EXPLORING SPATIO-TEMPORAL DYNAMICS IN ECONOMIC EXCHANGE:
A DYNAMIC MODELING APPROACH
MATTHIAS RUTH
Center for Energy and Environmental Studies
and the Department of Geography
Boston University
675 Commonwealth Avenue
Boston, MA 02215
mruth@bu.edu
http://cees-server.BU.edu/readmoreMR. html
Introduction
Economics is a discipline rich in models designed to elucidate the behavior of
potentially complex economic processes. The reduction of complex processes to
analytically solvable models, however, shifted focus away from the spatio-temporal
dynamics representative of economic processes, and excluded to a significant extent
experimentation from the repertoire used to understand these processes (Allen 1988, Ruth
1993).
In the illustrations below, special attention is given to three issues that are found at
the sidelines of traditional economic analysis (Hannon and Ruth 1994, Ruth and Hannon,
in press). The first of these issues concerns the dynamics of economic systems on their
way to equilibrium points. The second is the spatial context within which economic
activity takes place. The third are temporal and spatial discontinuities of economic
processes.
Three models of simple exchange economies are developed that illustrate the role of
spatio-temporal dynamics and the contribution dynamic modeling can make to the
understanding of economic processes. Conclusions are drawn for new ways of exploring
the fundamental principles that underlie potentially complex economic processes, for model
development and experimentation, and for teaching economics.
Models
Dynamic Edgeworth Model
The first of the models of economic exchange is based on a traditional economic
model of two players who engage in barter trade with each other. In contrast to the
traditional Edgeworth model dealing with the two-player barter economy, it is assumed that
the utility U derived from two goods X and Y that are exchanged between players A and B
is a function of the goods that have been accumulated at a given time period T:
Yu
Oi
Bi
» +8) S1Vi=A,B
7
Ui -[{ Xjidt
0
7
{ Yidt
Exchange quantities per time period are assumed to be proportional to the change in utility.
Given these simplified assumptions, several cases are explore—including envy and
altruism. It is shown that even in the absence of discounting, the assumptions on the
players’ preferences influence the speed at which an equilibrium is reached.
Discontinuities and Chaos
The second model captures dynamics of supply-demand interactions on markets
and exhibits potentially chaotic behavior. The demand curve is a linear function of
observed prices P(t)
QW = D(P(t)) = A - B*P(t)
The supply curve, in contrast, is the
nonlinear function in expected prices P’(t)
shown in the figure to the right. Price
expectations P’(t+1) are formed as a
linear combination of actual and expected
prices:
P’(t+1) = (1-W) * P’(t) + W * P(t)
The following price path results:
P(tel) = (L-W) * P) - ABW 4 w+ SEO) Th a
7
iP ; I: Py. PT-DT
0.504- .
|
0.00 555 30°00 60.00 9000 1200 0.50 F359 O75 7.00
4
Time
Alternative values of W result in damped oscillations, oscillations with one, two and higher
periods, and ultimately chaos which is shown in the two figures above. Despite the
simplicity in its assumptions, the model exhibits a wide range of behaviors that vividly
Ur
contrast the traditional equilibrium notion, and invites experimentation into the analysis of
market mechanisms. .The number of questions that can be answered through this
experimental approach is large, and so is the opportunity to use dynamic modeling to
explore the behavior of systems of economic exchange.
Spatio-Temporal Dynamics in Economic Exchange
The third model demonstrates the use of cellular automata (von Neumann 1966) to
capture economic system behavior in space and time. It does not assume that a single
market exists, nor that the players have perfect knowledge who the potential trading
partners are, where they are located and at what price they are willing to exchange their
goods and services. Thus, this model describes an extreme case of market exchange to
provide a contrast to the traditional models.
Players in the core of the 1: Corner Location 3: Center
economic landscape enjoy a higher 28 ie lL
likelihood of encounters with their
neighbors. As expected, the number of
140]
encounters declines towards _ the
periphery. The average number of
encounters per time period follows a 0 Oki) 5 7501000
ime
random walk. If trading partners retain 4.7 Average Number.of Encounters,
knowledge of their past trading partners ‘
and preferentially seek out those partners pin A, an f 4 pn ‘yl
with whom they happened to “meet” 2 ‘a hoo ott EE
more frequently, the system tends to . - ‘
settle down in the long-run. The case
04
: B . 500. . .00
shown here of zero knowledge retention Time
and of exchange with only close
neighbors is a special case of high discounting in space and time—assumptions that can be
easily relaxed to investigate the dynamics of a large set of real-world spatial exchange
processes.
Conclusions
Models are the basis of every-day life decision making and are an integral part of
any scientific inquiry. They provide the basis for assembling, communicating and
evaluating information, for assessing cause-effect relationships and for generating
le
knowledge. The three models developed in this paper provide examples of a specific type
of models—causal models developed to illucidate the dynamics of economic exchange
processes. The first of these models is based on a traditional economic model of two
players who engage in barter trade with each other. Even in the absence of discounting, the
assumptions on the players preferences are found to influence the speed at which an
equilibrium is reached. The second model captures dynamics of supply-demand
interactions on markets with price expectations and exhibits potentially chaotic behavior.
The third deals with economic exchange that is not coordinated by markets or contractual
agreements. This model demonstrates the use of cellular automata to capture system
behavior in space and time.
Each of the models described in the paper have been designed to capture dynamics
of economic exchange. Each of them tells a story that enriches our intuition and knowledge
of economic exchange processes irrespective of the precise numerical values generated by
these models. They are heuristic devices that help us visualize the implications of
behavioral assumptions on the dynamics of an economic system.
Developing and running these models has learning as a desired result, rather than
numeric predictions. The former is a prerequisite for the latter as it encompasses the
generation of knowledge—rather than derived facts; it is also an essential prerequisite for
decision-making in an ever-changing world. The dynamic modeling approach, and the
models used here to illustrate it, is gradually beginning to open the doors for
experimentation in economics, to reduce the use of mechanistic assumptions and models in
what is in essence a behavioral science, and to instill in a new generation of decision
makers an appreciation of potentially complex spatio-temporal system dynamics.
References
Allen, P.M. 1988. Evolution, Innovation and Economics, in G. Dosi, C. Freeman, R.
Nelson, G. Silverberg, and L. Soete (eds.) Technical Change and Economic
Theory, Pinter Publishers, London, New York, pp. 95 - 119.
Hannon, B. and M. Ruth. 1994. Dynamic Modeling, Springer-Verlag, New York.
Ruth, M. 1993. Integrating Economics, Ecology and Thermodynamics, Kluwer
Academic Publishers, Dortrecht, The Netherlands.
Ruth, M,. and B. Hannon. in press. Modeling Dynamic Economic Systems, Springer
Verlag, New York.
von Neumann, J. 1966. Theory of Self-Reproducing Automata, University of Llinois
Press, Chicago, Illinois.
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