Table Of ContentLecture Notes in Economics and Mathematical Systems 672
Alexander P. Abramov
Balanced and
Cyclical Growth
in Models of
Decentralized
Economy
Lecture Notes in Economics
and Mathematical Systems 672
FoundingEditors:
M.Beckmann
H.P.Künzi
ManagingEditors:
Prof.Dr.G.Fandel
FachbereichWirtschaftswissenschaften
FernuniversitätHagen
Hagen,Germany
Prof.Dr.W.Trockel
MuratSertelInstituteforAdvancedEconomicResearch
IstanbulBilgiUniversity
Istanbul,Turkey
and
InstitutfürMathematischeWirtschaftsforschung(IMW)
UniversitätBielefeld
Bielefeld,Germany
EditorialBoard:
H.Dawid,D.Dimitrov,A.Gerber,C-J.Haake,C.Hofmann,T.Pfeiffer,
R.Slowin´ski,W.H.M.Zijm
Forfurthervolumes:
http://www.springer.com/series/300
Alexander P. Abramov
Balanced and Cyclical
Growth in Models
of Decentralized Economy
123
AlexanderP.Abramov
DorodnicynComputingCentreofRAS
RussianAcademyofSciences
Moscow
Russia
ISSN0075-8442 ISSN2196-9957(electronic)
ISBN978-3-319-07916-5 ISBN978-3-319-07917-2(eBook)
DOI10.1007/978-3-319-07917-2
SpringerChamHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2014944557
©SpringerInternationalPublishingSwitzerland2014
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To
MyParents
andto
Anna,Nikolai,Denis,and Olga
Preface
Thisbookisdevotedtothemathematicalmodelingofthedynamicsofdecentralized
economicsystems.Theauthorbecameinterestedinthistopicwhileanalyzinggov-
ernmenteconomicregulationmethodsincountrieswithpredominantlycentralized
management.Asitturnedout,insuchcountries,a significantpartofmanagement
decisions related to economics is made at the local level. This can be explained
by the fact that—contrary to what the authorities might wish for—any modern
economy,beingaverycomplexsystem,cannotfunctioninasatisfactorywayunder
totally centralized management. The range of products being enormous and the
networkofproductionandconsumptionrelationsbeingextremelylarge,itissimply
notpossibletomanageeverythingfromasinglecontrolcenter.Asaresult,evenin
countriesthatemploytotalitariangovernmentmethods,partofeconomicdecisions
aredelegatedtothelevelofindustrialsectorsoreventothelevelofenterprises.
On the other hand, the complete economic autonomy of economic agents is a
key propertyof any market economy.In the modern world, this type of economy
has been embraced by most countries, which allows them—despite a number of
problemsthatremainunresolved—tofurtherscientificandtechnologicaladvances
andimprovethequalityoflifefortheirresidents.Atthesametime,intheauthor’s
opinion,theimpactofthedecentralizedmanagementfactoroneconomicdynamics
isyettoreceivedueattentionfromtheresearchcommunity.
Thefieldrelatedtotheuseofmathematicalmethodsforstudyingdecentralized
economic systems is extremely broad, but the author selected a relatively narrow
subfield,onededicatedtotheexistenceofandreachingbalancedgrowthinmodels
of systems that use Leontief technologies. A presentation of the results obtained
while studying this subfield constitutes most of this book. However, the author
remainedsomewhatunsatisfiedwithsomeoftheassumptionsmadewhilebuilding
the models. An attempt was made to move the assumptions closer to the real
economicworld.Intheresulting,modifiedmodels,someoftheeconomicindicators
showedanasymptotictendencytocyclicity.Thisbooksalsocontainsananalysisof
thedynamicsofthesemodels.
It should be stressed that all the considered models are extremely simplified
representationsofreal-worldeconomicprocesses.Nevertheless,theobtainedresults
vii
viii Preface
allow the author to put forward the following bold hypothesis: Decentralized
systemsshouldbeconsideredfromtheperspectiveofcyclicaldynamicsratherthan
thatofbalancedgrowth.
As noted above, modern economic systems are extremely complex. However,
thehistoryofmathematicaleconomicstellsusthatsomeoftheaspectsofeconomic
life can be studied successfully provided that an appropriate mathematical model
is developed. The author hopes that this book will help draw the attention of the
research community to the important topic of using mathematical methods for
studyingthedynamicsofdecentralizedeconomicsystems.
It is presumed that the reader is familiar with basic matrix analysis methods.
Nevertheless, the book includes a brief overview of the propertiesof nonnegative
matrices,whichcanbereferredtowhenreadingthemainchaptersofthebook.
This book will be of interest to professionals studying the dynamic models of
economic systems. It may also be of help to senior undergraduate students and
graduatestudentsstudyingtheapplicationofmathematicalmethodsineconomics.
TheauthorwouldliketothanktheRussianFoundationforBasicResearchforits
financialsupport(projectsno.07-07-104,10-07-00286,and13-07-00730).
Moscow,Russia AlexanderP.Abramov
April2014
Contents
1 Introduction .................................................................. 1
References..................................................................... 6
2 BalancedGrowthinDecentralizedEconomies........................... 7
2.1 ModelDescription ...................................................... 8
2.2 PlanningBasedonProfitMaximization ............................... 15
2.3 PaymentBalancesofSectors........................................... 20
2.4 CounteractingDecreasesinProfit...................................... 23
2.5 PersonalizedPricesforConsumers .................................... 26
2.6 AveragePricesandPersonalizedDiscounts ........................... 33
2.7 GeneralizedPriceFormula ............................................. 36
References..................................................................... 40
3 TransitiontoBalancedGrowth............................................. 41
3.1 BasicAlgorithmforTransitiontoBalancedGrowth.................. 42
3.2 DynamicsofDualVariables............................................ 51
3.3 AutonomousEstimatesoftheExpansionRate........................ 54
3.4 Demand-BasedPlanning................................................ 57
3.5 ForwardandCurrentPlanning ......................................... 59
3.6 UnbalancedSupplyofResources ...................................... 61
3.7 AgreeingonEstimatesoftheExpansionRate......................... 68
3.8 TheBasicTransitionAlgorithmandtheMIMModel................. 72
References..................................................................... 78
4 TheFinanceoftheTransitionPhase....................................... 81
4.1 TransitiontoBalancedGrowthBasedonFinancialIndicators....... 82
4.2 TheDynamicsofBasePrices .......................................... 86
4.3 TheAsymptoticBehaviorofPaymentBalances ...................... 90
4.4 PaymentBalancesandSelf-Financing................................. 95
References..................................................................... 98
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