophers have
questioned the appropriateness of utilities for the evaluation of social jus-
tice. If social objectives are not deﬁned in the space of utilities; eﬃciency
must therefore be deﬁned in another more appropriate space. This paper’s
objective is to address this question. A brief overview of the philosophical
debate is presented in section 2. Section 3 presents the formal deﬁnition of
eﬃciency. A simple example is presented in section 4. A brief conclusion
then follows.
2 An Overview of the Debate
From the eighteenth century until the twentieth century, utilitarianism,
in the tradition of Bentham and Mill, was the main political philosophy in
the anglo-saxon tradition. This position was ﬁrst criticized by Rawls (1971)
who argues that the appropriate space for evaluation of social justice is not
individual utilities but the space of social primary goods. Those goods are
civil liberties, free access to social position and socio-economic advantages.
The Theory of Justice is so important in political philosophy literature that
since it has been published, every author in this ﬁeld has to explain the
diﬀerences and similarities between his view and Rawls’. In this section,
I present brieﬂy the most known piece of work in post-rawlsian political
philosophy.
Nozick (1974) criticizes Rawls and argues that the criterion of social
justice must be procedural and that the appropriate space to assess social
justice is the space of formal liberties.
Sen (1980) argues that although Rawls properly demonstrates that uti-
lity is not an appropriate space for social justice evaluation, he eliminates
too many of the diﬀerences between individuals. Some diﬀerences, such as
handicap, gender or race may be important. Thus, he proposes to evaluate
social justice in the space of capabilities which are sets of social function-
nings available to each individual. Sen (1980) was also the instigator of the
debate on “equality of what?”.
2Dworkin (1981a and b) formalizes the principle of individual accounta-
bility which was inherent in Rawls (1971) and Sen (1980). In this context,
he argues that social justice must be evaluated in a space deﬁned by the
resources available to individuals.
Arneson (1989) criticizes Dworkin on the link he draws between resources
and preferences. He argues that the appropriate link between resources and
preferences should be opportunities of welfare. He thus proposes to evaluate
social justice in the space of opportunities of welfare. Cohen (1989) argues
that the space of opportunities of access to socio-economic advantages is
more appropriate 1.
Van Parijs (1995) adopts a completely diﬀerent framework and proposes
to assess social justice in the space of real liberties.
3 Deﬁtinions
As brieﬂy discussed in the previous section, a social planner’s objectives
may be evaluated in diﬀerent spaces. An eﬃciency criterion must then be
associated to each respective space. In order to do so, let us consider an eco-
nomy of I individuals may be described by the individuals initial allocation,
Ω = ($1,$2,...,$I), by the procedure ψ that transforms those initial alloca-
tions and by the ﬁnal allocation X = (x1,x2,...,xI). Let Θ = (φ1,φ2,...,φI)
be a social evaluation space associated with this economy. If this space is
individual utilities, then φi is the utility of individual i. If we consider op-
portunities of welfare than φi is the opportunities of welfare available to
individual i, etc. We can now give a ﬁrst deﬁnition.
Deﬁnition 1: Θ-eﬃciency. An economy (Ω,ψ,X) is Θ-eﬃcient ↔ @
(Ω0,ψ
0,X0) : {φ
0
1 ≥ φi∀i ∧ ∃k : φ
0
k > φk}
In this context, it is easy to see that Pareto eﬃciency is a particular case;
such that the economy (Ω,ψ,X) is eﬃcient in the space of individual utilities
if and only if @ (Ω0,ψ
0,X0) : {ui (x0
i) ≥ ui (xi)∀i ∧ ∃k : uk (x0
k) > uk (xk)}.
As economist, we may face situations in which policy makers do not agree
on the appropriate social evaluation space. It is then interesting to identify
situations which are eﬃcient for a wide spectrum of social evaluation spaces.
1Roemer (1993) formalizes the theory of equal opportunities. Fleurbaey (1994, 1995),
Bossert (1995) and Bossert and Fleurbay (1996) adopt an axiomatic approach to those
theories
3Let Λ :=

Θ1,Θ2,...,ΘN	
be a set of N diﬀerent social evaluation spaces.
We can now give a second deﬁnition.
Deﬁnition 2: Λ-eﬃciency. An economy (Ω,ψ,X) is Λ-eﬃcient ↔ @
(Ω0,ψ
0,X0) : {φ
n0
1 ≥ φ
n
i ∀i ∧ ∃k : φ
n0
k > φ
n
k} ∀Θn ∈ Λ
4 Two Simple Examples
In this section, we consider Λ0 := {Utility, Resources, Formal Liberties}.
This set of social evaluation spaces will be used in two simple examples. First
we will consider a purely competitive economy and analyze its eﬃciency.
Secondly, we will discuss the case of provision of a public good.
First, consider a purely competitive economy (Ω1,ψ1,X1) of I individuals
with private goods, perfect and symmetric information and complete mar-
kets. From the First Fundamental Theorem of Welfare Economics, we know
that this economy is Utility-eﬃcient. Since it is impossible to increase $i
without decreasing $j for at least one j 6= i, this economy is also Resources-
eﬃcient. If ψ1 is such that all production decisions and all exchanges bet-
ween individuals are non coercive, this economy is also “Formal Liberties”-
eﬃcient. This economy is thus Λ0-eﬃcient.
Let us now consider Dworkin’s (1981b) proposition for social justice. Af-
ter choosing resources as the appropriate space, Dworkin suggest that justice
requires the equality of resources. As some resources are non-transferable,
he suggest that the just distribution will transfer resources from one in-
dividual to another in order to mimic an insurance system that will have
been chosen by the individuals if they were placed behind the veil of igno-
rance. This yields a new procedure ψ2. This redistribution of resources yields
another Resources-eﬃcient outcome of the economy. The Second Fundamen-
tal Theorem of Welfare Economics also insures that (Ω1,ψ2,X1) will also
be Utility-eﬃcient. However, coercion is needed to transfer resources from
an individual to the other. As a result, some individuals experience a de-
crease in their formal liberties without increasing anyone else’s. This im-
plies that (Ω1,ψ2,X1) is not “Formal Liberties”-eﬃcient. We conclude that
(Ω1,ψ2,X1) is Λ1-eﬃcient where Λ1 := {Utility, Resources}
Let us now consider our second example which is the provision of a public
good. Suppose now an economy where (Ω2,ψ1,X2). Here, X2 incorporates a
non rival public good without exclusion. This implies that this public good
is consumed in equal quantity by every agent. Note that the procedure ψ1 is
such that all production and consumption is chosen by the individuals who
4interact through market mechanism. Introductory public economics teaches
us that (Ω2,ψ1,X2) is not Utility-eﬃcient. However, since it is impossible
to increase $i without decreasing $j for at least one j 6= i, this economy is
Resources-eﬃcient. The use of procedure ψ1 also implies that it is also “For-
mal Liberty”-eﬃcient. We conclude that (Ω2,ψ1,X2) is Λ2-eﬃcient where
Λ2 := {Resources}
Let us now consider a new procedure ψ3 which consist of free markets
with the exception imposing a tax on the initial allocation of resources in
order to produce a quantity of public good that is compatible with Samuel-
son’s rule. This new economy (Ω2,ψ3,X2) is Resources-eﬃcient since it is
impossible to increase $i without decreasing $j for at least one j 6= i. Stan-
dard public economics teaches us that (Ω2,ψ3,X2) is also Utility-eﬃcient.
However, taxing individuals implies coercion. So, all individuals experience
a decrease in their formal liberties. This implies that (Ω2,ψ3,X2) is not
“Formal Liberties”-eﬃcient. We conclude that (Ω2,ψ3,X2) is Λ1-eﬃcient.
5 Conclusion
In this paper, we have introduced a more general deﬁnition of economic
eﬃciency for which Pareto-eﬃciency is just a particular case. We have also
introduced a deﬁnition of eﬃciency dominance for which an economy is
eﬃcient for a wide spectrum of social evaluation spaces.
Our discussion of some simple examples has shown that analysts need to
identify the social evaluation space that they refer to before stating that an
economy is eﬃcient. In other words, even in some simple cases, there may be
divergence in opinion if two analysts chose diﬀerent social evaluation spaces.
References
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