On the weak axiom of revealed preference without demand continuity assumptions

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E U I W O R K I N G P A P E R N°84/116 ON THE WEAK AXIOM OF REVEALED PREFERENCE

WITHOUT DEMAND CONTINUITY ASSUMPTIONS by

Reinhard JOHN*

♦University of Bonn, Sonderforschungesbereich 21.

I wish to thank Karl-Josef Koch for many helpful discussions. Part of this work has been done while I was visiting the European University

Institute in Florence, Italy.

Financial support from this institu tion is gratefully acknowledged.

BADIA FIESOLANA, SAN DOMENICO (FI)

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No part of this paper may be reproduced in any form without

permission of the author .

(C) Reinhard JOHN

Printed in Italy in October 1984 European University Institute

Badia Fiesolana 50016 San Domenico (FI)

Italy © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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Abstract

Abstract: We consider two versions of the weak axiom of revealed preference for demand functions which are not necess arily continuous, and study their relationship to preference maximizing behavior. In particular, we characterize demand

functions satisfying these axioms and obtain some results con cerning the existence of a nontransitive consumer.

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« ’ • ■ / f x ■ • ' _* * - 1' © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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1. Introduction

Recently the weak axiom of revealed preference has proved to be of some importance to the theory of aggregate demand. For it was shown by W.Hildenbrand (1983) that under some assumptions on the income distribution of a group of consumers the market demand satisfies the weak axiom if all individual demand func tions have this property. In a first version of his paper he raised the question whether there is a representative consumer for such a group, i.e. a preference relation from which the

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2

aggregate demand function can be derived.

Of course, this relation cannot be assumed to be transitive for it has been shown by J.Lenninghaus (1984) that in general such a market demand function does not satisfy the strong

axiom of revealed preference. Therefore Hildenbrand1s question is related to a conjecture of R.Kihlstrom, A.Mas-Colell,

H.Sonnenschein, and W.Shafer (1976), which claims the existence of a representing nontransitive consumer in the sense of

W.Shafer (1974) for continuous demand functions satisfying

the axiom. For the special case in Hildenbrand's paper W.Shafer has given an essentially positive answer.

Our concern here is the "noncontinuous" nontransitive con sumer, i.e. the purpose of this paper is to study the relation ship between preference maximizing behavior and demand functions which satisfy the weak axiom but are not necessarily continuous.

We examine two versions of this axiom. The first one which we shall call the "weak axiom" seems to be the weakest form known from the literature. The second one is Samuelson's notion and, like in Hildenbrand (1983), denoted as "axiom".

After having given the basic definitions in the next section, we shall study the weak version in Section 3. Although we are primarily interested in demand functions it turns out that in this case we can generalize the results to demand correspondences at no additional cost. Roughly speaking, we can characterize de mand functions (resp. correspondences) satisfying the weak axiom as selections of a demand correspondence which is derived from a preference relation with nice properties. By "nice" we mean that the preference relation should fulfill conditions which

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guarantee that nonempty, compact, and convex sets have best elements. In particular, they should imply the existence of a derived demand correspondence defined for all budget sets. In the context of the weak version without continuity, this seems to be a natural requirement in accordance with the idea which is behind Shafer's definition of a nontransitive con sumer.

The axiom of revealed preference will be considered in Section 4. Since this notion implies unique demand, a "nice" preference relation in that case should additionally ensure the uniqueness of best elements in convex sets.The first the orem in this section characterizes demand functions satisfying the axiom as derived from preferences which do not have the required properties. But a second theorem shows that some further assumptions on the demand function imply that it can be derived from such a nice preference at least on its range.

Finally, the paper is finished by some concluding remarks in Section 5.

2. Definitions l

Let ]R+ be the nonnegative orthant of the ^-dimensional Euclidean space 1R and define P={x€ 3R^ | 0<<x) . For each

0

p€P, B(p)={x€ JR^|px<1} is the budget set with respect to the vector p of price-income ratios.

A de.ma.nd f u n c t i o n [ c o r r e s p o n d e n c e ) assigns to each budget set an element (a subset) of it, i.e. it is a function (corres

1) a « b means a^fc^ for h=19 • • • /Z

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I" '

4

-l

pondence) f:P-*-]R+ such that pf(p)<1 for all p €P.^

A demand function f satisfies the weak axiom (0|$ Aevealed pAefieAence) iff for all p,q6P

pf(q)<1 implies qf(p)>1.

f satisfies the axiom (ofi Aevealed pAefieAence) iff for all p,q£P

pf(q)^1 and qf(p)<1 implies f(p)=f(q).

Observe that the weak axiom implies the budget identity pf(p)=1 for all p. Therefore it does not follow from the axiom if this identity is not assumed.

A demand correspondence f satisfies the (weak) axiom iff each selection of f has this property. Of course, the validity of the axiom implies single-valued demand, i.e. f can be con sidered as a function.

t Now let X be a subset of 3R+ .

A binary relation R defined on X is called a pAe.fieAe.nce. (Aelatlon) on X. If (x,y)€R we call x as least as good as y and denote it equivalently by xRy or x£R(y).

A preference relation R on X is called uppeA continuous, iff R(x) is closed in X, convex, iff R(x) is convex,

weakly monotone, iff x<<y implies x^R(y), monotone, iff x<y implies x£R(y),

complete, iff x£R(y) or y£R(x),

antisymmetAlc, iff x€R(y) and y£R(x) implies x=y, asymmetAlc, iff x£R(y) implies y£R(x),

where each condition holds for all x,y€X. 2 2) Inequality for sets is defined pointwise

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Let R be a preference relation on X.

If Y E X then y€Y is an R-be.it e l e m e n t I n Y iff y£R(x) for all x€Y.

If p£P then fR (p) denotes the set of all R-best elements in BX (p):={x€X|px<1}.

A demand function (correspondence) f is called derived. 15-iom R on X, if (f(p)}=fR (p) (f(p)=fR (p)), and w e a k l y d e r i v e d , if f(p)efR (p) (f (p)£ fR (p) )# for all p€P.

The revealed preference relation V of a demand correspon dence (function) f is defined by

xVy iff there is p£P such that x€f(p) and pys1.

3. Demand correspondences satisfying the weak axiom

In this section we shall characterize demand correspondences (and, therefore, demand functions) satisfying the weak axiom as weakly derived from preference relations with certain prop erties.

A fundamental step towards this goal is provided by the following result of H.Sonnenschein (1971).

t

Lemma 1; Let R be a relation on Xcjr with the following

properties:

(i) R is upper continuous.

(ii) conv F E U R(x) for all finite subsets F of X . ^ x£F

Then every nonempty, compact, and convex subset of X has an R-best element. 3

3) conv S denotes the convex hull of a set S.

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6

Proof: For the sake of completeness we repeat the main argument of H.Sonnenschein (1971).

Let C be a nonempty, compact, and convex subet of X. Consider the collection {R(x)nc|x€C} of subsets of C, which is nonempty because C is nonempty. Since R(x) is closed,

o every set R(x)OC is compact and therefore closed in 1R . Take any finite collection (R(xi )f1C)^_1 and any subset F £ {x.,. . . ,x } . Since C is convex, conv F 5 U R(x)flC

x€F

= U (R(x)nc). By a corrollary to the Knaster-Kuratowski- x€F

Mazurkiewicz Lemma (see Sonnenschein (1971), Corollary 5) it n

follows that fl (R(x. )nc) ^ 0. Therefore, {R(x)nc|x€C} has

i= 1 1

the finite intersection property which implies n R(x)nC/0. x€C

Q.E. D. The next result gives a sufficient condition for a preference relation having a derived demand correspondence which satisfies the weak axiom.

/

Proposition 1: If R is a relation on 3R+ such that for all x,y6 3R^

x<<y implies x 0conv R(y),

then any demand correspondence weakly derived from R satisfies the weak axiom.

Proof: For p,q€P let x€fR (p), yefR (q), and py<1. As sume that qx<1. Since px^1 and py^1, we obtain

p(ax+(1-a)y)<1 and q(ax+(1-a)<1 for 0<a<1. It follows the existence of z£B(p)nB(q) such that ax+(1-a)y«z. Since

x,y€R(z), we get ax+(1- a ) y € conv R(z) which contradicts the as sumption. Therefore, qxs1. Q.E.D. © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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In the sequel, we will prove the converse of this propostion. For that we need the following

Lemma 2; Let f be a demand correspondence which satisfies the weak axiom. If p ^ ,...,pn£P, then

n

conv( p. ,-- ,p ) £ U S(p,),

, n i=1

where S (p^ : = {q€ | qf (p± ) >1 }

n

Proof: Let p 6 conv (p, ,. . . ,p_ ) , i.e. p= I a^p. , a.>0,

n 1 n i=1 1 1 1

a,=1. Assume that p£ U S(p.), i.e. for each i there is i— 1 1

xiGf(pi) with pxi<1. This implies the existence of q>>p such that c3xi<1 for all i. Since f ' satisfies the weak axiom, we get p if(q) > 1 for all i. Take any y£f(q). Then

n

1< £ ctHP Hy=py<qy which contradicts qf(q)s1

i=1 1 n

Therefore p€ U S ( p .).

i=1 Q.E.D.

Using this result we can show that for a demand correspon dence satisfying the weak axiom each set of elements revealed

l

preferred to x€ 1R+ can be separated from x by a hyperplane with positive normal vector. Since this is trivial for x£P, we state this result as follows:

Proposition 2 : Let f be a demand correspondence satisfying l

the weak axiom. Then for each x6P there exists s£ ]R+ such that (a) sx^1

(b) sf(p)>1 for each p6P with px<1. /

Proof: Define a relation S on 3R+ by S(p)= 0

{q€ IR^ | p£P ■* qf (p) >1} . If x€P, then any S-best element s in B(x) has the properties (a) and (b): sGB(x) implies sxs1 and for p€P with pxs1, i.e. p£B(x), we know that s€S(p),

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i. e. sf(p)>1.

Since for any x€P the set B(x) is nonempty, compact, and convex, we can prove the proposition by applying Lemma 1 to the relation S, i.e. it remains to show the properties (i) and (ii) in Lemma 1 for S.

By definition of S, it is obvious that S(p) is closed for all p.

p

Now let F be any finite subset of 1R+ . If there is q£F^P p

then U S (p)^S (q) = IR, and we have conv F £ U S(p). Otherwise

p€F p£F

F c p and we obtain this inclusion by direct application of

Lemma 2. Q.E.D.

A straightforward consequence of Propositions 1 and 2 is a characterization of demand correspondences satisfying the weak axiom.

Theorem 1: Let f be a demand correspondence. Then the following conditions are equivalent:

(1) f satisfies the weak axiom.

(2) The revealed preference relation V has the property: P

y<<x implies y £ conv V(x) for all x,y€ IR+ .

(3) f is weakly derived from a convex and weakly monotone p

preference relation on 3R+ .

Proof: (1) ■* (2): If y<<x then x€P and, by Proposition 2, p

there is s£ 3Rj~ such that sxs1 and sV(x)=s U f(p) &1. This px<; 1

implies sy<1 and sconv V(x)s1, i.e. y £ conv V(x).

(2) ■» (1): Define a relation R on 3R^ by R(x)=conv V(x). R is convex by definition; (2) states that R is weakly mono tone, and V Ç R trivially implies that f is weakly derived from R.

(3) ■* (1): Proposition 1. Q.E.D. © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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A weak point of the theorem is the fact that in general the preference relations in the characterizing class do not have nice properties. A convex and weakly monotone relation

does not ensure the existence of a derived demand correspondence. One would like to characterize demand correspondences satisfying the weak axiom by a class of preferences which guarantee that at least any nonempty, compact and convex set has best elements. The next result shows that this is possible. Moreover, by

applying a duality argument to Proposition 1 and Lemma 2 we can derive the demand correspondences from preferences R where the sets R(x) are closed convex cones with vertex x which do

not contain any y<<x.

Theorem 2 : If f is a demand correspondence satisfying the weak axiom, then f is weakly derived from a preference relation

on with the following properties: 1) R is upper continuous and convex. 2) R is weakly monotone. 3) conv F £ U R(x) for , x£F p any finite F£1R+ . 4) R is complete. p More specifically, R can be chosen such that for x€ 1R+

R(x)={y£ IR^ | x€P=*s (x) y>1 } ,

where s(x) is a (dual) demand correspondence which satisfies the weak axiom.

Proof; If f is weakly derived from a relation R which is P defined by a correspondence s as stated above, then s:P->!IR+ must have the property that x£B(p)HP implies f(p) 5R(x), i.e.

s(x)f(p)£l. This means that for any s£s(x) the inequality

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sf(p)>1 holds for each p£P with px^1. Therefore it is necessary to define s(x) to be a subset of all s which satisfy conditions (a) and (b) of Proposition 2.

We choose for s any such correspondence whose existence is guaranteed by Proposition 2.

Since s is a (dual) demand correspondence which is weakly derived from the relation S defined in the proof of that proposition, s satisfies the weak axiom by (the dual of) Prop osition 1 if we can show that q<<p implies q £ conv S(p) for all p,q€ 3R+.

Observe first that S(p) is convex by definition. If q<<p then p€P and for any x6f(p) we obtain 1=px>qx, i.e. q£S(p).

We have proved that s is a demand correspondence satisfying the weak axiom and that f is weakly derived from R defined

D

by R (x) ={y£ | x€P=»s (x) y>1}. It remains to verify the properties 1) to 4).

1) follows immediately from the definition of R. To prove 2), let y « x . This implies x£P and 1=sx>sy for any s€s(x), i.e. y£R(x).

I

Now let F be any finite subset of IR+ . If there is yeF^P we get conv F Ç R ( y ) = U R(x). If F ç p we obtain 3) by

applica-x€F

tion of Lemma 2 to the correspondence s.

Finally, the completeness of R is an immediate consequence of the weak axiom for the correspondence s. Q.E.D. We remark that the largest weakly monotone relation M (de fined by x£M(y) iff x<<y) has all the properties mentioned in Theorem 2 except for convexity. Since any demand function satisfying the budget identity is weakly derived from M the

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weak version should not be interpreted as a property of con sistent behavior but as a consequence of rationality described by convex preferences.

4. Demand functions satisfying the axiom *12345

The first result of this section characterizes demand functions which satisfy the axiom of revealed preference. Its proof is

straightforward and the main argument can already be found in the work of M.K.Richter (1966,1971).

Theorem 3 : Let f be a demand function. Then the following conditions are equivalent:

(1) f satisfies the axiom.

(2) The revealed preference relation V is antisymmetric. / (3) f is weakly derived from an antisymmetric relation on 3R+ .

/ (4) f is derived from an antisymmetric relation on 3R+ .

t

(5) There is an asymmetric relation Q on 3R+ which ra-l tionalizes f in the sense that for all p€P, x€ 3R+ :

(i) xQf(p) implies px>1 .

(ii) px£l and x^f(p) implies f(p)Qx.

Proof: (1) ** (2): xVy and yVx imply the existence of p,q6P such that x=f(p), y=f(q), py<1, and qx<1. From the weak axiom it follows f(p)=f(q), i.e. x=y.

(2) (3): Since f(p)Vx for all x€B(p), f is weakly derived from V.

(3) *» (4) : If R is antisymmetric, there can be at most one

< © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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R-best element in any set. Since f is weakly derived from R, f(p) is an R-best element in B(p). Therefore it is the only one, i.e. f is derived from R.

(4) ■* (5): Define xGQ(y) iff x€R(y) and y£R(x). Q is asymmetric since x£Q(y) implies y£R(x), i.e. ygQ(x).

To prove (i), assume x€Q(f(p)). By definition of Q, f(p)gR(x) Since f is derived from R, f(p)£R(y) for yGB(p). Therefore xf?B (p) , i.e. px>1 .

To prove (ii), assume px<1 and x^f(p). Since f is derived from R, f(p)£R(x). Antisymmetry of R implies x£R(f(p)). By definition of Q, we get f(p)€Q(x).

(5) «* (1): Let Q be a relation satisfying (i) and (ii) and assume pf(q)<1 and qf(p)<1. (i) implies f (q) £Q (f (p) ) . By

(ii), it follows f(p)=f(q). Q.E.D.

This characterization theorem is not fully satisfactory for the criticism of Theorem 1 applies here too: An antisymmetric relation does not guarantee the existence of a derived demand function. Of course, if we would have a demand function f such that the budget identity pf(p)=1 holds for each p€P then the axiom implies the weak axiom and we could apply Theorem 2. But that would not ensure unique best elements in each budget set which in this case would be desirable.

Even if the smallest relation R within the class described in Theorem 2 is chosen, the following example shows that in general demand functions different from f can be derived from R (this would be the case even if R is restricted to the range of f, as a slight modification of the example can demon strate) . © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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Example : defined by

Consider the demand function f :P JR2 + f (P1fP2 ) 0) ( 0 ' £ ’ if p.,<1. if p 1al. which is

The axiom can be easily verified and the smallest relation of the form described in Theorem 2 is given by

y£R(x) iff x€P, sx<1<sV(x) implies sy>1.

Straightforward checking (Fig.1) shows that for x=(x1,x2) with

2

CKx.jd and x 2>0 there is only one s CJR+ satisfying the in equality sx<1<sV(x). It is normal to the straight line through x and (1,0), i.e. s=(1 , (1-x1)/x2 ).

If p is chosen such that p^ = 1, then no point on the budget line given by p is below the straight line through (1,0) and any x€P with px<1. It follows that all points on the budget line are R-best elements in B(p).

Nevertheless there is a positive result. For if the range X of t e demand function is convex there exists a preference

re-© The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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lation R on X such that each nonempty, compact and convex subset of X has a unique R-best element.

Theorem 4 ; Let f be a demand function with convex range X such that pf(p)=1 for all pGP.

If f satisfies the axiom, then f is derived from a pre ference relation R on X with the following properties:

(1) R is upper continuous and convex.

(2) conv F E U R(x) for any finite F £ X . xGF

(3) R is complete. (4) R is monotone.

(5) x, y€R(z) for all' zG[x,y] implies x=y.

Proof: Observe first that the validity of the budget identity implies the weak axiom (pf(q)<1 implies f(q)^f(p) and there fore, by the axiom, qf(p)>1).

Define a relation R on X by R(x) = {yex|s(x)ys1 },

where s : X + P is a selection of f 1.

Since this relation is not exactly a restric-o

tion of a relation on ]R^ as defined in Theorem 2 (it is dif ferent for x£XSP) we cannot get 1) to 3) by direct application of this theorem although the arguments of the proof are essen tially the same.

1) follows immediately from the definition. n

To prove 2), let x^,...,xn €X, x= Z aix i' ais0' Ea^=1 and assume xgRfx^ for all i. This implies s(x^)x<1 and, by the axiom, s(x)x^>1 for all i. Summing up, we obtain

n

s(x)x= E a.s(x)x.>1, which is a contradiction to the budget i=1 1 1 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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n

identity. Therefore, x€ U R(x.). i=1 1

If y£R(x) then s(x)y<1. The axiom implies s(y)x>1, i.e. x€R(y). By definition, this means that R is complete.

To prove 4), let x,y€X such that y<x. s(x)CP implies s (x) y<s (x) x=1 , i.e. ygR(x) .

Assume now x,y€R(z) for all zG[x,y] and x^y. Choose two points x',y'e]x,y[ such that x'^y'. Since x€R(x') and y€R(x')f it follows s(x')x>1 and s(x')y>1. But x'€]x,y[ and s(x')x'=1 implies s(x')x=s(x')y=1, i.e. s(x')[x,y]=1 and therefore s(x')y'=1.

By the same argument we obtain s(y')x'=1. The axiom implies x 1= y ' which contradicts the assumption x'^y', i.e. we have proved 5).

It remains to show that f is derived from R on X, i.e. that f(p) is the unique R-best element in B (p) for each p.

If x€X such that px<1 and s(x)f(p)<1, the axiom implies X x=f(p), i.e. s(x)f(p)=1. Therefore s(x)f(p)s1 for all x€B (p),

X i.e. f(p) is an R-best element in B (p).

It follows from 5) that f(p) is the unique R-best element

in BX (p). Q.E.D.

This theorem corresponds to an analogous result for demand functions satisfying the strong axiom of revealed preference

which is stated as Theorem 1 in L.Hurwicz and M.K.Richter (1971), and where a convexity assumption on the range is also needed.

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5. Concluding remarks

While the examination of the weak axiom in Section 3 has led to a satisfactory characterization we cannot claim the same for the results of Section 4. Theorem 3 characterizes demand func tions satisfying the axiom essentially by properties of the re vealed preference relation which is too small to meet the de sired requirements discussed above. To put it differently, this theorem is almost a reformulation of the definition.

On the other hand, the weakness of Theorem 4 is that it only proves the existence of a nice representing preference relation

l

on a subset of ]R+ . Moreover we need a convexity assumption on the range of the demand function.

Nevertheless, the result is related to the conjecture of Kihlstrom, Mas-Colell, Sonnenschein, and Shafer (1976). This conjecture claims that continuous demand functions satisfying the axiom can be represented by a nontransitive consumer in the sense of Shafer (1974), i.e. they are derived from a complete,

a continuous and strongly convex preference on 1R+ .

By Theorem 4, we have almost shown the corresponding state ment for the noncontinuous case if the demand function is sur jective. The representing preference is complete, upper continu ous and has some properties comparable to strong convexity (of course, it cannot be continuous since this would imply continu ous demand which we do not assume).

In other words, if a demand function with convex range X satisfies the axiom, it can be represented by some kind of a noncontinuous nontransitive consumer with consumption set X.

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Modifications of the example given in the previous section indicate that one cannot hope to get much better results without assuming continuity. But avoiding the convexity assumption and

9

obtaining a representing preference on the whole set IR+ seems to be possible for the continuous case which we shall examine in a subsequent paper. © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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References

HILDENBRAND,W. : "On the 'Law of Demand"', E c o n o m e t r l c a 51 (1983), 997-1019

HURWICZ,L. and M.K.RICHTER: "Revealed Preference Without Demand Continuity Assumptions", in Pref e r e n c e * , U t i l i t y , a n d D e m a n d , ed. by J.S.CHIPMAN, L.HURWICZ, M.K.RICHTER, and H.F.SONNEN- SCHEIN, New York: Harcourt Brace Jovanovich, 1971

KIHLSTROM,R., A.MAS-COLELL, and H .SONNENSCHEIN: "The Demand

Theory of the Weak Axiom of Revealed Preference", E c o n o m e t r i c a 44 (1976), 971-978

LENNINGHAUS,J.: "On a Market Demand Function Satisfying the Weak but not the Strong Axiom of Revealed Preference", E c o n o m i c s

L e t t e r * 14 (1984), 149-153

SHAFER,W.J.: "The Nontransitive Consumer", E c o n o m e t r i c a 42 (1974), 913-919

SONNENSCHEIN,H.F.: "Demand Theory Without Transitive Preferences, with Applications to the Theory of Competitive Equilibrium", in P r e f e r e n c e * , U t i l i t y a n d D e m a n d , ed. by J.S.CHIPMAN,

L.HURWICZ, M.K.RICHTER, and H .F .SONNENSCHEIN, New York: Harcourt Brace Jovanovich, 1971

RICHTER,M.K.: "Revealed Preference Theory", E c o n o m e t r i c a 34 (1966), 635-645

RICHTER,M.K.: "Rational Choice", in P r e f e r e n c e * , U t i l i t y a n d D e m a n d , ed. by J.S.CHIPMAN, L.HURWICZ, M.K.RICHTER, and H.F.SONNENSCHEIN, New York: Harcourt Brace Jovanovich, 1971

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10 :Kumaraswamy VELUPILLAI When Workers Save and Invest: Some Kaldorian Dynamics

11:Kumaraswamy VELUPILLAI

i

A Neo-Cambridge Model of Income Distribution and Unemployment

12:Kumaraswamy VELUPILLAI/ Guglielmo CHIODI

On Lindahl's Theory of Distribution

13:Gunther TEUBNER Reflexive Rationalitaet des Rechts 14:Gunther TEUBNER Substantive and Reflexive Elements in

Modern Law © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research

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PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE July 1984

15:Jens ALBER Some Causes and Consequences of Social

Security Expenditure Development in Western Europe, 1949-1977

16:Ian BUDGE Democratic Party Government: Formation

and Functioning in Twenty-One Countries

17:Hans DAALDER Parties and Political Mobilization: An Initial Mapping

18:Giuseppe DI PALMA Party Government and Democratic

Reproducibility: The Dilemma of New Democracies

19:Richard S. XATZ Party Government: A Rationalistic Conception

20 :Juerg STEINER Decision Process and Policy Outcome: An Attempt to Conceptualize the Problem at the Cross-National Level

21:Jens ALBER The Emergence of Welfare Classes in

West Germany: Theoretical Perspectives and Empirical Evidence

22:Don PATINKIN Paul A. Samuelson and Monetary Theory

23.'Marcello DE CECCO Inflation and Structural Change in the Euro-Dollar Market

24:Marcello DE CECCO The Vicious/Virtuous Circle Debate in the '20s and the '70s

25:Manfred E. STREIT Modelling, Managing and Monitoring Futures Trading: Frontiers of Analytical Inquiry

26:Domenico Mario NUTI Economic Crisis in Eastern Europe - Prospects and Repercussions

27:Terence C. DAINTITH Legal Analysis of Economic Policy 28:Frank C. CASTLES/

Peter MAIR

Left-Right Political Scales: Some Expert Judgements

29:Karl HOHMANN The Ability of German Political

Parties to Resolve the Given Problems: the Situation in 1982 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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if: \HOHWAO cam oriT: ^

30:Max KAASE The Concept of Political-Culture : Its

Meaning for Comparative Political Research

31:Klaus TOEPFER

32:Ronald INGLEHART

33:Moshe LISSAX

34:Jean-Paul FITOUSSI

Possibilities and Limita^i.qns. ,,of a Regional Economic Development Policy in the Federal Republic of Germany

3-L IMlHUTHSV B'lbhfisaslA:

The Changing Structure of Political Cleavages Among West European Elites and Publics

’ MIWGOOD A b'lBdoi)!: Tl Boundaries and Institutional Linkages Between Elites: Some Illustrations

L u u o u j - •- t. a U . O P from Civil-Military Elites, in Israel Modern Macroeconomic Theory: An Overview

*3

ff j ry[

35:Richard M. GOODWIN/ Kumaraswamy VELUPILLAI

Economic Systems and their Regulation

i-ti" ÎJJ3TTSQ3WS8 .A omiaasM:0$ 36:Maria MAGUIRE 3 7 :G. LOWELL FIELD/ John HIGLEY 38:Dietrich HERZOG . '103 & “1.0 V.S i_i

The Growth of Income Maintenance Expenditure in Ireland, 1951-1979

The States of National Elites and the Stability of Political Institutions in 81 Nations, 1950-1982, „ s

i/nsqnoO 'io

New Protest Elites in the Political System of West Berlin; The Eclipse of Consensus?

39 :Edward 0. LAUMANN/ David KNOXE

A Frajnework for Concatenated Event Analysis

40:Gwen MOOR/ Richard D. ALBA

Class and Prestige Origins in the American Elite

41:Peter MAIR Issue-Dimensions and Party Strategies

in the Irish republic, 1948-1981: The Evidence of Manifestos

42:Joseph H.H. WEILER Israel and the Creation of a Palestine State. The- Art of the Impossible and the Possible

43:Franz Urban PAPPI Boundary Specification and Structural Models of Elite Systems: Social Circles Revisited © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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.1 I A

-PUBLICATIONS OF THS EUROPEAN UNIVERSITY INSTITUTE July 1934

44:Thomas GAWRON/ Ralf ROGOWSKI

Zur Implementation von

Gerichtsurteilen. Hypothesen zu den Wirkungsbedingungen von Entscheidungen des Bundesverfassungsgerichts

45:Alexis PAULY/ René DIEDERICH

Migrant 'Workers and Civil Liberties

46 : Alessandra VENTURINI Is the Bargaining Theory Still an Effective Framework of Analysis for Strike Patterns in Europe?

47:Richard A. GOODWIN Schumpeter: The Man I Knew 48 :J .P . FITOUSSI/

Daniel SZPIRO

Politique de l'Emploi et Réduction de la Durée du Travail

49: Bruno DE WITTE Retour à Costa. La Primauté du Droit Communautaire à la Lumière du Droit

International

50:Massimo A. BENEDETTELLI Eguaglianza e Libera Circolazione dei Lavoratori: Principio di Eguaglianza e Divieti di Discriminazione nella Giurisprudenza Comunitaria in Materia di Diritti di Mobilità Territoriale e Professionale dei Lavoratori

51:Gunther TEUBNER Corporate Responsability as a Problem of Company Constitution

52:Erich SCHANZE Potentials and Limits of Economic

Analysis: The Constitution of the Firm 53:Maurizio COTTA Career and Recruitment Patterns of

Italian Legislators. A Contribution of the Understanding of a Polarized System

54:Mattei DOGAN How to become a Cabinet Minister in Italy: Unwritten Rules of the Political Game

55:Mariano BAENA DEL ALCAZAR/ Narciso PIZARRO

The Structure of the Spanish Power Elite 1939-1979

56:Bere RUSTEM/

Xumaraswamy VELUPILLAI

Preferences in Policy Optimization and Optimal Economic Policy

57:Giorgio FREDDI Bureaucratic Rationalities and the

Prospect for Party Government

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59 :Christopher Hill/ James MAYALL 60:Jean-Paul FITOUSSI ôlrPhilippe LEFORT 6 2 :Peter BROCXMEIER 6 3 :Hans-Martin PAWLOWSKI 64:MarceIlo DE CECCO 65:Gianpaolo ROSSINI 66:Wolfgang GEBAUER

The Sanctions Problem: International and European Perspectives

Adjusting to Competitive Depression. The Case of the Reduction in Working Time

Idéologie et Morale Bourgeoise de la Famille dans le Ménager de Paris et le Second Libro di Famiglia, de L.B. Alberti

Die Dichter und das Kritisieren Law and Social Conflict

Italian Monetary Policy in the 1980s Intraindustry Trade in Two Areas: Some Aspects of Trade Within and Outside a Custom Union

Euromarkets and Monetary Control: The Deutschemark Case

6 7 :Gerd WEINRICH On the Theory of Effective Demand un der Stochastic Rationing

68 :Saul SSTRIN/ Derek C. JONES

The Effects of Worker Participation upon Productivity in French Producer Cooperatives

69: Bere RUSTEM

Xumaraswainy VELUPILLAI

On the Formalization of Political. Preferences: A Contribution to the Frischian Scheme

70:Werner MAIHOFER Politique et Morale

71:Samuel COHN Five Centuries of Dying in Siena:

Comparison with Southern France

72:Wolfgang GEBAUER Inflation and Interest: the Fisher Theorem Revisited

7 3 :Patrick NERHOT 7 4 :Philippe SCHMITTER

75:Sheila A. CHAPMAN

Rationalism and the Modern State

Democratic Theory and Neo-Corporatist Practice

Eastern Hard Currency Debt 1970-83. An Overview © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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-6-PÜBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE July 1984

76:Richard GRIFFITHS

77:Scott NEWTON

Economic Reconstruction Policy in the Netherlands and its International Consequences, May 1945 - March 1951 The 1949 Sterling Crisis and British Policy towards European Integration 78:Giorgio FODOR Why did Europe need a Marshall Plan in

1947?

79:Philippe MIOCHE The Origins of the Monnet Plan: How a Transistory Experiment answered to Deep-Rooted Needs

80:Werner ABELSHAUSER The Economic Policy of Ludwig Erhard 8 1 :Helge PHARO

82 :Heiner R. ADAMSEN

The Domestic and International

Implications of Norwegian

Reconstruction

Investitionspolitik in der

Bundesrepublik Deutschland 1949-1951 83:Jean BOUVIER Le Plan Monnet et l'Economie Française

1947-1952 84:Mariuccia SALVATI

85:William DIEBOLD, Jr.

86:Frances LYNCH

Industrial and Economic Policy in the Italian Reconstruction

Trade and Payments in Western Europe in Historical Perspective: A Personal View by an Interested Party

French Reconstruction in a European Context

87:Gunther TEUBNER

88 :Maria SPINEDI

89 : Jelle VISSER

90:Will BARTLETT

Verrechtlichung. Begriffe, Merkmale, Grenzen, Auswege

Les Crimes Internationaux de l'Etat dans les Travaux de Codification de la Responsabilité des Etats Entrepris par les Nations Unies

Dimensions of Union Growth in Postwar Western Europe

Unemployment, Migration and

Industrialization in Yugoslavia, 1958- 1977 © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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91:Wolfgang GE3AUER Xondratieff ' s Long 'Waves 9 2 :Elisabeth DE GHELLINCK/

Paul A. GEROSKI/ Alexis JACQUEMIN

Inter-Industry and Inter-Temporal Variations in the Effect of Trade on Industry Performance

93:Gunther TEUBNER/ Helmut WILLKE

Kontext und Autonomie.

Gesellschaftliche Selbststeuerung durch Reflexives Recht

94:Wolfgang STREECK/ Philippe C. SCHMITTER

Community, Market, State- and Associations. The Prospective

Contribution of Interest Governance to Social Order

9 5 :Nigel GRIFFIN "Virtue Versus Letters": The Society of Jesus 1550-1580 and the Export of an Idea

96:Andreas KUNZ Arbeitsbeziehungen und

Arbeitskonflikte im oeffentlichen

Sektor. Deutschland und

Grossbritannien im Vergleich 1914-1924 97:Wolfgang STREECX Neo-Corporatist Industrial Relations

and the Economic Crisis in West Germany

98:Simon A. HORNER The Isle of Man and the Channel Islands - A Study of their Status un der Constitutional, International and European Law

99:Daniel ROCHE Le Monde des Ombres

84/100:Gunther TEUBNER After Legal Instrumentalism?

84/101:Patrick NERHOT Contribution aux Débats sur le Droit Subjectif et le Droit Objectif comme Sources du Droit

84/102:Jelle VISSER The Position of Central Confederations in the National Union Movements

84/103:Marcello DE CECCO The International Debt Problem in the Inter-War Period

84/104:M. Rainer LEPSIU3 Sociology in Germany and Austria 1918- 1945. The Emigration of the Social Sciences and its Consequences. The

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PUBLICATIONS OF THE EUROPEAN UNIVERSITY INSTITUTE November 1984

Development of Sociology in Germany after the Second World War, 1945-1967 84/105:Derek JONES The Economic Performances of Producer

Cooperations within Command Economies: Evidence for the Case of Poland

84/106:Philippe C. SCHMITTER Neo-Corporatism and the State

84/107:Marcos BUSER Der Einfluss der Wirtschaftsverbaende auf Gesetzgebungsprozesse und das Vollzugswesen im Bereich des Umweltschutzes

84/108:Frans van WAARDEN Bureaucracy around the State:Varieties of Collective Self-Regulation in the Dutch Dairy Industry

84/109:Ruggero RANIERI The Italian Iron and Steel Industry and European Integration

84/110:Peter FARAGO Nachfragemacht und die kollektiven

Reaktionen der Nahrungsmittelindustrie 84/111:Jean-Paul FITOUSSI/

Kumuraswamy VELUPILLAI

A Non-Linear Model of Fluctuations in Output in a Mixed Economy

84/112:Anna Elisabetta GALEOTTI Individualism and Political Theory 84/113 : Domenico Mario NUTI Mergers and Disequilibrium in Labour-

Managed Economies

84/114:Saul ESTRIN/Jan SVEJNAR Explanations of Earnings in Yugoslavia: The Capital and Labor Schools Compared

84/115:Alan CAWSON/John BALLARD A Bibliography of Corporatism

84/116:Reinhard JOHN On the Weak Axiom of Revealed

Preference Without Demand Continuity Assumptions © The Author(s). European University Institute. Digitised version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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