POST KEYNESIAN PERSPECTIVES AND COMPLEX ECOLOGIC

POST KEYNESIAN PERSPECTIVES AND COMPLEX ECOLOGIC-ECONOMIC DYNAMICS J Barkley Rosser, Jr James Madison University rosserjb@jmu.edu January, 2010 Abstract: This paper considers the implications of complex ecologic-economic dynamics for three broad, Post Keynesian perspectives: the uncertainty perspective, the macrodynamics perspective, and the Sraffian perspective Catastrophic, chaotic, and other complex dynamics will be seen as reinforcing the conceptual foundations of Keynesian uncertainty Predatory-prey models will be seen as deeply linked to Post Keynesian macrodynamic models Finally, certain cases in ecologic-economic systems will be seen as generating such Sraffian, capital theoretic conundra as reswitching Ecologic-economic models considered besides predator-prey will include fisheries, forestry, lake dynamics, and global climatic-economic dynamics Acknowledgement: I acknowledge valuable input from three anonymous referees I Introduction Post Keynesian economics has been riven by deep splits within its ranks What was arguably its first self-conscious school, the Sraffian (Sraffa, 1960), or neo-Ricardian, school has for all practical purposes been expelled from the group, to the extent that it did not pick up and leave on its own voluntarily, arguably ironic in that it was a friend of that group, Joan Robinson, who has long been reported to have coined the term “postKeynesian.”1 A sign of this expulsion is the absence of any chapters relying on the Sraffian perspective in A New Guide to Post Keynesian Economics (Holt and Pressman, 2001) This group found itself in sharpest conflict with the school that draws on Keynes (1936) to emphasize the role of fundamental uncertainty in economics, with Davidson (1982-83, 1994) being the leading advocate of this view, which has criticized the Sraffian group for its reliance on comparing long-run equilibrium states and downplaying the role of money in the economy Between these two groups has been one that has focused more on specific models of macroeconomic dynamics, or macrodynamics,2 often relying upon nonlinear relations in the economy that can lead to endogenous fluctuations, including of various complex varieties This group often looks to the work of Kalecki (1935, 1971) for its inspiration, although such figures as Kaldor (1940), Goodwin (1951), and even Hicks (1950) played important roles in its development Among those discussing the development of these divisions have been Harcourt (1976), Hamouda and Harcourt (1988), and King (2002) While “post-Keynesian” continues to be used, especially in Great Britain, its use by Paul Samuelson as a label for the neoclassical synthesis has made it somewhat less popular, becoming supplanted largely by “Post Keynesian,” which I shall use in this paper The term “macrodynamics” was first used in print by Kalecki (1935), but it appears that he probably got it from Ragnar Frisch during a 1933 conference of the Econometric Society, and the original Polish version of his paper used a term that is derived from the German konjunctur instead (Sawyer, 1985) While the deepest of these splits are probably unbridgeable, Rosser (2006) has proposed that the fact that each of these approaches can be viewed as drawing partly from or influencing the perspective of complex economic dynamics may provide one way of seeing some degree of unity in the diversity and conflicts between these schools This paper can be seen as a direct extension of this argument, with the focus now being more specifically on ecologic-economic systems and their various forms of dynamic complexity While intellectually there have been influences from ecology onto economics and vice versa in terms of developing complex nonlinear dynamical models, the focus here will be on how combined ecological-economic systems such as fisheries or the global climate-economic system can particularly generate such complex dynamics Such dynamics can be viewed as an ontological foundation of Keynesian uncertainty, given the nature of such complex dynamics.3 This paper will pursue this theme by first reviewing briefly what constitute complex dynamics Then it will focus on ecologic-economic dynamics as a foundation of fundamental uncertainty of the Keynesian sort, including the implications for the broader debates among Post Keynesians Then will be a presentation of the links between complex ecologic and macrodynamic models Finally, it will be shown that capital theoretic paradoxes of the Sraffian sort can arise from complex ecologic-economic systems, with the reminder that these in turn can generate complex dynamics It will conclude by a final consideration of the implications for the relations between the schools of these ideas and arguments Certainly this discussion can be viewed as part of the broader existence of nonlinear systems in many parts of nature and society, although the combined ecologic-economic systems are special because of how often these nonlinear complexities arise out of the human-nature interaction II What Are Complex Dynamics? Asking “what are complex dynamics?” simplifies our discussion somewhat, given the substantial controversies that swirl about the general concept of “complexity,” even if one keeps the discussion strictly to “economic complexity.” The MIT physicist, Seth Lloyd, famously collected at least 45 different definitions of “complexity” (Horgan, 1997, p 303, footnote 11), with many of these involving some form or variation of algorithmic or other computationally related definitions of complexity Some have long advocated the use of such definitions in economics (Albin with Foley, 1996), with a recent upsurge of such advocacy (Markose, 2005; Velupillai, 2005) However, while these approaches may involve more rigorous definitions than other approaches, they are less useful for the analysis of ecologic-economic systems than more explicitly dynamic definitions Indeed, curiously enough, some of the critics of dynamic approaches criticize them precisely because of their dependence on biological analogies and concepts (McCauley, 2004, Chap 9).4 Therefore we shall stick with the definition used by Rosser (1999), which in turn comes from Day (1994) This definition is that a system is dynamically complex if it endogenously does not converge on a point, a limit cycle, or an explosion or implosion.5 This definition provides a reasonably clear criterion for distinguishing dynamical systems in this regard, even if one may have difficulty in determining whether or not a particular real world system meets fulfills it A characteristic of dynamically complex systems as Rosser (2009a) provides a detailed discussion of this controversy, noting that while algorithmic definitions allow for measures of degrees of complexity, they not generally allow for a clear division between complex and non-complex systems unless one defines complex systems as those that are not computable at all Dynamic definitions allow for such a reasonable criterion for useful such economic systems Curiously, Day (2006, p 63) has since moved toward favoring a more general definition of complexity taken from the Oxford English Dictionary: “a group of interrelated or entangled relationships.” While we shall not dispute this, it should be noted that it is not easy to use this definition to distinguish complex from non-complex systems we have defined it here is that they will usually involve some degree of nonlinearity, although the presence of nonlinearity is no guarantee that a system will be dynamically complex This is true for a single equation system, although Goodwin (1947) showed that a system of coupled linear equations with lags might behave in the manner described here as complex, even though the uncoupled, normalized equivalent is nonlinear Such systems were studied by Turing (1952) in his analysis of morphogenesis in complex systems Rosser (1999) characterized this definition as a “broad tent” one, which included within itself “the four C’s,” cybernetics, catastrophe theory, chaos theory, and “small tent” complexity, associated with heterogeneous interacting agents models These four approaches appeared on the scene publicly in turn decade after decade, one after the other, even though the mathematical roots of each had been developing over much longer periods of time going back even from the 19th century (Rosser, 2000, Chap 2) Arguably, the first of these has become folded into the last of these currently, while the other two continue to develop on their own separate paths, with numerous applications in pure biology and ecology Broadly speaking, catastrophe theory studies endogenous discontinuities in certain kinds of dynamical systems that arise as given control variables change continuously,6 while chaos theory focuses on systems that exhibit sensitive dependence on initial conditions, also known as “the butterfly effect.” Regarding the “small tent complexity,” this can be seen as having its origins in certain models from the 1970s (Schelling, 1971; Föllmer, 1974) in which immediate neighbors affect each other without necessarily directly affecting an entire system, even though these local effects Rosser (2007) provides a discussion of how catastrophe theory in particular fell strongly out of favor in economics, even though it provides useful tools for studying important phenomena, with arguments for bringing it back more into use We shall see some of those uses below in this paper can lead to broader systemic effects through complex emergence.7 It would be in the 1990s that there would be a fuller development of such approaches III Complex Ecologic-Economic Dynamics and (Post) Keynesian Uncertainty A The Debate Paul Davidson (1994) is the acknowledged leader of what he calls the “Keynes Post Keynesian” school of economic thought,8 which emphasizes particularly the role of fundamental uncertainty from the work of Keynes (1921, 1936) and also the importance of the role of money in the economy We shall focus here on first of these rather than the second, which has little relationship with ecological economics A long running debate between Davidson (1996) and other Post Keynesians (Rosser, 2001a, 2006) has involved the relationship between complexity theory and the concept of Keynesian uncertainty While Davidson has rejected complexity theory as not providing an ontological foundation for Keynesian uncertainty He argues (1982-83) that the foundation of Keynesian uncertainty is the ubiquity of nonergodicity in economic dynamics, which must be accepted as axiomatically true Others have argued that instead that it is the ubiquity of complex dynamics in economic systems that is the source of this nonergodicity, providing a theoretically and empirically valid foundation for the concept We shall consider some ecologic-economic systems that exhibit forms of dynamic complexity that may imply nonergodic Keynesian uncertainty Indeed, the problem of The concept of “emergence” was developed in the early 20th century in Britain, ultimately drawing on arguments of Mill (1843) This concept has been criticized by some of the computability complexity approach such as McCauley and Markose on grounds that it is not rigorous However, a recent, rigorous mathematical presentation that draws on biological examples with economic parallels such as “flocking,” has been made by Cucker and Smale (2007) Some have labeled this school as being “fundamentalist Keynesian,” (Coddington, 1976), although Davidson has disliked this label and introduced the “Keynes Post Keynesian” one in his 1994 book non-quantifiable uncertainty has been one of the biggest issues facing both standard environmental as well as more heterodox ecological economists for some time, with many of these uncertainties deriving from the limits of our scientific knowledge about the environment.9 Keynes’s (1937) emphasis in his later direct references to fundamental uncertainty involve such matters as the price of copper or the nature of the economic system of Britain twenty years in the future However, the foundation of this uncertainty in Keynes’s view is discussed in more detail in his 1921 Treatise on Probability, as discussed by Rosser (2001a) Thus, whereas it is often argued that the subjectivist Keynes saw such uncertainty as reflecting situations without any underlying probability distribution due to free will, in fact he saw a broader array of possible cases Indeed, he recognized the possibility of essentially standard classical probability for certain kinds of situations, such as the throwing of a fair die where there are clear probabilities that can be analytically determined, allowing for a profit-making insurance industry In between these extremes are various intermediate cases Thus there may be two series of events with events being able to be ranked ordinally within each series but not across the series, even when there might be an event common to both series A source of such non-cardinality or non-comparability might be if each event has a different type of probability, such as one being skewed and another not.10 Another case, perhaps more of Davidson’s critique involves arguing that these complexity approaches and presumably also these scientific limits of environmental knowledge are “merely epistemological” problems rather than ontological, and that therefore they are not sufficiently fundamental to found Keynesian uncertainty on If somehow our scientific knowledge or our knowledge of the dynamics of complex systems were to become sufficiently great, then such systems or models would be seen as classical in their essence 10 Rowley and Hamouda (1987) and O’Donnell (1990) have discussed this in terms of the debate between Keynes and Tinbergen over econometrics Koppl and Rosser (2002) argue that infinite regress problems associated with the Keynesian beauty contest can also lead to such problems, and Rotheim (1988) argues that Keynes also at times sympathized with emergentist “organicism” in which “the whole is not equal to the sum of its parts” and “small changes produce large effects” as in catastrophe or chaos theory an epistemological issue, is where there might be probabilities, but they cannot be estimated or determined due to data unavailability Complex dynamics can generate all of these We shall first consider ecologic-economic systems that are susceptible to catastrophic discontinuities, whose timing and scale are both difficult to predict Then consider ecologic-economic systems exhibiting chaotic dynamics, whose tendency to exhibit the butterfly effect make them unpredictable B Catastrophically Discontinuous Ecologic-Economic Systems Even without interactions with human beings and their economically driven conduct in relation to the natural environment, strictly ecological systems are known to exhibit dynamic discontinuities on their own.11 Some are known to exhibit multiple equlibria with discontinuities appearing as systems move from one basin of attraction to another dynamically, even without any human input, including the periodic mass suicides of lemmings (Elton, 1924), coral reefs (Done, 1992; Hughes, 1994), kelp forests (Estes and Duggins, 1995), and potentially eutrophic, shallow lakes (Schindler, 1990) The latter can be exacerbated by human input as well in combined systems, as humans can flip such a lake from a clear oligotrophic state to a murky eutrophic state by loading phosphorus from fertilizers or other sources (Carpenter, Ludwig, and Brock, 1999; Wagener, 2003) Figure 1, taken from Brock, Mäler, and Perrrings (2002, p 277) shows the basic dynamics of this system as a function of phosphorus loadings 11 A deep question we shall not pursue here is whether or not evolution itself is fundamentally a continuous or discontinuous process, with Darwin (1859) arguing the former and Gould (2002) arguing the latter For further commentary, see Rosser (1992), Hodgson (1993) See Rosser (2008) for a more complete discussion of discontinuities in ecologic-economics systems Figure 1: Hysteresis effects in the management of shallow lakes Figure 2: Spruce-Budworm Dynamics A famous example of a cyclical pattern involving two species interacting in which the explosion of population of one leads to a catastrophic collapse of the other is the spruce-budworm cycle of about 40 years in Canadian forests, wherein budworms eat the leaves of the spruce trees (Ludwig, Jones, and Holling, 1978) Now, there is a substantial degree of predictability in this system, given its roughly periodic nature However, human intervention can affect it in various ways In particular, human efforts to avoid or overcome the cycle can actually lead to greater discontinuities and larger catastrophic collapses, an observation that underlay Hollings’ (1973) innovation of the concept of a tradeoff between stability and resilience in ecosystems Furthermore, Holling (1986) has argued that this system can be substantially impacted by small changes in quite distant ecosystems, as for example the draining of wetlands in the mid-US that can lead to fewer birds arriving in Canada from Mexico that eat the budworms and help keep their population under control, an example of “local surprise, global change.” The dynamics of this system are given as follows, from Ludwig, Jones, and Holling (1978) Let B equal the budworm population, rB their natural population growth rate, KB the budworm carrying capacity (determined by the amount of leaves on the spruce trees), α the predator saturation parameter (a proportion of the budworm carrying capacity), β the maximum rate of predation on the budworms, and u* the equilibrium leaf volume, then the budworm dynamics in their early stages are given by dB/Dt = rBB(1 – B/KB) – βB2/(α2 + B2) (1) Nonzero equililbria are solutions of (rBKB/β) = u*/[(α/K2) + u*2)(1 – u*)] (2) The set of solutions implied by this system is depicted in Figure 2, with the zone of multiple equilibria and associated catastrophic hysteresis loops representing an infected forest This system is a variation on a predator-prey system, which we shall discuss further below, but note here that the original predatory-prey models studied by Lotka 10 buying any property that would be flooded by the dam Benefits were seen to accrue in the future, mostly associated with flood control, although possibly some for recreation or irrigation as well Thus, in such simple situations it was unequivocal: using a higher discount rate would lead to less dam building Thus, in the period when environmental impacts were not being counted, environmentalists seeking to block the building of dams supported the use of higher discount rates in these evaluations, and when a uniform discount rate of 10% was imposed in 1970 throughout the U.S government for all projects by President Nixon’s OMB Director, Roy Ash, many environmentalists made alliance with cost-cutting conservatives to support this “pro-conservation” move.18 More generally it came to be realized that when it comes to the environment, particular actions may have upfront costs, but then delayed environmental costs as well, such as with nuclear power or strip mining of coal, where there is a cost to begin the activity up front, then a period of positive net benefits, but then delayed environmental costs associated with waste disposal or cleanup (Herfindahl and Kneese, 1974; Porter, 1982; Asheim, 2008) Prince and Rosser (1985) studied the example of strip mining of coal in the U.S Southwest and found that for reasonable figures, reswitching could occur between strip mining of coal and cattle grazing, with the former more beneficial at rates between about and percent, with cattle grazing dominating at rates lower than percent and higher than percent, due to this time pattern effect An area of ecological economics where such phenomena may well arise is in forestry, especially when forests can have multiple uses that have varying and complicated time patterns connected with them The equation for the optimum rotation 18 Hannesson (1987) has made a similar argument with respect to fisheries with the capital-intensity of modern, commercial fishing technologies making it possible that a lower interest rate could lead to higher risks of overfishing fisheries 24 period, T, of a forest, allowing for functions besides timber, is due to Hartman (1976), with p being the price of timber, f(t) is the timber growth function, c is the (constant) marginal cost of harvesting the timber, r is the real discount rate, and g(t) gives the stream of net amenities that are not due to timber cutting, some of which may be social in nature, although they may be private and appropriable, such as cattle grazing: pf’(T) = rpf(T) + r[(pf(T) – c)/(erT – 1)] – g(T) (10) The interpretation of this is essentially that one should cut when the trees are growing at the real rate of interest (an old solution of Irving Fisher, 1907), but corrected for the benefits of getting more rapidly growing younger trees in the ground and accounting for the non-timber amenities The timber growth function tends to decline in rate with time However, the non-timber amenities may take a variety of patterns Thus on timber lands in Montana, grazing can occur when the forest is young, and the benefits of grazing tend to rise to about 12.5 years and then sharply decline after that Combining this with the timber function gives a non-monotonic function of the present value as T varies This is shown for the Montana forests in Figure 7, drawing on Swallow, Parks, and Wear (1990), with MBD representing the marginal benefit of delaying cutting, and MOC, the marginal opportunity cost of doing so 25 Figure 7: Optimal Hartman rotation on Montana forest lands An even more complicated situation presents itself in the eastern deciduous forests such as the George Washington National Forest in Virginia In this forest there is an effort to maximize net social benefit, taking into account non-marketed benefits such as to hunters Given the time pattern of the broader ecosystem after timber harvesting, one finds three different peaks of benefit for different activities Thus, about five to six years after a clearcut, deer population is maximized, with deer liking the edges of recent clearcuts with new trees just beginning to grow About 20-25 years in there is a maximum degree of biodiversity achieved, with much undergrowth Turkeys and quails are maximized in this period and environment However, bear populations maximize in older growth forests more than 60 years old, as undergrowth disappears and old tree 26 trunks fall that the bear can inhabit The net benefit function from the standpoint of various groups of hunters is shown in Figure 8, taken from Rosser (2005, p 198), drawing on the FORPLAN analysis of Johnson, Jones, and Kent (1980) While no comparison with an alternative use was made, the possibility of some sort of paradox and anomaly of the sort already discussed is clearly much higher in such situations t ime Figure 8: Virginia Deciduous Forest Hunting Amenity Thus, while there probably remain such deep differences between the Sraffian neo-Ricardian branch of Post Keynesian economists and the fundamentalist Keynes Post Keynesians who focus uncertainty and the role of money that they cannot be bridged, in the area of complex ecologic-economic analysis, common features present themselves.19 19 See Rosser (1991, Chaps and 13) for further discussion of these issues We note here that the link between Sraffian issues and ecologic-economic analysis exists even when no complex dynamics occur 27 VI Policy Implications and Conclusions The existence of complex dynamics in ecologic-economic systems complicates policy-making considerably Rosser (2001) argued that two well-known principles are more important in the face of the threats of possible sudden discontinuities or more erratic dynamic patterns: the precautionary principle and the scale-matching principle The first is pretty obvious The existence of thresholds beyond which catastrophic outcomes can occur should induce considerable caution, especially when irreversibilities are involved (Kahn and O’Neill, 1999) How we deal with discovering where those thresholds are and what to about them remains a problem that veers into that of Keynesian uncertainty, even though some make efforts to estimate probabilities in these situations In some cases, such as with the various reports on global warming, probabilities are estimated, but they are done so while ignoring the probabilities of these more disturbing potentially catastrophic events Scale-matching is another matter that involves making sure that any policy action is directed at the appropriate level of the ecological hierarchy Global problems should be dealt with globally; local ones locally This may seem obvious, but it becomes less obvious when decisionmaking must interact with the assignment or assessment of property rights These two must align themselves relevantly with the environmental or ecological effects of a policy or an action (Rosser and Rosser, 2006) It should be kept in mind that mere ownership is not sufficient (Ciriacy-Wantrup and Bishop, 1975), as implied by such analysts of the “common property resource problem” as Gordon (1954) Control of access is the key, and the assignment of property rights must align itself with 28 the ability to control access and achieve environmentally sustainable outcomes, a point emphasized in the work of Ostrom (1990) Finally, just as argued by Rosser (2006a) that there was an important influence from Post Keynesian economics on the development of complexity theory, so too here we see some elements of influence on the more specifically ecological-economic complex systems theory Indeed, the influence has been both ways as was seen with the role of predator-prey models in Post Keynesian macrodynamics Many of the deepest themes of the various schools of Post Keynesian economics are most clearly seen in the cases of complex ecologic-dynamics, from fundamental uncertainty to capital theoretic paradoxes References Albin, P S with Foley, D K (1998): Barriers and bounds to rationality: essays on economic complexity and dynamics in interactive systems, Princeton University Press, Princeton Asheim, G B (2008): ‘The occurrence of paradoxical behavior in a model where economic activity has environmental effects’, Journal of Economic Behavior and Organization, 65, pp 529-546 Brauer, F , Soudack, A E (1985): ‘Optimal harvesting in predator-prey systems’, International Journal of Control, 41, pp 111-128 Brock, W A , Mäler, K.-G , Perrrings, C (2002): ‘Resilience and sustainability: the analysis of nonlinear dynamic systems’, in Gunderson, L.H , Holling, C.S (eds.): Panarchy: understanding transformations in human and natural systems, Island Press, Washington Carpenter, S R , Ludwig, D , Brock, W A (1999): ‘Management of eutrophication for lakes subject to potentially irreversible change’, Ecological Applications, 9, pp 751-771 Chen, Z (1997): ‘Can economic activity lead to climate chaos? an economic analysis on global warming’, Canadian Journal of Economics, 30, pp 349-366 Chiarella, C (1988): ‘The cobweb model: its instability and the onset of chaos’, Economic Modelling, 5, pp 377-384 29 Chiarella, C, , Flaschel, P, , Franke, R (2005): Foundations for a disequlibrium theory of the business cycle: qualitative analysis and quantitative assessment, Cambridge University Press, Cambridge Christensen, P P (1989): ‘Historical roots for ecological economics – biophysical versus allocative approaches’, Ecological Economics, 1, pp 17-36 Ciricacy-Wantrup, S V , Bishop, R C (1975): ‘’Common property’ as a concept in natural resources policy’, Natural Resources Journal, 15, pp 713-727 Clark, C W (1985): Bioeconomic modelling and fisheries management, WileyInterscience, New York Clark, C W (1990): Mathematical bioeconomics: the optimal management of renewable resources, 2nd edn, Wiley-Interscience, New York Coddington, A (1976): ‘Keynesian economics: the search for first principles’, Journal of Economic Literature, 14, pp 1258-1273 Conklin, J E , Kolberg, W C (1994): ‘Chaos for the halibut?’, Marine Resource Economics, 9, pp 153-182 Copes, P (1970): The backward-bending supply curve of the fishing industry’, Scottish Journal of Political Economy, 17, pp 69-77 Cucker, F , Smale, S (2007): ‘On the mathematics of emergence’, Japanese Journal of Mathematics, 2, pp 197-227 Darwin, C (1859): The origin of the species by means of natural selection or the preservation of favored races in the struggle for life, John Murray, London Davidson, P (1982-83): ‘Rational expectations: a fallacious foundation for studying crucial decision-making processes’, Journal of Post Keynesian Economics, 5, pp.182197 Davidson, P (1994): Post Keynesian macroeconomic theory Edward Elgar, Aldershot Davidson, P (1996): ‘Reality and economic theory’, Journal of Post Keynesian Economics, 18, pp 479-508 Day, R H (1994): Complex economic dynamics: an introduction to dynamical systems and market mechanism, volume I, MIT Press, Cambridge 30 Day, R H (2006): ‘The complex problem of modelling economic complexity’, in Setterfield, M (ed.): Complexity, endogenous money and macroeconomic theory: essays in honour of Basil J Moore, Edward Elgar, Cheltenham Desai, M (1973): ‘Growth cycles and inflation in a model of class struggle’, Journal of Economic Theory, 6, pp 527-545 Done, T J (1992): ‘Phase shifts in coral reef communities and their ecological significance’, Hydrobiology, 247, pp 121-132 Doveri, F , Scheffer, M , Rinaldi, S , Muratori, S , Kuznetsov, Ya (1993): ‘Seasonality and chaos in a plankton-fish model’ Theoretical Population Biology, 43, pp 159-183 Ellner, S , Turchin, P (1995): ‘Chaos in a noisy world: new methods and evidence from time series analysis’, American Naturalist, 145, pp 343-375 Elton, C S (1924): ‘Periodic fluctuations in the number of animals: their causes and effects’, British Journal of Experimental Biology, 2, pp 119-163 Elton, C S , Nicholson, M (1942): ‘The ten year cycle in the numbers of lynx in Canada’, Journal of Animal Ecology, 11, pp 215-244 Embrechts, P, , Küppelberg, C , Mikosch, T (2003): Modelling extremal events for insurance and finance, Springer, Berlin Estes, J A , Duggins, D 1995 ‘Sea otters and kelp forests in Alaska: generality and variation in a community ecological paradigm’, Ecological Monographs, 65, pp 75-100 Fisher, I (1907); The rate of interest, Macmillan, New York Föllmer, H.( 1974): ‘Random economies with many interacting agents’, Journal of Mathematical Economics, 1, pp 51-62 Foroni, I , Gardini, L , Rosser, J B., Jr (2003): ‘Adaptive and statistical expectations in renewable resource markets’, Mathematics and Computers in Simulation, 63, pp 541567 Gilpin, M E (1979): ‘Spiral chaos in a predator prey model’, American Naturalist, 113, pp 306-308 Goodwin, R M (1947): ‘Dynamical coupling with especial reference to markets having production lags’, Econometrica, 15, pp 181-204 Goodwin, R M (1951): ‘The nonlinear accelerator and the persistence of business cycles’, Econometrica, 19, pp 1-17 31 Goodwin, R M (1967): ‘A growth cycle’, in Feinstein, C H (ed.): Socialism, capitalism and economic growth: essays presented to Maurice Dobb, Cambridge University Press, Cambridge Goodwin, R M (1990): Chaotic economic dynamics, Oxford University Press, Oxford Gordon, H S (1954): ‘Economic theory of a common property resource: the fishery’, Journal of Political Economy, 62, pp 124-142 Gould, S J (2002): The structure of evolutionary theory, The Belknap Press of Harvard University, Cambridge Grandmont, J.-M (1998): ‘Expectations formation and stability of large socioeconomic systems’, Econometrica, 66, pp 741-781 Gu, E.-G , Huang, Y (2006): ‘Global bifurcations of domains of feasible trajectories: an analysis of a discrete predator-prey model’, International Journal of Bifurcations and Chaos 16, pp 2601-2613 Gunderson, L H., Holling, C S, , Pritchard, L., Jr., Peterson, G (2002): Understanding resilience: theory, metaphors, and frameworks’, in Gunderson, L H , and Pritchard, L., Jr., (eds.): Resilience and the behavior of large-scale systems, Island Press, Washington Hamouda, O F , Harcourt, G C (1988): Post Keynesianism: from criticism to coherence’, Bulletin of Economic Research, 40, pp 1-33 Hannesson, R (1987): ‘The effect of the discount rate on the optimal exploitation of renewable resources’, Marine Resource Economics, 3, pp 319-329 Harcourt, G C (1976): ‘The Cambridge controversies: old ways and new horizons – or dead end?’, Oxford Economic Papers, 28, pp 25-65 Hartman, R (1976): ‘The harvesting decision when a standing forest has value’, Economic Inquiry, 14, pp 52-58 Hassell, M P., Lawton, J H , May, R M (1976): ‘Patterns of dynamical behavior of single-species populations’, Journal of Animal Ecology, 45, pp 471-486 Herfindahl, O C , Kneese, A V 1(974): Economic Theory of Natural Resources, Charles Merril, Columbus Hicks, J R (1950): A contribution to the theory of the trade cycle Oxford University Press Oxford Hodgson, G M (1993): Economics and evolution: bringing life back into economics University of Michigan Press Ann Arbor 32 Holling, C S (1973): ‘Resilience and stability of ecological systems’, Review of Ecology and Systematics, 4, pp 1-24 Holling, C S (1986): ‘Resilience of ecosystems: local surprise and global change’, in W.C Clark, W C , Munn, R E (eds.): Sustainable development of the biosphere, Cambridge University Press, Cambriidge Holt, R P F , Pressman, S (eds.): 2001 A new guide to post Keynesian economics, Routledge, London Hommes, C H , Rosser, J B., Jr (2001): ‘Consistent expectations equilibria and complex dynamics in renewable resource markets’, Macroeconomic Dynamics, 5, pp 180-203 Hommes, C H , Sorger, G (1998): ‘Consistent expectations equilibria’, Macroeconomic Dynamics, 2, pp 287-321 Horgan, J (1997): The end of science: facing the limits of scientific knowledge in the twilight of the scientific age, pbk edn., Broadway Books, New York Howarth, R B , Norgaard, R B (1990): ‘Intergenerational resource rights, efficiency, and social optimality’, Land Economics, 66, pp 1-11 Hughes, T.P (1994): ‘Catastrophes, phase shifts, and large-scale degradation of a Caribbean coral reef’, Science, 265, pp 1547-1551 Jones, D D , Walters, C J (1976): ‘Catastrophe theory and fisheries regulation’, Journal of the Fisheries Resource Board of Canada, 33, pp 287-300 Johnson, K N., Jones, D B , Kent, B M (1980): A user’s guide to the forest planning model (FORPLAN), USDA Forest Service, Land Management Planning, Fort Collins Kahn, J R , O’Neill, R V (1999): ‘Ecological interaction as a source of economic irreversibility’, Southern Economic Journal, 66, pp 391-402 Kaldor, N (1940): ‘A model of the trade cycle’, Economic Journal, 50, pp 78-92 Kalecki, M (1935): ‘A macrodynamic theory of business cycles’, Econometrica, 3, pp 327-344 Kalecki, M (1971): Selected essays on the dynamics of the capitalist economy, Cambridge University Press, Cambridge Kaneko, K , Tsuda, I (2001): Complex systems: chaos and beyond, a constructive approach with applications in life sciences, Springer-Verlag, Berlin 33 Keynes, J M (1921): Treatise on probability, Macmillan, London Keynes, J M (1936): The general theory of employment, interest and money, Macmillan, London Keynes, J M (1937): ‘The general theory of employment’, Quarterly Journal of Economics, 51, pp 209-223 King, J E (2002): A history of post Keynesian economics since 1936, Edward Elgar, Cheltenham Koppl, R , Rosser, J B., Jr (2002): ‘Everything I might say will have already passed through your mind’, Metroeconomica 53, pp 339-360 Leopold, A (1933): ‘The conservation ethic’, Journal of Forestry, 31, pp 634-643 Lorenz, H.-W (1992): ‘Multiple attractors, complex basin boundaries, and transient motion in deterministic economic systems’, in Feichtinger, G (ed.): Dynamic economic models and optimal control, North-Holland, Amsterdam Lotka, A J (1920): ‘Analytical notes on certain rhythmic relations in organic systems’, Proceedings of the National Academy of Sciences, United States, 6, pp 410-415 Lotka, A J (1925): Elements of physical biology, Williams and Williams, Baltimore (reprinted in 1945 as Elements of mathematical biology) Ludwig, D , Jones, D D , Holling C S 1978 ‘Qualitative analysis of insect outbreak systems: spruce budworm and forest’, Journal of Animal Ecology 47, pp 315-332 Ludwig, D , Walker, B H , Holling, C S (2002): ‘Models and metaphors of sustainability, stability, and resilience’, in Gunderson, L H, , Pritchard, L., Jr (eds.): Resilience and behavior of large-scale systems, Island Press, Washington Markose, S M (2005): ‘Computability and complexity: markets as complex adaptive systems (CAS)’, Economic Journal, 115, pp F159-F192 May, R M (1974): ‘Biological populations with non-overlapping generations: stable points, cycles, and chaos’, Science, 186, pp 645-647 McCauley, J P (2004): Dynamics of markets: econophysics and finance, Cambridge University Press, Cambridge Mill, J S (1843): A system of logic: ratiocinative and inductive, Longmans Green, London 34 Muradian, R (2001): ‘Ecological thresholds: a survey’, Ecological Economics, 38, pp 724 Noy-Meir, I (1973): ‘Desert ecosystems: environment and producers’, Annual Review of Ecology and Systematics, 4, pp 353-364 O’Donnell, R M (1990): ‘Keynes on mathematics: philosophical foundations and economic applications’, Cambridge Journal of Economics, 14, pp 29-47 Ostrom, E (1990): Governing the commons: the evolution of institutions for collective action, Cambridge University Press, Cambridge Peitgen, H.-O , Jürgens, H , Saupe, D (1992): Chaos and fractals: new frontiers of science, Springer-Verlag, New York Pohjola, M T (1981): ‘Stable, cyclic, and chaotic growth: the dynamics of a discrete time version of Goodwin’s growth cycle’, Zeitschrhift für Nationalökonomie, 41, pp 738 Poincaré, H (1880-1890): Mémoire surles courbes définies par les equations différentialles I-IV, oeurve I, Gauthier-Villars, Paris Porter, R C (1982): ‘The new approach to wilderness through benefit cost analysis’, Journal of Environmental Economics and Management, 9, pp 59-80 Prince, R , Rosser, J B., Jr (1985): ‘Some implications of delayed environmental costs and reswitching between food and energy production in the western United States’, Growth and Change, 16, pp 18-25 Rosser, J B., Jr (1991): From catastrophe to chaos: a general theory of economic discontinuities, 1st edn, Kluwer, Boston Rosser, J B., Jr (1992): ‘The dialogue between the economic and the ecologic theories of evolution’, Journal of Economic Behavior and Organization, 17, pp 195-215 Rosser, J B., Jr (1999): ‘On the complexities of complex economic dynamics’, Journal of Economic Perspectives, 13(4), pp 169-192 Rosser, J B., Jr (2000): From catastrophe to chaos: a general theory of economic discontinuities: mathematics, microeconomics, macroeconomics, and finance, Vol I, 2nd edn, Kluwer, Boston Rosser, J B, Jr (2001a): ‘Alternative Keynesian and post Keynesian perspectives on uncertainty and expectations’, Journal of Post Keynesian Economics, 23, pp 545-566 35 Rosser, J B, Jr (2001b): ‘Complex ecologic-economic dynamics and environmental policy’, Ecological Economics, 37, pp 23-37 Rosser, J B., Jr (2005): ‘Complexities of dynamic forest management policies’, in Kant, S , Berry, R A (eds.): Economics, sustainability, and natural resources, Springer, Dordrecht Rosser, J B., Jr (2006): ‘Complex dynamics and post Keynesian economics’, in Setterfield, M (ed.): Complexity, endogenous money and macroeconomic theory: essays in honour of Basil J Moore, Edward Elgar, Cheltenham Rosser, J B., Jr (2007): ‘The rise and fall of catastrophe theory applications in economics: was the baby thrown out with the bathwater?’, Journal of Economic Dynamics and Control, 31, pp 3255-3280 Rosser, J B, Jr (2008): Dynamic disontinuities in ecologic-economic systems’, in Allen, C , Holling, C S (eds.): Discontinuity in ecosystems and other complex systems, Columbia University Press, New York Rosser, J B., Jr (2009a): ‘Computational and dynamic complexity in economics’, in Rosser, J B., Jr (ed.): Handbook of complexity research, Edward Elgar, Cheltenham Rosser, J B., Jr (2009b): ‘Chaos theory before Lorenz’, Nonlinear Dynamics, Psychology, and Life Sciences, 13, pp 255-267 Rosser, J B., Jr , Rosser, M V (2006): ‘Institutional evolution of environmental management under global economic growth’, Journal of Economic Issues, 40, pp 421429 Rotheim, R J (1988): Keynes and the language of probability and uncertainty’, Journal of Post Keynesian Economics, 11, pp 82-99 Rowley, R , Hamouda, O (1987): ‘Troublesome probability and economics’, Journal of Post Keynesian Economics, 10, pp 44-64 Ruitenback, H.J (1996): ‘The great Canadian fishery collapse: some policy lessons’, Ecological Economics, 19, pp 103-106 Sakai, K (2001): Nonlinear dynamics and chaos in agricultural systems, Elsevier, Amsterdam Samuelson, P A (1967): ‘A universal cycle?’, in Henn, R (ed.): Methods of operations research, III, Verlag Anton Hain, Muhlgasse 36 Sardanyés, J , Solé, R V (2007): ‘Chaotic stability in spatially-revolved host-parasite replicators: the red queen on a lattice’, International Journal of Bifurcations and Chaos, 17, pp 589-606 Sawyer, M C (1985): The economics of Michal Kalecki, Macmillan, London Schaefer, M B (1957): ‘Some considerations of population dynamics and economics in relation to the management of marine fisheries’, Journal of the Fisheries Resource Board of Canada, 14, pp 699-681 Schaffer, W M (1984): ‘Stretching and folding in lynx fur returns: evidence for a strange attractor in nature?’, American Naturalist, 124, pp 796-820 Schelling, T C (1971): ‘Dynamic models of segregation’, Journal of Mathematical Sociology, 1, pp 143-186 Schindler, D W (1990): ‘Experimental perturbations of whole lakes as tests of hypotheses concerning ecosystem structure and function’, Oikos, 57, pp 25-41 Solé, R V , and Bascompte, J (2006): Self-organization in complex ecosystems, Princeton University Press, Princeton Spath, C L (2002): Greenhouse economics: value and ethics, Routledge, London Sraffa, P (1960): Production of commodities by commodities: prelude to a critique of economic theory, Cambridge University Press, Cambridge Strotz, R H., McAnulty, J C , Naines, J B., Jr (1953): ‘Goodwin’s nonlinear theory of the business cycle: an electro-analog solution’, Econometrica, 21, pp 390-411 Swallow, S.K., Parks, P J , Wear, D N (1990): ‘Policy-relevant non-convexities in the production of multiple forest benefits’, Journal of Environmental Economics and Management, 19, 264-280 Turchin, P (2003): Complex population dynamics: a theoretical/empirical synthesis, Princeton University Press, Princeton Turing, A M (1952): ‘The chemical basis of morphogenesis’, Philosophical Transactions of the Royal Society B, 237, pp 37-72 van der Pol, B , van der Mark, J (1927); ‘Frequency demultiplication’, Nature, 120, pp 363-364 Velupillai, K V (2005): Introduction’, in Velupillai, K V (ed.): Computability, complexity and constructivity in economic analysis, Blackwell, Victoria 37 Volterra, V (1926): ‘Fluctuations in the abundance of a species considered mathematically’, Nature, 118, pp 558-600 Volterrra, V (1931): Lecons sur la théorie mathématique de la lutte pour la vie, GauthierVillars, Paris Wagener, F O.O (2003): Skiba points and heteroclinic bifurcations with applications to the shallow lake system’, Journal of Economic Dynamics and Control, 27, pp 15331561 Zimmer, C (1999): Life after chaos’, Science, 284, pp 83-86 38 ... ‘Alternative Keynesian and post Keynesian perspectives on uncertainty and expectations’, Journal of Post Keynesian Economics, 23, pp 545-566 35 Rosser, J B, Jr (2001b): ? ?Complex ecologic- economic... neo-Ricardian branch of Post Keynesian economists and the fundamentalist Keynes Post Keynesians who focus uncertainty and the role of money that they cannot be bridged, in the area of complex ecologic- economic... of Post Keynesian Economics, 5, pp.182197 Davidson, P (1994): Post Keynesian macroeconomic theory Edward Elgar, Aldershot Davidson, P (1996): ‘Reality and economic theory’, Journal of Post Keynesian