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CONSUMPTION AS AN ACTIVITY AND THE ROLE OF KNOWLEDGE IN ENVIRONMENTAL DYNAMICS Mario Cogoy Department of Economics - University of Trieste - Piazzale Europa 1 - 34127 Trieste – Italy Phone: ++39040-5587041- Fax: ++39040-567543 - Email: [email protected] Abstract This paper combines a time-allocation approach with a model of economic dynamics, based on the accumulation of human capital. Consumption is modelled as an activity embedded in the environment, taking place in time, and using knowledge in order to reduce the labour effort in production, and to improve the quality of life. The accumulation of knowledge improves both the efficiency of production and consumption activities, and technical progress is therefore extended to the realm of consumption. This implies, that knowledge and technology accumulated in the consumption sector directly affect welfare, and that the structure of preferences on time, consumption goods and consumption knowledge significantly determines the dynamics of the economy and the environmental impacts of consumption activities. Keywords: Time Allocation; Human Capital; Consumption Activity; Consumption Knowledge JEL Classification: D11; J22; O30; O41 1. INTRODUCTION In modern societies consumption requires a significant amount of effort. Consumption takes time; it must be planned in advance, prepared and organised. Time, skills and knowledge are inputs as necessary to consumption as are commodities, and the pattern of combination of these inputs significantly determines the outcome. Consumption has to be regarded therefore as a complex activity, rather than as an effortless absorption of effortfully produced commodities. Consumption is embedded in the natural environment. The environment influences the quality of consumptive actions and serves as a receptacle for their outputs. All ingredients of consumption activities (e.g.: consumption goods, time, knowledge, skills, consumption capital, infrastructures, environmental quality, information, social networks, etc.) are interwoven in a complex pattern of interaction, which determines both the pleasure derived from consumptive activities, and also the impact of consumptive activities on the environment. The pattern of interaction between different components of consumptive actions may change over time, and these changes obviously influence the use of the environment as an input and as a receptacle of consumptive outputs. I shall focus in this paper on four basic ingredients of consumptive activities: time, commodities, knowledge and the environment. Substitution between these inputs (Spreng, 1993) affects the consumptive use of the environment. In particular, the possibility of increasing the role of time and knowledge and of reducing the flow of consumption goods entering consumptive actions may become an important instrument for achieving sustainable consumption. For this reason, studying consumption as an activity (and not just as an absorption of consumption goods) is the most appropriate approach to identifying paths of sustainable consumption. All kinds of activities require time, and therefore consumption also requires time, since no pleasure, or “utility”, or “welfare” can be derived from consumption without making use of a portion of the permanent flow of time. Spending time in a pleasant way is the main target of consumption activities and I shall call the pleasant share of disposable time of each individual: enjoyment time1. A certain amount of time has to be allocated therefore to enjoyment, and enjoyment time delivers an important contribution to welfare2. The intensity of enjoyment experienced in consumption activities depends 2 however not only on the duration, but also on the quality of these activities. I shall consider three factors influencing enjoyment quality: the flow of consumption goods supporting each unit of enjoyment time, the knowledge applied to improving the performance of consumptive actions, and the quality of the environment in which consumptive activities take place. Enjoyment time is serviced by a flow of commodities, entering as inputs into consumptive activities. Individuals can choose a higher level of commodity intensity for their consumption activities, if they feel that more elaborate lifestyles yield a better quality of enjoyment. I shall assume a constant population of N identical individuals involved in the same kinds of consumptive activities. Time available to each individual is normalized to 1. E (enjoyment time) is the portion of time which each individual allocates to enjoyment ( 0 ≤ E ≤ 1 ). C is total social consumption. Per capita consumption c is: c= C N (1) Consumption intensity of action, or material lifestyle, can be then defined as: ϕ= c E (2) where ϕ is per capita consumption per unit of enjoyment time. The quality of consumption is also influenced by knowledge and skills. Knowledge and skills directly affect welfare in two ways. Welfare can be positively influenced by personal individual skills of the consumer: a car trip will be more pleasant if the consumer is a good driver; a match of tennis is more interesting, if it is played by skilful players, etc. In complex modern societies however, knowledge plays a more pervasive role, since in advanced industrial societies consumption is less and less dependent on the direct use of individual commodities, and becomes increasingly rooted in sociotechnical systems, i.e. in networks of commodities, infrastructures and services. For example, cars alone do not provide any transportation service, but only as components of a network including roads, parking lots, repair shops, gasoline stations, insurance, traffic rules and legislation, traffic police, and the like. In a similar way, energy services depend on distribution networks, end use technologies, the quality of buildings, etc. 3 Residential comfort depends on neighbourhoods, on urban planning, on commuting time, and on the aesthetic and energetic quality of buildings. The performance of consumptive systems significantly depends therefore on the quality of the interactions between the system parts, and commodities are only one component among many others. The welfare deriving from socio-technical systems significantly depends on the social knowledge which is embodied in the design, and applied to the control, the operation, and the evolutionary adaptation of such systems. For this reason, with increasing complexity of consumption, the relative weight of knowledge in consumptive activities raises, as compared to commodities (Cogoy, 2004). This implies, that a new space opens up for the use of knowledge: knowledge does not only contribute to the design of more efficient processes in the production of commodities, but also to the efficient design and the operation of socio-technical systems. The same endowment with time and commodities can lead to a higher level of welfare, if it is supported by a higher level of knowledge and technology, since knowledge and technology serve to make a better use of resources, not only in production, but also in consumption activities. This is a direct consequence of assuming that technical progress pertains not only to the realm of production, but also to the realm of consumption. In other words, knowledge and technology do not only affect welfare indirectly, as they improve the efficiency of production activities, but also directly, as they make a more efficient use of given consumptive resources possible (Michael/Becker, 1973; Becker, 1976). Human capital influences therefore the efficiency of consumption efforts in the production of welfare, in a similar way, as the accumulation of human capital increases the efficiency of factors in production. Finally, the quality of consumptive actions is also influenced by the state of the environment. I shall assume that, in a finite world, environmental quality basically depends on the quantity of materials discharged into the environment. Materials are lost in productive transformations, and are emitted into the environment after consumption and as a consequence of capital depreciation. Although it is true, that eco-efficiency and recycling can reduce materials emissions per consumptive unit, limits exist for technological solutions, and it is not possible to sustain any level of consumption without causing severe environmental disruption (Huesemann, 2003). I shall neglect 4 capital depreciation and focus on the level of consumption as the main cause of environmental degradation. I shall measure environmental quality A therefore as a distance between actual total consumption cN and an hypothetical level of unsustainable consumption C * which would cause unacceptable environmental disruption. A = C * − cN (3) In an activity oriented approach, commodities, time, knowledge and environmental quality are functionally related to each other, and their interaction defines the “enjoyment technology” individuals are adopting. Consider first the effects on consumptive actions of a marginal increase in E . An increase in enjoyment time with constant ϕ implies a temporal extension of activities of the same type, whereas an increase, or a decrease in ϕ reflects a switch to activities of higher, or lower, commodity intensity (or to higher, or lower, material lifestyles). For this reason, a marginal increase in E will influence enjoyment activities in a contradictory way. On the one hand enjoyment time will increase, but on the other hand commodity intensity ϕ will decrease because of (2). The per capita flow of commodities c will have to be “diluted” over an increased flow of time. Each unit of time will be serviced by a reduced commodity flow, and this in turn means, that the type of consumptive activity has changed to an activity of lower commodity intensity. A marginal increase in E will therefore only have a positive influence on enjoyment, if the effect of an increase in time prevails over the negative effect of a lower commodity intensity of action. Consider next a marginal increase in commodity intensity ϕ . Again, such an increase may have contradictory effects on welfare. If an increase in ϕ derives from an increase in per capita consumption c , the positive effect on lifestyles will be matched by a negative impact on the environment. A marginal increase in ϕ will only result in an improvement in welfare, if the positive effects on lifestyles prevail over the negative effects on the environment. The functional relationship between time, commodity intensity, knowledge and the environment makes the difference between the “doing” and the “having” approach in welfare economics. In the “having approach “ a portion of time called “leisure” can be 5 directly enjoyed by simply abstaining from labour (Chase, 1967; Oulton, 1993; Baldassarri / De Santis / Moscarini, 1994; Ladrón-de-Guevara / Ortigueira / Santos, 1999). In the leisure approach, commodities and time are not related to each other by the functionality of action, and no question arises of what consumers will do with an additional quantity of time. Strictly speaking, leisure does not exist in the present paper, since disposable time can only be enjoyed if it is embedded in activities transforming consumption goods, knowledge and environmental quality into time-dimensional enjoyment of life. Enjoyment time is therefore not just a different word for leisure, but rather denotes the difference between a leisure approach and an activity oriented approach to enjoyment. Under the above premises the welfare of each individual can be defined as: U = U (E ,ϕ , H C , A) U E ,U ϕ ,U H C , U A > 0 U EE ,U ϕϕ ,U H C H C ,U AA < 0 (4) where H c is human consumption capital improving the design of socio-technical systems in which enjoyable activities are embedded. ( U x is the partial derivative of U with respect to argument x ). U = U (E ,ϕ , H C , A) can be interpreted as the individual’s enjoyment technology, describing how time, commodity services to time units, the quality of consumptive designs and of the environment are combined into activities generating welfare. Knowledge and environmental quality play the role of public goods in enjoyment activities, since the quality of socio-technical designs, as expressed in the level of human consumption capital, and the quality of the environment improve the intensity of enjoyment of all of society’s members. It is important to note, that the level of commodity intensity ϕ and the level of consumption knowledge H C are independent from each other. It may be historically true that the progress of knowledge and technology has been accompanied by an increase in the commodity intensity of enjoyable actions. No necessary causality between the two should be assumed however. The level of commodity intensity is a free choice of individuals, and different types of material lifestyles are compatible with the same level of knowledge in consumption. 6 Of course, consumers may also have preferences on items other than E , ϕ , H C and A . They may like other types of time expenditure, as e.g. research time spent in accumulating human capital, or even production time. They may also appreciate “conspicuous” commodities independently of their use in actions. The enjoyment technology function may be extended therefore to contain other arguments, but I shall use (4), in order to stress the main point of the present paper: enjoyment activities have a time-dimensional output, and the production of qualified enjoyment time is the primary final result of the economic process. In an activity framework consumers can substitute to a certain extent between different inputs to consumptive actions. They may be equally happy, for instance, if enjoyment time is reduced and such a reduction is compensated by an increased commodity intensity of action and/or an improved quality of the environment and/or of the design quality of socio-technical systems. Because of (2), it is feasible for individuals to increase ϕ to infinity by setting E = 0 , and choosing in this way an infinite commodity intensity of action, without allocating any time to enjoyable activities. I shall call this kind of behaviour: commodity hoarding, since welfare is derived in this case from “having” commodities, instead of “doing” something with them. Commodity hoarding is a rather uninteresting oddity, and the enjoyment technology has to be specified therefore in such a way, as to rule out commodity hoarding and deliver interior solutions for E and ϕ . If enjoyment time, commodity intensity and consumptive knowledge are bad substitutes, consumers will not be interested in an unlimited expansion of commodity intensity at the expenses of enjoyment time. Formally, if we specify the consumption technology as: U = ( 1 λ λ E + ϕ λ + H C + Aλ λ ) λ<0 (4a) commodity hoarding will not occur. I shall therefore study enjoyment dynamics in sections 3 to 5 under the assumption of bad substitutability. λ < 0 is quite reasonable an assumption, since it means, that time is essential in consumptive actions, and that consumers are not willing to adopt enjoyment technologies based on commodity hoarding. 7 The focus of the present paper is not on the choice of individuals between different types of consumption activities, but rather on the impacts of human capital accumulation on the aggregate social process of consumption and on the aggregate social use of time. The utility function has to be interpreted therefore as a description of the aggregate consumption technology of an individual. Since all individuals are assumed to be equal, social welfare is expressed by: NU , and the production of aggregate social welfare is similar to the description of aggregate production in a single production function. The above described approach has some points in common with Becker’s theory of “time allocation” and with household economics (Becker, 1965, 1976; Michael / Becker, 1973; Stigler / Becker, 1977; Gronau, 1977, 1986; Juster/Stafford, 1991). Along with Becker, utility is not defined on commodities, but on the outputs of activities. Moreover, if enjoyment production is an effort requiring activity, and if technical progress is considered to be a means of reducing effort to obtain a given result, there is no reason to confine the effects of technical progress to the realm of production. The accumulation of knowledge can improve the efficiency of enjoyment activities similar to the way it fosters production (Becker, 1976; Michael/Becker, 1973; Stigler / Becker, 1977). The present paper focuses however on the fact that the output of enjoyment activities is time-dimensional, so that it is necessary to allocate time not only to production, but also to enjoyment. Enjoyment time is vital in consumptive actions and cannot be rationalized away by “improvements” in the enjoyment technology. The consumption technology has been introduced in this section. The other elements of the model will be introduced in section 2. Sections 3 to 5 discuss the solution of the model. Section 6 concludes. 2. PHYSICAL PRODUCTION AND HUMAN CAPITAL ACCUMULATION I shall model production and research along similar lines as are familiar from human capital models of endogenous growth (Lucas, 1988; Rebelo, 1991), with only a few minor changes. 8 Output Y is produced with the aid of capital K , labour and labour-augmenting productive knowledge ( H P ): Y = K ψ ( NPH P ) 1−ψ (5) P is time allocated by each individual to production, NP is total social production labour. Productive and consumptive knowledge add to total social human capital: H = H P + HC (6) Research time and human capital contribute to the accumulation of non-depreciating human capital: H& = δNRH δ >0 (7) where δ is a fixed productivity coefficient, H is the overall stock of social knowledge (i.e. the sum of consumption human capital and production human capital), R is time spent by each individual in research. NR is therefore total social research time. Production and consumption knowledge act as externalities to assist labour in research. Production and consumption are therefore rival uses of human capital, whereas its use in research is non-rival. The time budget constraint for the individual is: E + P + R =1 (8) There are three types of time expenditure for each individual: enjoyment time ( E ), production time ( P ) and research time ( R ). It is assumed, that only enjoyment time delivers welfare, whereas production and research are only justified, if they contribute to the task of increasing the quality of enjoyment time. For this reason, the economy can be described as a process of production of time by means of time. In this process, production and research time contribute to the generation of time of higher quality (enjoyment time), which is the final outcome of the economic process3. Non-depreciating physical capital accumulates according to: K& = Y − cN (9) 9 Equation (7) acts analogous to Lucas (1988) and Rebelo (1991) as a potential engine of growth in the economy. The planner in charge of searching for the social optimum can in principle turn off this engine by allocating no labour time to research and waiving in this way the external benefits of human capital accumulation. Whether this is optimal or not, depends on how individuals evaluate enjoyment time, lifestyles, the environment, and the design quality of consumptive actions. Section 4 defines a stationary state in which it is optimal not to use the growth engine. 3. A MODEL OF TIME ALLOCATION AND CONSUMPTIVE ACTION WITH ENVIRONMENTAL CONSTRAINTS An optimal enjoyment path can be identified by solving the problem: max ∫ ∞ 0 e − ρt ( ) 1 λ λ E + ϕ λ + H C + A λ dt λ (10) subject to (2), (3) and (5) to (9). ρ is the rate of discount. First-order conditions and the transversality conditions for this problem are: µ1δNH = E µ2 = ϕλ − E (11) ϕ λ −1 − A λ −1 NE E λ −1 − HC λ −1 λ −1 (12) ϕλ Y = (1 − ψ ) P E = (1 − ψ ) Y HP ϕ λ −1 − A λ −1 NE ϕ λ −1 − A λ −1 NE H µ& 1 = ρ − δN (1 − E ) − δNP C µ1 HP µ& 2 Y = ρ −ψ µ2 K lim e − ρt µ1 H = 0 t →∞ (13) (14) (15) (16) (17) 10 lim e − ρt µ 2 K = 0 (18) t →∞ µ1 and µ 2 are the shadow prices of human and physical capital respectively. (11) to (18) together with the model constraints describe the optimal path. Equations (13) and (14) state the optimal allocation conditions for time and human capital respectively. An additional unit of enjoyment time has two opposite effects on welfare. Additional time in consumptive actions increases welfare but at the same time the commodity intensity of consumptive activities is reduced, since the same flow of commodities now services an increased flow of time. The left hand of (13) summarizes the net marginal welfare effect of an increase in enjoyment time. On the other hand, an increase in production time contributes to output, and therefore to the commodity intensity of consumptive actions, but also negatively affects the environment. The right hand of (13) summarizes therefore the net welfare effect of a marginal time unit in production. Similarly, equation (14) equates a marginal effect of a design improvement of consumptive activities with the marginal effect of an increase of knowledge in production. The above described model will not generate unbounded growth, since the economy is constrained by the negative effects of consumption on the environment and by bad substitutability in consumptive activities. Section 4 analyses the stationary state of the economy. Section 5 describes the transitional path to the stationary state. 4. THE STATIONARY STATE The stationary point can be obtained from (2), (3), (5) to (9) and (13) to (16) by setting: µ& 1 = µ& 2 = H& = K& = 0 . After eliminating all other variables, one can obtain stationary values for enjoyment time E and per capita consumption c from: (1 − ψE )E − 2λ −c −λ (1 − E ) − (1 − ψ )N λ E 1− λ cN * C − cN 1− λ =0 (19) 11 [ c= E − 2λ +E 1− λ (1 − E ) − 2λ ] Ω( E ) −1 λ (20) where: λψ ρ 1−ψ ρ − δ N (1 − E ) Ω(E ) = δN ψ λ −1 (21) The graph of (19) has an initial point: c = 0 for E = 0 , and a final point C* c= N+N 1 1− λ for E = 1 . The graph of (20) has a discontinuity at E = δN − ρ and a final point: c = 1 for E = 1 . δN The shapes of the graphs depend on the values of the parameters. For parameter values: δ = 1; ρ = 0.6; λ = −0.5; ψ = 0.5; C * = 50; N = 2 the graphs of the two functions are: Figure 1 For the two graphs to cross N+N 1 1−λ < C* (22) must be satisfied. This condition requires that the size of the population does not exceed limits compatible with environmental sustainability. From (5), (9), (15) and (16) the stationary values of physical and human capital can be derived: K= ψ cN ρ (23) ψ c ρ 1−ψ HP = 1 − E ψ (24) 12 HC = c (1 − E ) 2 ρ ψ ψ 1−ψ ρ − δ N (1 − E ) δN (25) Figures (2) to (4) illustrate the effects of variations in ρ , λ and N on the stationary values of c and E . Figure 2 Figure 2 shows the effects of discounting on the stationary state of the economy: the lower the rate of discount, the more will enjoyment time approach its maximum level of 1 (which means that production labour is substituted by human and physical capital), and the closer will per capita consumption approach its maximum level, which is equal to: C* N+N 1 1− λ . Since consumption is higher, environmental quality will be lower in the stationary state with a lower rate of discount. This result is in contradiction with conventional wisdom on the environmental effects of the rate of discount. In this model high discounting is good for the environment, since high discounting discourages the development of economic forces at an earlier stage. The result is that stationary consumption will be lower, and the state of the environment will therefore be better, if the rate of discount is higher. Figure 3 Figure 3 shows similar effects of an increase in λ on the stationary state: Figure 4 Figure 4 shows that the effects of a population increase will be positive on enjoyment time in the stationary state. Per capita consumption will not necessarily rise. For a 13 population increase from N = 2 to N = 4 the graph shows a decline in per capita consumption. The reason for this behaviour of the economy is straightforward: an increase in the size of the population will boost the potentialities of research. Given environmental constraints on physical output, research will be directed towards substituting labour in production (and extending in this way enjoyment time), and improving the design of socio-technical systems. 5. TRANSITIONAL DYNAMICS Transitional dynamics can be numerically calculated for given parameter values. I shall use GAMS-CONOPT to calculate optimal paths. For the state variables I assume initial values: H (0) = 5; K (0) = 1 . The results of the calculations are summarized in Figure 5. Figure 5 Time is initially allocated to research, production and enjoyment. As time elapses and human capital is accumulated, time is shifted from research and production to enjoyment and the rate of discount decides how far this shift will go. Total consumption increases and environmental quality therefore declines to its stationary state level. Productive knowledge is required to increase output and to substitute for productive labour as time is shifted from production to enjoyment. For this reason productive knowledge grows faster than consumptive knowledge in the first section of the transitional path. The capital-labour relationship is continually rising, since capital accumulates and labour time is shifted to enjoyment. The capital-augmented labour relationship reveals a more complex pattern: it declines first, as a consequence of the rapid increase in productive knowledge and increases in the second section of the transitional path as productive human capital approaches its stationary level. In this way, shifts in the time structure reflect themselves in the capital-labour dynamics. 14 6. CONCLUSIONS In the preceding sections I have argued, that considering consumption as an activity significantly affects the description of the dynamic behaviour of the economy. In an activity framework, not only consumption goods, but also other ingredients of consumptive actions, as enjoyment time and the design quality of consumptive activities, become important in the production of welfare. The long run dynamics of the system depends therefore on the behaviour of all components of consumptive activities over time. Environmental constraints limit the physical growth of the system in the long run. Bad substitutability makes of enjoyment time an essential ingredient of action, and the extension of enjoyment time becomes one of the outcomes of the progress in knowledge and technology. The dynamic forces of the system are also directed at increasing the design quality of consumption to levels determined by the rate of discount. “Leisure” is not a credible candidate for modelling the complexity of consumption in modern societies, since the notion of leisure admits a third use of time besides production and research, but ignores the functional relation between time, commodities, knowledge and the environment in consumptive actions. Know-how in consumption is as important as know-how in production. Insisting on skills, knowledge and technical progress in consumption activities 4 serves to move a step towards a more realistic view of technical progress in the process of growth. It may be argued, that one of the outstanding features of technical progress is the opening up of alternative possible choices in lifestyles. At a high level of knowledge and technology, extending enjoyable time and improving the design quality of consumptive systems are valid alternatives to the target of increasing per-capita consumption. Economic theory should provide an analytical framework to investigate such possibilities. The approach presented here also has implications for environmental policies (Cogoy, 1999), since the absolute mass of commodity production is, with all necessary qualifications, a major source of environmental damage (Daly, 1992). The expansion of enjoyment time and the design quality of consumption are valid alternative targets to pursue in view of the progress of knowledge and technology. For this reason, it is 15 important, that models adopted to investigate dynamics and change allow for more alternative sources of welfare, than just material consumption. The study of the endogenous structure of time and of the role of knowledge in consumption is therefore not only a realistic tool for the analysis of the effects of technical progress in modern societies, but also an important analytical element for the study of sustainable paths of economic development. 16 Notes 1 “Enjoyment of life” is, according to Georgescu-Roegen (1966, p.97), the final result of the economic process. 2 I ignore the survival sector of the economy in this paper, and assume therefore, that economic activities are mainly directed at delivering amenities of life, after the fundamental needs of society have been satisfied. 3 It must be noted, that the conceptualisation introduced in this paper has nothing in common with the conceptualisation (paid work and leisure) commonly used in timebudget-analysis (Gershuny, 1993). Production labour refers to the output of the process (commodities) and not to the forms of payment. Enjoyment time can be paid, if people manage to get payments for doing what they like. The distinction between production and consumption activities does not necessarily coincide with the distinction between the market and the non-market sector of the economy. Since I do not address the question of how production and consumption processes are socially organised (market vs. non-market social organisation), the question of payments is here irrelevant. (On market vs. non-market organisation and the social embeddedness of consumption, cf. Cogoy, 1999) 4 Although “consumption skills” and “consumption knowledge” are rarely recognised in models of economic dynamics, they are widely accepted as important analytical tools in time-use studies (Gershuny, 1993) and in consumer research (Park / Mothersbaugh / Feick, 1994). “Consumption capital” and learning in consumption (“beneficial addiction”) are central ideas in Stigler/Becker, 1977. 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A Theory of Wants and the Growth of Demand, Max-Planck-Institute for Research Into Economic Systems, Jena, WP 9806 19 15 c 10 5 E 0 0,6 0,8 1 The stationary state Parameter values: δ = 1; ρ = 0.6; λ = −0.5; ψ = 0.5; C * = 50; N = 2 Figure 1 20 15 c 10 5 E 0 0,6 0,8 1 A decrease in the rate of discount Parameter values: δ = 1; ρ = 0.6; λ = −0.5; ψ = 0.5; C * = 50; N = 2 Broken line: ρ = 0.5 Figure 2 21 15 c 10 5 E 0 0,6 0,8 1 An increase in λ Parameter values: δ = 1; ρ = 0.6; λ = −0.5; ψ = 0.5; C * = 50; N = 2 Broken lines: λ = − 0.4 Figure 3 22 15 c 10 5 E 0 0,6 0,8 1 A population increase Parameter values: δ = 1; ρ = 0.6; λ = −0.5; ψ = 0.5; C * = 50; N = 2 Broken lines: N = 4 Figure 4 23 60 HP 40 HC 20 t 0 0 10 20 30 15 C 10 K 5 t 0 0 10 20 30 1 E 0,5 P R t 0 0 10 20 30 24 8 ϕ 4 t 0 0 10 20 30 K 40 NP 20 t 0 0 10 20 30 1 K NPH P 0,5 t 0 0 10 20 30 Transitional dynamics Parameter values: δ = 1; ρ = 0.6; λ = −0.5; ψ = 0.5; C * = 50; N = 2 Initial values: H (0) = 5; K (0) = 1 Figure 5 25