Modeling Foundations of Economic Property Rights Theory: An Axiomatic Analysis of Economic Agreements

248 Pages·2005·1.94 MB·English

by  Vesna Pasetta

Studies in Economic Theory
Editors
Charalambos D.Aliprantis
Purdue University
Department ofEconomics
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USA
Nicholas C.Yannelis
University ofIllinois
Department ofEconomics
Champaign,il61820
USA
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Mathematical Methods in Economics
and Social Choice
Vesna Pasetta
Modeling Foundations
of Economic Property
Rights Theory
An Axiomatic Analysis
of Economic Agreements
With 38 Figures
and 5 Tables
123
Professor Vesna Pasetta
EPRSA
PO Box 4242
Ithaca NY 14852
USA
E-mail:[email protected]
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To my father Franc, who taught me to embrace life, and
both of my mothers – Toncka , who gave me life, and
Ljudmila, who saw me through it.
Preface
This is an introduction to the foundations of economic property rights the-
ory (EPRT). In this volume, a first step in the EPRT research program, rules
concerningeconomicpropertyrights(e.p.r.s),entrepreneurialagreements,and
enterprises are discussed. Introduced concept of e.p.r.s is an extension of the
traditional concept of pairing of residual rights of control and residual rights
of returns in the economic theory. Its importance in economics is generated
fromageneralimpossibilityofmakingacompletecontract,concerninge.p.r.s,
for any nontrivial economic transaction. The volume offers a theoretical ex-
tension of mathematical economics, applying recent results of Hopf algebras,
quasi-Hopfalgebras,representationtheory,theoryofcategories,anddeforma-
tion theories, in looking for suitable mathematical methodology of economic
property rights theories and foundations of general theory of economic agree-
ments. The idea is to construct a kind of mathematical application in which
any fundamental formal entity and/or operation has an empirical economic
interpretation. This approach is seen as a way to cope with an extreme com-
plexity of economic phenomena under consideration and requests for precise
formulationofmodelswheremeaningfulanswersandsolutionsofproblemsare
only those which are obtained rigorously. The proposed extensions in math-
ematical economics and property rights theory are to provide rich enough
foundations to follow complexity of economic property rights in the exact
way, and to identify where there is an appropriate method providing ade-
quate solution, and also to find problems where in general there is no such
methodology.
The program of EPRT is addressed primarily toscientists and researchers
wishing to beginworkonissuesofeconomicpropertyrightsandeconomic in-
stitutions.Forthosewithlessformalmathematicalbackground,theintention
is to provide full details and line-by-line proofs of all basic relations that are
needed for research in the field. The hope is that unessential formalism has
been avoided. For those more interested in this application of mathematics,
mathematical economics and OR, I have adopted a theorem-proof schema,
VIII Preface
tryingnottoproposeeconomicstatementsthatarenottechnicallycorrect,so
that the main results can be understood clearly. The intention is to achieve
thebalancebetweenreadabilityandrigorousformalitybytakingacompletely
algebraic approach in this volume. Discussions on the equally interesting ver-
sions of e.p.r.s institutions applying methodologies of C∗-algebras and other
algebrashavebeenleftforvolumeII,whilethosefocusingonnoncommutative
probabilitytheory,braidingstatistics,stochasticmodelsonpatternsofe.p.r.s
flows, and stochastic calculus of institutions in general, are left for volume
III. In other words, in this volume the algebraic approach is applied in for-
mulation of EPRT, while the functional-analytic and stochastic approaches
to EPRT are explored in the next two volumes. Note that it is not a survey,
thusmanyinterestingissuesandmethodologicalproceduresarenotdiscussed
in any detail. Such as, for example, issues primarily linked to the political
economy, law and legislative institutions, and particular forms of economic
rights(intellectualpropertyrights,particularsecurities,wagecontracts,some
elements from warranties, inheritance, parenthood, or many other forms of
concrete types of economic contracts).
The fundamentals of mathematical economics in which concepts of the
super-micro-economic analyses of economic property rights have their begin-
nings are over fifty years old; von Neumann (1928, 1937) [58], Kantorovich
(1948) [39], Neumann and Morgenstern (1944) [59], Koopmans (1950) [41],
Allias (1943) [6], Nash (1950) [56], Meade (1965) [50], and many others that
have contributed to mathematical economics, game theory, and mathemati-
cal models of decision making, artificial intelligence and the reliability of ex-
pert systems. It is noteworthy that the complexity of the e.p.r.s phenomena,
implying noncommutativity of economic relations, imposes an extension of
mathematicaltoolsappliedtoeconomics.Thecommutativityconditionswere
defined and discussed by the founders of the game theory in economics von
Neumann and Morgenstern [59]. Later on, these issues have been considered
by many others, although, more often analyzing the economic and behavioral
consequencesofaviolationoftheseconditionsthanaddressingthemdirectly.
Recall that the simplest form of the noncommutativity is that of the zero-
sum games without a unique saddle-point and/or games of mixed strategies.
Moreover,theyconcernmoderneconomictheoriesandalsorapidlydeveloping
ones, and in the applications of our concern one may think of two essential
points for the extension:
(1) The existence of many natural economic spaces for which the tradi-
tionalset-theoreticaltoolsofanalysisarenotsophisticatedenoughtocapture
economic phenomena of concern. One may recall that within the frame of
Euclidean geometry, combined with symmetries and linear spaces, and with
traditional pointwise multiplication and addition, many important classes
of functions applied in economics can be modeled. Having on hand the
Grothendieck’s algebraic geometry, via the notion of affine scheme, one can
show that there is no need, in general, to ask anything more. However, one
Preface IX
can ask less, particularly concerning underlying economic axioms. From for-
malpointofviewthisleadsverynaturallytoanoncommutativealgebra.Such
spaces arise in mathematics (see Connes [23] for example), and in other ap-
pliedsciences,butherewearefocusedontheirapplicationsineconomicsand
inparticulartoe.p.r.sissues.Theseseemtogiveanewoutlooktoboth,quite
traditional and modern topics in economics.
(2) The extension of the traditional tools of mathematical economics involves
an algebraic reformulation where passing from the commutative to the non-
commutativesettingisalmostneverstraightforward.Ititselfoffersaninsight
intocompletelynewphenomenaarisinginthemorecomplexeconomicissues.
So, it seems to open a possibility for identifying the existence of a concept of
thecanonicalevolutionforcomplicatedeconomicfactors(asintangibleassets
for example), that are particularly important for understanding and formula-
tion of dynamics in economics. One should also have in mind that developing
a theory in the noncommutative framework leads to a new point of view,
andnewtoolsapplicabletothetraditionaleconomicphenomena,(suchasthe
proceduresoncycliccorrespondenceofstructureandpropertiesofcopartners,
and advanced differential calculus), which unlike the theory of distributions
seem to be particularly interesting and naturally adoptable to economic ap-
plications.
Apart from the above mentioned, modern computational devices, com-
munications, information and new technologies and algorithms involved have
extendeddomainsofeconomics.Theneweconomictheoriesandexperimental
approacheshavebecomeavailabletakingintoaccountideasincorporatedinto
the concepts of data compression, superdense coding, information transmis-
sion and entanglement concentrations. These exemplify nontrivial extensions
of traditional economic relations between agents, and how modern market
channels, implying modern communication and computation devices, can be
used, alone or combined with classical market channels, to transmit tradi-
tionalmarketaswellasanyotherinformation.Morerecentlyadditionalcom-
putational procedures based on so called super-computers and those that are
within experimental phase, have opened possibilities of extremely precise for-
mulation, experimentation and controllability of data entanglements. These
should enable one to substitute uncertain channels of economic transactions
for certain ones in these applications. Naturally, there are issues that are to
be clarified and corresponding procedures in calculations improved. For ex-
ample, questions of finding exact expressions, rather than upper and lower
bounds, for the traditional and more advanced unconventional securities still
appeartobeopenandcallforfurtherresearchinadvancedriskmanagement,
informational economics and economics of intangibles. It is noteworthy that
recent results in variety of applied sciences on their R&D programs, com-
munications and technological developments have imposed the importance
of the economic property rights phenomena in economics more openly and
directly. Here, modern communication and information technologies make it
X Preface
possible to capture an e.p.r.s effect that plays a central role in the enlarged
concept of economic information theory. It is complementary in several re-
spects to the role of traditional concept of market information in economics
and is discussed and promoted in the sequel to this volume. Namely, the in-
troduced concept of an entrepreneurial e.p.r.s provides ability of connecting
different types of e.p.r.s institutions and/or clubs, characterized by different
appropriationrules.Itmaybenoteworthythatthesemaydiffersubstantially.
The introduced concept of e.p.r.s entanglement provides somehow extraordi-
nary properties of control of information in an economic transaction. It plays
a significant role in a better understanding of intrinsic security of informa-
tion concerning economic transactions, for example. The idea is that e.p.r.s
informationcanneitherbereproducednorcanwealthbetransferred,manipu-
lated,cheatedoreavesdroppedwithoutbeingidentifiedbymembersofaclub.
At the same time these transactions cannot be an object of only traditional
market transactions. Ordinary market information, by contrast, is available
to any agent in the market, in general, and can be replicated, reproduced
and/or copied at will with or without costs. To ensure privacy of economic
transactions and/or protect “business secrets” traditional economic concept
implies an institutional formation concerning externalities somehow out of
economic domain. Such an approach implies a paternalistic structure of the
economic agreements that are to follow, and agents are supposed to count on
ane.p.r.sprotectionbysome,out-off-economics,legislativeregulativeinstitu-
tions. This appears to lack a full economic argumentation, at least from the
EPRT point of view where transaction costs could not be ignored. Contrary
to the traditional market approach, here one bases security and/or privacy
of economic transactions on the fact that an e.p.r.s agreement among agents
contains: (i) a traditional market communication and transactions of wealth
by linear relations, and (ii) an appropriation operator making e.p.r.s typical
irreversibleeconomicphenomena.Recallthatwithinthetraditionaltheoryof
general economic equilibrium (GET), an appropriation operator is fixed and
is assumed as the pure private relation which makes the theory consistent
on the issue of property rights. On the contrary, the information context of
EPRT, among others things, enables one to distinguish two different natural
economic notions of information: traditional market information on value of
an economic object and an information on an appropriation operator embod-
iedintheobject.Theseissuesandothersoninstitutionalizationareaddressed
in the sequel to this volume.
Theconceptofeconomicpropertyrightsisintuitivelylinkedwitheffective
incentivestocreate,innovate,maintainandimproveeconomicwealthandas-
sets. The traditional economic theories assume, explicitly or implicitly, given
pure private relations or some given fixed structure which makes the particu-
lar case (model) theoretically consistent. In that way these theories actually
avoiddiscussionontheissuesatamoregenerallevel(seeArrow[8]).Theliter-
ature in economics concerned implicitly or explicitly with economic property