Sustainable use of renewable resources: an identity ... - Springer Link

J Bioecon (2011) 13:97–123 DOI 10.1007/s10818-011-9102-4

Sustainable use of renewable resources: an identity approach Isabel Almudi · Julio Sánchez Chóliz

Published online: 10 March 2011 © Springer Science+Business Media, LLC. 2011

Abstract Despite the achievements obtained by environmental economics over recent decades, it shares the same failings as economic theory in general. In this sense, regarding preferences, very little attention has been paid to three elements; the long-term change in social preferences, the incorporation of non-economic factors in the structure of preferences, and the need to consider some kind of heterogeneity in social preferences. In this paper we deal with these three issues by developing a new framework which encloses non-economic factors as one of the driving forces to explain consumer behavior and which allows us to endogeneize preference and consider heterogeneity. After setting up our approach, we pose the question as to how far such a framework modifies the levels of use and consumption of a renewable resource. Our findings have enabled us to draw interesting conclusions regarding environmental policies in place since the 1970s. Keywords Endogenous preference change · Identity · Heterogeneity · Renewable resources · Environmental policies JEL Classification

Q28 · Q58 · C61 · C62 · B41

1 Introduction The presence of environmental issues in most political-economic debates has been a major feature of the last third of the twentieth century. For this reason, since the I. Almudi (B) · J. Sánchez Chóliz Departamento de Análisis Económico, Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía, 2-4, 50005 Zaragoza, Spain e-mail: [email protected] J. Sánchez Chóliz e-mail: [email protected]

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I. Almudi, J. Sánchez Chóliz

1970s economic theory has made a great effort to introduce the question of natural resources as one of the essential explicative factors of economic dynamics. The result has been the emergence of a new branch, called environmental economics, developed within the optimizing neoclassical framework. Despite the achievements obtained by environmental economics, it shares the same failings as economic theory since it uses the same theoretical and methodological tools economic theory provides us with. In this sense, regarding preferences, very little attention has been paid to three elements; the long-term change in social preferences, the incorporation of non-economic factors into the structure of preferences, and the need to consider some kind of heterogeneity in social preferences. In this paper we deal with these three issues by developing a new framework which includes non-economic factors as one of the driving forces to explain consumer behavior and which allows us to endogeneize preference and to consider heterogeneity. The long-term change in social preferences, considered unnecessary and not taken into account from 1940 to 1990 (see Stigler and Becker 1977), is now a requirement in economic theory for several leading economists (i.e. Landa 1981, 1994; Bowles 1998; Akerlof and Kranton 2000, 2005). Its use is justified in environmental economics because of the essentially dynamic character of the object being studied (Beltratti 1997). The need to incorporate non-strictly economic factors as variables to explain the behavior of agents has been demanded by a growing number of authors. Prominent scholars such as Akerlof (2007) or Tsakalotos (2005) have pointed out that a failure to recognize that non-strictly economic motivations and distinct values exist, underlying an agent’s choices, leads to explanatory biases. Furthermore, new findings from the relatively new field of experimental economics (associated with the thinking of Kahnemann, Tversky and Plott1 ), which have shown that agents behave in a manner more prone to cooperation than that predicted by the Rational Choice Paradigm, confirm that some important factors are missing when neoclassical economic theory tries to explain the behavior of agents. Regarding the above, the seminal contribution of Landa (1981, 1994) in the realm of the economics of identity represented a real advance in incorporating non-strictly economic motivations into a consumer’s behavior. The basic idea of her pioneering work rests on the fact that agents do not make their choices as isolated entities, but rather as individuals embedded in social structures which provide them with norms and values (i.e. the ones provided by Confucian ethics) constraining their behavior. That is to say, for this author, that the existence of specific social categories implicitly means the acceptance of certain norms of behavior. As these norms become known, they facilitate exchange, offer stability and, save transaction costs. Furthermore, Landa argued that, in conditions of uncertainty, individuals do not choose an anonymous partner to exchange with (as orthodox economics assumes). Rather, individuals ‘will equip themselves with a calculus of relations’2 which allows them to grade (or even rank) other individuals according to these specific social categories. Subsequently, Folbre (1994)

1 See, for example, Fehr and Fischbacher (2002). 2 Landa (1994, p. 103). Not in italics in original text.

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argued that identities (especially, but not always, those related to minority collectives) can justify some forms of collective action, and Kevane (1994) studied the economic implications of considering identities as ‘imaged communities’3 attached to individuals. Recently, Akerlof and Kranton (2000) have proposed the incorporation of these ideas and others, offered by social psychology within a neoclassic utilitarian framework, which leads to a higher analytical tractability of the concept of identity (see, also, Akerlof 1997; Akerlof and Kranton 2005; Sen 1977, 2000; Journal of Economic Methodology 2006). Following on from the research path pointed out in the aforementioned works various significant scholars from environmental economics have pointed out the need to consider the environmental dimensions of well-being (see, for example, Dasgupta 2001), including factors different from traditional economic ones in the analysis, such as: identity (Brekke et al. 2003) or altruism (Erikkson 2004; Conrad 2005). Finally, the strong assumption made in the general equilibrium analysis with the supposition that ‘society as a whole behaves as if it were a single individual’4 has been, also, criticized for being unrealistic by, for example, Kirman (1989), Rizvi (1994) or Hodgson (2007). As mentioned before, we have developed a new framework, in line with some of the previous contributions already mentioned, which allows us to deal with endogenous change preference in the long term and heterogeneity, incorporating non-economic factors (such as identity) as factors that consumers take into account when deciding the level of consumption of a final good. Since we assume that the final good is produced using a renewable resource as an input, our framework enables us to infer the effect our assumptions have on the final level of the resource stock. Traditionally, within the dynamic optimizing utilitarian framework used for the development of works incorporating the question of natural resources into their analysis, social preferences have been dealt with from two different perspectives. The first one regards final consumption as the only source of satisfaction (Dasgupta and Heal 1974, 1979; Stiglitz 1974, Solow 1974; Grossman and Helpman 1991; Aghion and Howitt 1992). The second one, taken from a wider viewpoint, considers an intrinsic valuation of natural resources as an additional element for personal well-being (Krautkraemer 1985; Beltratti et al. 1993, 1995, 1998; Chichilnisky 1997; Heal 1998, 2001; Lafforgue 2005; Wirl 1999, 2004). Despite the theoretical advances offered by this inclusion of the intrinsic evaluation of natural resources as a source for personal satisfaction, the framework defined by the authors in this field is insufficient to analyze how certain non-economic factors, such as the existence of identities promoting cooperative attitudes regarding the environment, can bear an influence on the behavior of agents. Hence, the need to design a new framework which includes existing relationships between identity, choice and the exploitation of natural resources seems essential. To do that, we have defined a dynamic identity function which rests upon the idea that a social identity exists in the economy which we will call Environmentally Friendly Identity (EFI). It is known by all consumers and characteristically promotes

3 Kevane (1994, p. 2). Not in italics in original text. 4 Hodgson (2007, p. 8).

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a respectful behavior towards the use of renewable resources in the productive sector. Such an identity can be considered to be a social reference of behavior and it contains a set of actions which allows the consumer to approach it. As can be seen, our conception of identity is in line with the findings shown by social psychology and with Landa (1981, 1994), who considered that the existence of specific social categories are linked to the acceptance of certain norms and values. At the same time, as we have considered preference heterogeneity, each agent can identify with EFI to a greater or lesser degree depending on their environmental concerns. The result is that, the greater the level of identification with EFI, the greater the reduction in consumption of the final good that a consumer is willing to accept. At the same time, since EFI is considered a social reference of behavior, approaching EFI becomes a source of satisfaction, so the identity function itself is an argument of the utility function. After setting up our approach, we pose the question as to how far the identification of each agent with the social standard characterized by EFI modifies the levels of use and consumption of the natural resource. We see that those economies characterized by incorporating the identity function into the preference structure of consumers show a higher level of resource stock and lower levels of final consumption, resource withdrawals and physical capital stock in their steady state. Therefore, we have shown that, as long as heterogeneity regarding preferences is considered, consumption levels, capital stock (physical and natural) and resource extraction do not only depend on a greater or lesser identification with EFI, but also on the proportion of the population incorporating the personal identity function into their structure of preferences. These findings enable us to draw interesting conclusions relating to environmental policies in place since the 1970s. The use of environmental policies to limit direct access to certain renewable natural resources was common in the late 70s. For example, the overexploitation of some fishing resources, such as herrings or whales, had led to the stock of these species dropping to a critical level. To alleviate these problems, the governments of the stakeholder countries decided to implant policies to restrict the extraction of these resources. For instance, Norway regulated the captures of herring in 1981, establishing maximum quotas. Within the framework of the International Convention for the Regulation of Whaling, Iceland and Japan limited the capture of whales from 1982 onwards. The results of these policies were quickly seen and the respective stocks began to recover progressively. However, although we can see that these kinds of measures have been very effective in terms of species protection, most of these moratoriums have been suspended in recent years. For example, Iceland declared (just as Norway had already done) in October 2006 that they would permit whaling for commercial ends once more. We use our framework to analyze the reasons underlying the instability of this kind of environmental policies, showing that policies of limited extraction quotas will only be effective in the long term if they are accompanied by measures of environmental awareness and education to reduce demand for the resource. As is shown in our work, although including the personal identity function in the structure of preferences has the same effect on the economy as a fixed quota for extraction, the actual reductions in extraction obtained via the personal identity function are voluntary while any reductions derived from the quota policies are not.

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In accordance with the above-mentioned, the article is organized as follows: the next section is devoted to specifying the model assuming as a first step that all individuals are identical. In Sect. 3 we will include heterogeneity in preferences. Section 4 will see the implications of our framework for environmental policies which opt for the setting of fixed extraction quotas. Finally we offer a synthesis of our conclusions. 2 The model We define an economy with n individuals and a social planner in charge of the optimum intertemporal assignation of the consumption level of a final good and the extraction level of a renewable resource used as a production input for said final good. The planner’s optimization program will respond to the following expression5 :

Max

{cti ,σt }

∞ n 0

u it (cti , st , α i (cti ))e−θt dt, with θ > 0

i=1

•

s.t. k = f (kt , σt ) −

n

cti

i=1 •

s = r (st ) − σt where α i (·) is the personal identity function, cti represents the consumption level of the final good for each individual i at each of time, st represents the level of resource stock at each of time, kt shows us the physical capital level at each instant of time and σt , represents the amount of the natural resource used in the production of the final good at each of time. We characterize the personal identity function, α i (ct ), formally, from the framework proposed by Akerlof and Kranton (2000),6 with the following assumptions: 5 Let us remark that in this paper we set out an extended version of the model put forward previously by Beltratti et al. (1993, 1998), Chichilnisky (1997) or Heal (1998). 6 Akerlof and Kranton (2000) introduce the concept of identity into the neoclassic maximizing framework by considering that the image each agent has of themselves (that is, their personal identity) is an argument of the consumer’s utility function.

Ui = Ui (ci , c−i , αi ) where the well-being of each individual i would be determined by the individual’s consumption of goods and services (ci ), the consumption of goods and services by the other individuals in the economy, (c−i ), and the image each individual has of themselves, i.e., their personal identity (αi ). Likewise, this latter term is defined from the following function: αi = αi (ci , c−i , bi , i , T ) where the identity of each individual i depends principally on the social categories considered relevant by said individual, bi , on the way in which each agent perceives that their personal characteristics, represented by i , permit them to endogeneize all the prescriptions and behaviors, represented by T , associated with the social category and, once again, on the consumption of goods and services.

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Assumption 1 We will assume that a unique social identity exists, called Environmentally Friendly Identity ‘EFI’, whose main feature is to pose an environmentallyrespectful behavior regarding the environment. In line with social psychology7 and with Landa (1981, 1994) the term ‘Environmentally Friendly Identity’ will include the combination of values, ways of acting and thinking regarding the environment considered suitable by society. Said identity predisposes those individuals who value it to act following a determined behavior pattern in their choices.8 Assumption 2 We suppose that agents can decide to reduce their consumption level of the final good so as to approach the identity they value.9 Assumption 3 The consumption of goods and services by the other individuals in the economy (c−i ) does not have an influence on the identity of individual i. Assumption 4 We will consider that the degree of identification of each individual with the reference social standard is only determined by the different (intrinsic) environmental sensitivity each individual owns. If we use ∈i to represent the environmental sensitivity of agent i, the dynamic personal identity function will coincide with the following expression: αti = α(cti ; ∈i ) ≡ αti (cti ); with

∂α(cti ; ∈i ) > 0, with i = 1, . . . , n. ∂ ∈i

We can see that the environmental sensitivity of each agent (represented by ∈i ) determines the specific functional form of αi (·). The partial derivative captures the fact that the greater the environmental sensitivity is, the greater the personal identification with respect to the reference category and, for any of the possible consumption levels, the greater the predisposition to internalize the prescriptions associated with said social identity. 7 See, for example, Appiah (2005), Erikson (1959). 8 It is unquestionable that new concepts related to the environment have appeared over the last 40 years

(ecological products, renewable energy, responsible consumption, etc). This suggests the parallel emergence of a more or less generalized common collective identity relating to the environment. In this sense, the latest political campaign of Al Gore (former Vice-President of the United States) based on specific measures to limit the effects of the climate change (An Inconvenient Truth), or the May edition of the Vanity Fair magazine (called: The Green Issue: Politics and Power—May 2007), totally devoted to these issues, are clear examples of the common-place attitude to environmental questions nowadays. Equally, underlying the labels ecological products, “renewable energy” and so on, we find not only a new product or a new way of producing energy, but also a response which leads the behavior of those consumers who feel close to the new identity. 9 Thus, in terms of the framework proposed by Akerlof and Kranton (2000), we can see that for each instant of time:

cti = Tt

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Let us remark that, while in Landa (1981, 1994) and Kevane (1994) identities are mostly linked to ethnicity—that is, identity is given by the fact of being born in a specific ethnic group—in our work, identity (even if it is unique and known by all) is chosen by the individual according to their personal environmental sensitivity. Furthermore, such a distinct environmental sensitivity is, in this work, the question which allows us to explain heterogeneity in preferences (see Sect. 3—Definitions 1 and 2). Assumption 5 The personal identity function of individual i, αti (·), verifies for each level of consumption cti , that: α i (cti ) > 0; αci t < 0 and bounded; αci t ct < 0 and bounded; αti (0) = Ai ; with Ai > 0 As the first derivative indicates, the lower (greater) the consumption, the greater (lower) the identification of agent i with the reference standard (EFI). Furthermore, as the second derivative indicates, each additional reduction in consumption means a smaller and smaller increase in said identification. Being Ai the maximum identification which agent i can reach with respect to this standard reference. Thus, even if agent i reduces their resource consumption to zero, the identification with this standard will be, at most, Ai . Therefore, for function α i (·) to have the economic sense we wish to give it in this work, we will suppose that there exits a range of consumption levels, cti ∈ (0, c¯t ), wide enough hence, each agent can choose a level of consumption enclosed within such a neighborhood, then α i (cti ) > 0 (see next figure)

Assumption 6 The image each agent has of themselves is a source of personal satisfaction. Hence, the function α i (·), will be an argument of the consumer’s utility function. Assumption 7 We will suppose that the utility function is separable additive in its three variables and responds, for each agent i, to the following expression:

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u i (cti , st , αti (cti )) = u i1 (cti ) + u i2 (st ) + u i3 (αti (cti )) = U i (cti , st ) Assumption 8 The utility functions u ik (·) with k = 1, 2, 3 are continuous, twice differentiable and verify the usual properties: u i1ct > 0; u i1ct ct < 0; lim u i1ct = ∞ and lim u i1ct = 0; ct →∞

ct →0

lim

st →0

u i2st u i2st

>

u i3αt

> 0 and bounded; u i3αt αt < 0;

0; u i2st st

0 In the above expression we can see that an increase in resource consumption produces two opposing effects: an increase in utility via consumption of the final good, and a decrease derived from the level of identification of agent i with the reference standard. Assumption 9 states that this negative effect will never completely wipe out the satisfaction of consumption.10 Assumption 10 There is only one firm in charge of production of the final good. n i Assumption 11 The final good of consumption ct = i ct is produced at each instant of time using two productive inputs: physical capital (kt ) and a renewable natural resource (σt ). The function for the production of the final output responds to the following expression: yt = f (kt , σt ) and fulfills the usual properties: f kt , f σt > 0; f kt kt , f σt σt < 0; f kt σt = f σt kt > 0 f (0, σt ) = f (kt , 0) = 0 lim f kt = ∞ and lim f kt = 0

kt →0

kt →∞

10 Which is congruent with studies into the relative importance individuals give to the satisfaction of different human needs (see Maslow 1943, for example). Said studies say that the satisfaction of basic needs (which can be linked, in our case, to consumption of the resource as a final good) comes before any other superior need (in our case, identity questions).

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Assumption 12 The final output has two destinations, consumption of the final good (ct ) or investment in physical capital (kt ), with the accumulation dynamics of the latter option responding to the following expression: •

kt = f (kt , σt ) −

n

cti with i = 1, 2, . . . , n

i=1

where the above expression represents the variation produced in the level of physical capital after discounting the total amount destined for consumption from the level of final output. Assumption 13 We will suppose that, for each instant in time, the depreciation of physical capital is zero. Assumption 14 The biological function, r (st ) determines the natural growth of the renewable resource and fulfills the following properties: r (0) = 0; ∃¯s > 0 so r (st ) ≤ 0, ∀st ≥ s¯ ; ∀st ∈ (0, s¯ ), r (st ) is strictly concave and twice differentiable Hence the expression •

s = r (st ) − σt , represents the variation produced in the resource stock at each instant of time after the corresponding amount of natural input has been extracted for the production of the final good of the economy. Assumption 15 The size of population P is constant and equal to 1. To solve the above-mentioned program of optimization, in a first approximation we will suppose that all the consumers are identical. The corresponding Hamiltonian will be: H = [u 1 (ct ) + u 2 (st ) + u 3 (αt (ct ))] e−θt + μt ( f (kt , σt ) − ct ) + λt (r (st ) − σt ) The necessary conditions will be11 : ∂ H/∂ct = e−θt (u 1ct + u 3α αct ) − μ = 0 ⇒ μ = e−θt (u 1st + u α αct ) ∂ H/∂σt = μt f σt − λ = 0 ⇒ λt = μt f σt 11 Let us notice that c and σ are the control variables, s and k are the state variables, and λ and μ are the t t t t t t

shadow prices of the resource stock and physical capital, respectively. In our case, the necessary conditions are also sufficient if f σt σt f kt kt − ( f kt σt )2 > 0 is fulfilled (see annex). The transversality conditions assure the nil value of resource stock and physical capital in the steady state.

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I. Almudi, J. Sánchez Chóliz •

∂ H/∂st = − λt = u 2st e−θt + λt rst •

∂ H/∂kt = − μt = μt f kt ⇒ •

∂ H/∂λt = r (st ) − σt = s

•

∂ H/∂μ = f (kt , σt ) − ct = k lim (λt st ) = 0

t→∞

lim (μt kt ) = 0

t→∞

Operating with the necessary conditions and deriving with respect to time we obtain the following expressions which correspond to the dynamic equations12 of our model. •

c 1 U ct = (θ − f kt ) = ( f kt − θ ) c U ct ct c η

(1)

•

f σt ( fkt −rst ) σ 1 Us f σt kt • − t − = k σ σ fσ σ Uct σ f σt σt σ f σt σt t t 1 Us 1 fσ k • rst − f kt + t = + t t k ε Uct f σt f σt

(2)

•

f (kt , σt ) ct k = − k kt kt

(3)

s r (st ) σt = − s st st

(4)

•

Proposition 1 The steady state is characterized by the following four conditions: (i) The marginal rate of substitution between consumption and resource stock equals the marginal rate of transformation of the resource stock. (ii) The marginal productivity of capital equals the inter-temporal rate of discount. (iii) Production is equal to consumption. (iv) The capacity for self-renewal of a resource equals the extraction of said resource. Proof Taking into account that the steady state is that point (c∗ , k ∗ , s ∗ , σ ∗ ) at which the planner maximizes social well-being while consumption levels, physical capital stock, resource stock and resource extraction remain constant, we can obtain the expressions which characterize the steady state from conditions (1)–(4). In our case: u2s∗ = (θ − rs ∗ ) f σ ∗ u 3 α ∗ αc∗ + u 1c∗

(5)

12 Where η = − (u 1 ct ct +u αα αct αct +u 3 α αct ct )ct = − Uct ct > 0 is the elasticity of marginal utility with u 1 ct +u 3α αct U ct u 2 st U is the marginal rate of substitution between the final good and respect to consumption; Ust = u c +u α α ct ct 1 t f σ t σ t σt > 0 is the elasticity of marginal productivity of the resource. the natural resource stock, and ε = − f σt

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fk∗ = θ ∗

∗

(6) ∗

f (k , σ ) = c r (s ∗ ) = σ ∗

(7) (8)

These four conditions guarantee that the paths of consumption and resource extraction chosen by the social planner fulfill the dynamic efficiency conditions necessary for any equilibrium. At the maximum point there will be no further increase in stock levels (neither physical nor natural), and so all the production will be either consumed or extracted.

We can compare the conditions characterizing the steady state in our case, with the conditions obtained without considering the incorporation of personal identity function into the preference structure of the agents (see, for example, Beltratti et al. 1993, 1995, 1998 or Heal 1998, 2001). We can obtain that: Proposition 2 The economy which incorporates the personal identity function into the agents’ preference structure is characterized by having a steady state with a greater marginal relationship of substitution, lower levels of consumption, accumulation of physical capital and natural resource extraction, and a greater level of resource stock. Proof Two parts with different features can be seen in the system formed by these equations. On the one hand, we have Eqs. 6–8 which characterize the productive part of the economy and define all the possible steady states of the system, independent of the preferences of the agents. The influence of these preferences on the steady state are captured in Eq. 5 which determines, from all the possible optimal consumptions, the consumption of the steady state (c∗ ). We can see that, whatever the utility function may be, Eqs. 5–8 will be the same. Let us see some interesting relationships between variables {c∗ , s ∗ , σ ∗ , k ∗ } which we obtain from (5) to (8), bearing in mind that said relationships refer to the possible steady states of the system.

From (8) we obtain: rs∗ ds ∗ = dσ ∗ →

ds ∗ 1 = ∗ < 0, ∀s ∈ [smax , s¯ ] dσ ∗ rs

thus, for all the steady states, s ∗ and σ ∗ vary in an opposing sense. From (6) it can be deduced that: f k ∗ k ∗ dk ∗ + f k ∗ σ ∗ dσ ∗ = 0 →

dk ∗ fk∗σ ∗ =− >0 ∗ dσ fk∗ k∗

therefore, for all the possible steady states, k ∗ and σ ∗ vary in the same sense. From (7) it can be obtained that: dk ∗ dc∗ ∗ f k ∗ dk ∗ + f σ ∗ dσ ∗ = dc∗ → = f + fσ ∗ k dσ ∗ dσ ∗ fk∗ σ ∗ dc∗ + fσ ∗ > 0 → = fk∗ − ∗ dσ fk∗k∗

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and, thus, we can affirm that when considering all the steady states, c∗ and σ ∗ vary in the same sense.

Considering the relationship obtained from the following expression: fk∗ σ ∗ d f σ ∗ = f σ ∗ k ∗ dk ∗ + f σ ∗ σ ∗ dσ ∗ = f σ ∗ k ∗ − dσ ∗ + f σ ∗ σ ∗ dσ ∗ fk∗ k∗ fσ ∗k∗ fk∗σ ∗ < 0, = f σ ∗ σ ∗ dσ ∗ 1 − f k ∗ k ∗ f σ ∗ o∗ we can affirm that for all the possible steady states, f σ ∗ and σ ∗ vary in opposing senses. Finally, we can see the slope of the curve c–s associated with the possible steady states. fk∗ σ ∗ dk ∗ dσ ∗ dσ ∗ dc∗ rs ∗ + f σ ∗ rs ∗ = fk∗ ∗ ∗ + fσ ∗ ∗ = fk∗ − ds ∗ dσ ds ds fk∗k∗ fk∗ σ ∗ = rs ∗ −θ + fσ ∗ , fk∗ k∗ therefore, the curve c–s has a unimodal13 shape (see following figure), with the maximum point at the same point as r (st ) and with an increasing or decreasing character, coinciding with that of r (st ).

It can be seen that, in the above curve, moving from A towards B we know that s ∗ grows, and, so, given previous proofs, we know that σ ∗ , k ∗ , c∗ decrease and f σ ∗ grows. Given this information, let us see what the effect of an increased identification with EFI is. Suppose that A is the (s ∗ , c∗ ) corresponding to the steady state of an economy 13 It can be seen that the concavity or convexity at each point will depend on the different functions of the problem.

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characterized by its individuals—named with the superscript 2—presenting a lower level of identification. In (s ∗ , c∗ ) it can be verified that: Us2∗

= (θ − rs ∗ ) f σ ∗ Uc2∗ fk∗ = θ f (k ∗ , σ ∗ ) = c∗ r (s ∗ ) = σ ∗ If we now consider an economy made up of agents—denoted with superscript 1—presenting a higher level of identification with EFI, while taking into account Proposition 2, we can affirm that, for the same point A, it can be verified that14 : Us1∗

> (θ − rs ∗ ) f σ ∗ Uc1∗ fk∗ = θ f (k ∗ , σ ∗ ) = c∗ r (s ∗ ) = σ ∗ Thus, point A does not correspond to the steady state characterized by agents presenting a higher level of identification with EFI. It can be seen that, moving from A U∗ towards other steady states with a higher s ∗ (lower s ∗ ) we know that Us ∗ increases c ∗ (decreases) and that (θ − rs ∗ ) f σ ∗ , for s ≥ smax , increases (decreases). Therefore, those economies presenting a higher identification with the reference standard EFI characteristically offer steady states with a higher stock level and a lower level of consumption. Consequently, taking into account the evolutions of s ∗ , c∗ , k ∗ σ ∗ and f σ ∗ we can affirm that the greater the identification of individuals with EFI, the greater the marginal rate of substitution, the lower the resource extraction level, the lower the levels of production, capital and consumption, and the greater the stock level, in the steady state. One immediate consequence is the following proposition: Proposition 3 The higher the level of identification with the social reference category EFI, the greater the social valuation of stock in the steady state. Proof The above-mentioned proposition is confirmed if the marginal rate of substitution between consumption of the final good and the resource stock is higher for that economy which presents a higher level of identification. As seen in the previous proposition, a higher level of identification displaces the steady state from (s 2∗ , c2∗ ) towards (s 1∗ , c1∗ ) with s 1∗ > s 2∗ and c1∗ < c2∗ . In (s 2∗ , c2∗ ) we have a marginal utility value equal to (θ −rs 2∗ ) f σ 2∗ and, when we shift to (s 1∗ , c1∗ ), the value (θ −rs ∗ ) f σ ∗ increases. 14 It is easy to verify that the higher the level of identification with respect to EFI is, the higher the marginal

rate of substitution between consumption and stock becomes.

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Hence, in the new steady state, characterized by an increased identification with EFI,

the marginal relationship of substitution will be: (θ − rs 1∗ ) f σ 1∗ > (θ − rs 2∗ ) f σ 2∗ . Derived from all the afore-mentioned, we can affirm that those agents which incorporate a higher proximity to the reference standard into their preference structure and derive utility from this, are more disposed to voluntarily reduce their consumption of the final good in exchange for a higher level of resource stock. The reduction in final consumption generates an increase in stock levels for each and every generation t. This leads to the possibility that the conservation level of the stock increases in the long term. Therefore, the incorporation of “green” values in consumer behavior becomes crucial in terms of environmental conservation. 3 Heterogeneity, identity and production In this section we will try to further develop the results obtained previously by considering that there are agents with different degrees of environmental sensitivity in the economy. For simplicity, let us suppose that there are two kinds of consumers, which we shall call type i and type j, and whose relative proportion will be δ and (1 − δ), respectively. Definition 1 Between two individuals i and j we will say that:15 (1) Individual i is identical to individual j if these expressions are fulfilled: j (i) u ik (·) = u k (·), k = 1, 2, 3. (ii) α i (·) = α j (·). (2) Individual i is different in a weak sense from individual j if these are fulfilled simultaneously: j (i) u ik (·) = u k (·), k = 1, 2, 3 and i (ii) α (·) = α j (·). (3) Individual i is different in a strong sense from individual j if the following are fulfilled: j (i) u ik (·) = u k (·), k = 1, 2. j (ii) u i3 (·) = u 3 (·). (iii) α i (·) = α j (·). The previous definition establishes that, if there is heterogeneity in preferences, this is only due to the degree of identification with the reference standard and/or the utility derived from this, being either weak (in which case only the identification will vary) or strong (where both the identification and derived utility will vary). Let us remark that, the distinction between one type of agents and the other, based on the degree of attachment to a common code of behavior also appears in Landa (1981, 1994).16 15 For simplicity in naming, we will omit the subindexes referring to time in cases which cannot cause confusion. 16 In Landa (1981, 1994) the common behavior code is the group of norms contained in Confucian ethics.

In our case, the common behavior code is given by the “good practices” related to the collective identity, EFI.

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Definition 2 We will state that in an economy with different individuals, the (marginal) satisfaction with respect to the environmental standard (EFI) of individual i is greater than that of individual j when the following condition applies: j

j

u i3 α αci t < u 3jα αct , ∀ct ⇔ Ucit < Uct , ∀ct Definition 3 We will state that in an economy with different individuals, individual i has a marginal satisfaction in a strong sense greater than that of individual j when the following two conditions apply simultaneously: j

j

j

(i) u i3 α αci t < u 3 α αct , ∀ct ⇔ Ucit < Uct , ∀ct (ii) u i3 αα αci t αci t + u i3 α αci t ct
0 y 0 < δ < 1 •

st = r (st ) − σt Where the superscripts, i and j are used to distinguish the values of the variables and parameters of individuals i and j, at each of time, with δ, (1 − δ), ct , st , θ, σt , kt , being respectively: the proportion of population presenting each kind of preference, the final consumption, the resource stock, the inter-temporal discount rate, the level of natural resource used as productive input, and the level of physical capital.

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The Hamiltonian in this case responds to the following expression: H = e−θt [δ(u i1 (cti ) + u i2 (st ) + u i3 (αt (cti )) + (1 − δ)(u 1 (ct ) + u 2 (st ) + u 3 (αt (ct ))] j

j

j

j

j

j

+μt [ f (kt , σt ) − δcti − (1 − δ)ct ] + λt [r (st ) − σt ] The necessary conditions will be, in this case: ∂ H/∂cti = e−θt (u i3 α αci t + u i1 ct ) − μt = 0 ⇒ μt = (u i3 α α3i ct + u i1 ct )e−θt ∂ H/∂ct = e−θt (u 3jα α3 ct + u 1 ct ) − μt = 0 ⇒ μt = (u 3jα α3 ct + u 1 ct )e−θt ∂ H/∂σt = μt f σt − λt ⇒ λt = μt f σt j

j

j

j

j

•

∂ H/∂st = − λ = λt rst + [δu i2 st + (1 − δ)u i2 st ]e−θt = λt rst + u 2 st e−θt •

∂ H/∂kt = − μ = μt f kt •

∂ H/∂λt = r (st ) − σt = s

j

•

∂ H/∂μt = f (kt , σt ) − δcti − (1 − δ)ct = k lim (λt st ) = 0

t→∞

lim (μt kt ) = 0

t→∞

Deriving with respect to time, we obtain the dynamic equations when we consider the producing sector and heterogeneity among preferences: •

ci cti • cj j ct •

=

Ucit Ucit ct ci

(θ − f kt ) =

1 ( f kt − θ ) ηi

(9)

(θ − f kt ) =

1 ( f kt − θ ) ηj

(10)

j

=

U ct j U ct ct c j

σ f σt = σt σ f σt σt f σt = σ f σt σt

Usi 1 fσ k • − t t k f kt − rst − it Uct f σt f σt j

Us 1 fσ k • − t t k f kt − rst − jt f σt Uc f σt

•

(11)

t

j

f (kt , σt ) δcti (1 − δ)ct k = − − kt kt kt kt

(12)

s r (st ) σt = − st st st

(13)

•

Next, we will analyze the conditions which characterize the steady state: Proposition 4 For any steady state solution the following must be fulfilled:

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(i) The marginal rate of substitution between stock and consumption must be equal, for both groups of consumers, to the marginal rate of transformation. (ii) The marginal productivity of capital must equal the temporal discount rate. (iii) The sum of both groups’ consumptions, weighted for their relative size, equals the production level. (iv) The resource extraction level equals its capacity for regeneration. Proof Taking into account the fact that the variation rate of variables is zero in the steady state, from dynamic equations (11–13) the following expressions can be directly obtained: j

us∗

u is ∗

=

j j u iα αc∗ + u ic∗ u α αc∗ + u c∗ fk∗ = θ

= (θ − rs ∗ ) f σ ∗

f (k ∗ , σ ∗ ) = δci∗ + (1 − δ)c j∗ r (s ∗ ) = σ ∗

(14) (15) (16) (17)

which characterize the steady state of our economy when we consider that there are different consumers.

Proposition 5 Each group of consumers enjoys the consumption level which determines their preference structures. This is lower for the group showing a greater identification with the reference standard EFI. Proof It can be seen that starting out from (14) to (17), we can assure that ci∗ < c j∗ in the steady state.

The equations: fk∗ = θ f (k , σ ∗ ) = c∗ r (s ∗ ) = σ ∗ ∗

define the curve c∗ (s ∗ ) which we have seen previously. The steady state corresponds to a s ∗ such that c∗ (s ∗ ) = δci∗ + (1 − δ)c j∗ . Furthermore, this verifies that: Usi∗ Uci ∗

j

=

Us ∗ j

Uc ∗

= (θ − rs ∗ ) f σ ∗

(¯s i , c¯i ) is the point which verifies:

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fk∗ = θ ∗

f (k , σ ∗ ) = c∗ r (s ∗ ) = σ ∗ Usi∗ = (θ − rs ∗ ) f σ ∗ Uci ∗ and (¯s j , c¯ j ) the point which satisfies: fk∗ = θ f (k ∗ , σ ∗ ) = c∗ r (s ∗ ) = σ ∗ j

Us ∗ j

Uc ∗

= (θ − rs ∗ ) f σ ∗

See the following graph:

We know that, if F(s) = (θ − rs ) f σ , the following is verified: (θ − rs¯ j ) f σ j = F ∗ (¯s j ) < F ∗ (¯s i ) = (θ − rs¯i ) f

σi

i

,

given the previously mentioned explanation. Thus we can conjecture that the s ∗ of the steady state will verify: s¯ j < s ∗ < s¯ and we can see that this is so. For s¯ to be any ∈ (¯s j s¯ i ) we obtain that: j

j

Us¯

j

Uc¯ j

123

δ Therefore, given the continuity of the problem, we can assure that there is a value of s ∗ and to values ci∗ and c j∗ , such that: c∗ (¯s ) = δci∗ + (1 − δ)c j∗ ci∗ = c¯¯i < c¯i ; c j∗ = c¯¯ j > c¯ j and, thus, these ci∗ and c j∗ to verify the conditions for the steady state which, therefore, exists. It can be seen, likewise, that c j∗ > ci∗ and, thus, consumption is higher in the group with a lower level of identification with respect to the reference social category. It can also be seen that the Proposition 2 showed the relationship between different levels of identification with EFI and the resulting values for the main variables of the economy. In cases of heterogeneous preferences, levels of consumption, (physical and natural) capital stock, and resource extraction will not only depend on a greater or lower identification with EFI, but also on the proportion of the population incorporating the personal identity function into their preference structure. To be specific, as can be easily deduced from previous arguments, as δ increases, so will the resource stock level while the levels of consumption of the final good, capital, and natural input extraction fall. We can see that, although the consumption level is different for each group of consumers, the resource stock is common for both and satisfies neither. What is more, we can affirm that the group of consumers with a higher level of identification manages

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to increase the level of combined stock by yielding part of its consumption, which produces a transference of utility from the group with the greatest identification to that with the lowest. We will analyze some of the implications of this result in the following section.

4 An application to the analysis of policies setting extraction limits This section aims to show that the stability of those policies which set a constant resource extraction level (for example, fishing quotas) depends chiefly on the preference structure of society. Up to now, these policies have been implemented on a basis of bioeconomic models taking into account the characteristics of the regulated species and the costs and benefits associated with the fishing industry (see, for example, Gordon 1954; Schaefer 1954; Bjornal and Munro 1997). However, they do not take on board the social structure in its totality when deciding what the optimum rate17 for resource extraction should be. As we show, said policies, though, may turn out to be inefficient in the medium-term if they are not complemented with additional measures which modify the preference structure. As we shall see with the following propositions, ending the moratoriums and the permanent tension created in these countries as they desire to increase their annual capture rates,18 can be explained in the framework of models developed in this section. The main point we will explain is that if an exogenous capture rate is introduced which does not coincide with the optimum rate, in the long-term this rate will generate tensions between those in favor of protecting the resource and those who depend on it for economic reasons, especially if this latter group represent an important proportion of the population. To see this, we will introduce an exogenously set resource extraction level into the framework of the production sector model we have laid out previously.

17 That is: that obtained after solving the corresponding program of general optimization. 18 In the late 1970s the use of environmental policies to limit access to certain renewable natural resources

(TAC) was commonplace. The overexploitation of fishing resources such as the herring or whales had left the stocks of these species at a critical level. This even led to moratoriums in the captures of these species to avoid their eventual disappearance. The “free access” character of these resources and the introduction of new technology for fishing purposes allowed for captures to increase at a far quicker rate than with more traditional fishing methods. This caused an excess in supply of captures of certain species and, hence, a drastic fall in prices. These reduced profits for the industry led, in turn, to the fishing industry increasing its captures, thus accelerating even more the extraction of fishing resources. On the other hand, environmental groups, which had their roots principally in the USA in the early 60s, started to work on a wider, more international scale, and applied pressure on local and national governments to control access to free resources. Attempting to ease the problem, governments decided to develop policies to restrict the extraction of said resources. However, and in spite of the effectiveness of said policies, recently many of these moratoriums have been suspended. For example, the government of Iceland (and, before them, Norway) allowed the hunting of whales for scientific ends to recommence in October 2006. This has re-awoken the debate between those who believe that the moratorium has been useful for the recovery of these species (international organizations) and those who say that it has been harmful for the fishing industry, an extremely significant sector of the economy of Iceland (local and national organizations).

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Assumption 18 Let us suppose that the environmental planner sets a resource extraction level σ p∗ such that the stock level associated with it is equal to or greater than that of the MSY, that is to say: σ p∗ = r (s ∗p ) with s ∗p ∈ (smax , s¯ ) Therefore, the production function is now: y = f (kt , σ p∗ ), ∀(σ p∗ , s ∗p ) The planner’s problem in this case is:

Max

∞ n

{cti }

0

u it (cti , st , α i (cti ))e−θt dt, with θ > 0

i=1

•

s.a. k = f (kt , σ p∗ ) −

n

cti

i=1 •

s=

r (st ) − σ p∗

If we suppose that all individuals are identical, the Hamiltonian will correspond to the following expression: H = [u 1 (ct ) + u 2 (st ) + u 3 (αt (ct )] e−θt + μt ( f (kt , σ p∗ ) − ct ) + λt (r (st ) − σ p∗ ) We can see that in this case there are two state variables, capital and resource stock, and only one control variable—final good consumption. The necessary conditions in this case will be: ∂ H/∂ct = e−θt (u 1 ct + u 3 α αct ) − μt = 0 ⇒ μt = e−θt (u 1 ct + u α αct ) •

∂ H/∂st = − λt = u 2 st e−θt + λt rst •

∂ H/∂kt = − μt = μt f kt ⇒ •

∂ H/∂λt = r (st ) − σ p∗ = s

•

∂ H/∂μ = f (kt , σ p∗ ) − ct = k lim (λt st ) = 0

t→∞

lim (μt kt ) = 0

t→∞

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Thus, the dynamic equations with these new conditions will be given by: •

c U ct 1 = (θ − f kt (kt , σ p∗ )) = ( f kt (kt , σ p∗ ) − θ ) c U ct ct η

(18)

•

f (kt , σ p∗ ) ct k = − k k k • ∗ s r (st ) σ p = − s s s

(19) (20)

Proposition 6 If we set the resource extraction level exogenously, the levels of physical capital stock and final good consumption in the steady state will be given by the following conditions: f kt (kt , σ p∗ ) = θ f (kt , σ p∗ ) = ct r (s ∗p ) = σ p∗

(21) (22) (23)

That is to say: (i) The marginal productivity of capital equals the temporal discount rate. (ii) The consumption level corresponds to the production level. (iii) Self-renovation of the resource equals its extraction level. •

•

•

Proof It is straight-forward that making c = s = k = 0 in Eqs. 18–20 the following expressions are obtained: As seen in the proof of Proposition 2, in the second section of this paper, Eqs. 6–8 generate a map of all the possible steady states of the system, which we represent in the curve c∗ (s). It can be seen that setting an exogenous extraction rate means positioning ourselves in one of the steady states independently of the subjects’ preferences. If we consider a given σ p , the steady state we obtain will correspond to that of the general model if: (θ − r (s ∗p )) f σ p∗ = which is not certain in general.

Us ∗p Uc ∗

Hence, we can affirm that: Proposition 7 If, before measures of environmental policy are introduced, the economy was in a steady state (c∗ , s ∗ ) such that σ p∗ < σ ∗ , (i) said measure will generate a decrease in the accumulation levels of physical capital, consumption, production and an increase in resource stock. (ii) Likewise, the situation will only be steady (that is, the levels of variables will correspond to those of the steady state) if the real valuation of stock compared

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to consumption changes and adapts to that of σ p . If the social valuation corresponds to s ∗ , and does not change, this will be lower than that required by the environmental policies and their measures will not be stable. Proof Statement (i) is a direct consequence of the Proposition 6 and of the Proposition 2 of the general model. Statement (ii) is simply a consequence of whether or not the condition (5) of the steady state is verified.

As can be deduced from the above proposition, if the exogenous extraction rate does not coincide with that of the steady state of the general model, the environmental policy measures will generate tensions. If the imposed extraction rate is lower than that of the steady state of the general model, we will be in a situation in which the stock valuation is lower than that determined by the policy. In this case, therefore, the agents will apply pressure to achieve an increase in the extraction rate. If, on the other hand, the rate is greater than that of the steady state of the general model, this will lead to agents applying pressure to see it reduced. However, even more significantly, (as demonstrated in Almudi and Sanchez (2009) the existence of social pressure can fictionally alter the relative weight of a specific social group (making it more visible than it really should be when its actual size is taken into account). This means that it is very difficult to guarantee, in a general way, that the result of social pressure will be congruent with the majority’s preferences.19 All of this clearly shows the huge difficulties in implementing specific environmental policy measures, congruent with both the particular interests of agents and with society’s actual structure of preferences. These difficulties had been pointed out previously by Brennan (2006) who, in a partial equilibrium model, had already detected the instability associated with environmental policies as a consequence of the modification of social preferences.20 For all these reasons, we can conclude that policies setting maximum extraction levels will only be effective in the long term if they are accompanied by complementary measures of environmental awareness and education so as to relieve the pressure on the demand for the resource. We can see that incorporating the personal identity function into preference structures will generate the same effects on the economy as the extraction limiting policies, but while reductions in resource extraction via the personal identity function are achieved voluntarily, those derived from restrictive policies are not. 5 Concluding remarks In our work we explore the implications for the conservation levels of a renewable natural resource when we consider that economic agents decide the consumption level of a final good (using the natural resource as a productive input) while incorporating 19 Almudi and Sanchez (2009) studies the case of type i consumers exerting pressure on the planner with the aim of reducing the total consumption and increasing stock. This work reaches the conclusion that it is very difficult, in general, to guarantee that a higher pressure exerted by those who place a higher value on stock will lead to a reduction in the combined consumption of the resource. 20 It should be noted that Brennan (2006) analyzed the stability of environmental policies for CO polluting 2

activities whereas we analyze the environmental policies for a renewable resource.

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identity questions into their preference structures. To be specific, we suppose that there is a social identity, which we call EFI, characterized by promoting a respectful behavior towards the environment. Regarding this identity, the agents can identify with it to a greater or lower extent in function of the environmental sensitivity they have. The greater the degree of identification an agent shows, the greater the reduction in consumption of the final good that said agent is willing to accept. The results we obtain show that the greater degree of identification the agents present with respect to the social category and the greater is the proportion of the population with said level of identification, the greater the resource stock level and the lower the levels of consumption of the final good, resource extraction and physical capital accumulation. This result is obtained as a consequence of the fact that the existence of the social identity EFI alters the consumers’ preference structures, encouraging them to willingly reduce their level of consumption. This leads to a drop in resource extraction levels, which, in the long term, generates an increase in resource stock. Hence, the indirect consequence of the existence of a behavior model promoting a respectful behavior towards the environment is that those societies which internalize said social identity, eventually give more value to their natural resources. These findings enable us to draw interesting conclusions relating to environmental policies in place since the 1970s. The use of environmental polices to limit direct access to certain renewable natural resources was common in the late 70s. For example, the overexploitation of some fishing resources, such as herrings or whales, had led to the stock of these species dropping to a critical level. To alleviate these problems, the governments of the stakeholder countries decided to implant policies to restrict the extraction of these resources. As we have shown in this paper, incorporating the personal identity function into the agents’ preference structure means that, these agents are willing to voluntarily reduce their consumption of the final good and, hence, the resource extraction rate also decreases voluntarily. On the other hand, if the exogenous extraction rate, set by governments, does not coincide with that obtained from the society’s preference structure, then these environmental policies will not be stable in the long term and will lead to tension. For all the above-mentioned reasons, we can conclude that policies to set maximum levels of resource extraction will only be effective in the long term if they are accompanied by complementary measures of environmental awareness and education which reduce the pressure on demand of the resource. As we have shown in this work, although incorporating the personal identity function into the preference structure generates the same effects in the economy as policies which set limits for extraction, reductions in the extraction level via the personal identity function are voluntary, while those derived from limiting policies are not. Acknowledgments This work has been developed thanks to the financial support provided by the Fundación Ramón Areces and the financial aid received from the Spanish Ministry of Education (project: SEJ 2007-60960/ECON). Likewise, the authors are very grateful to Graciela Chichilnisky, Renan Goetz, Catarina Roseta-Palma, Santiago Rubio Jorge and Juan Perote-Peña for their very valuable comments and suggestions. An earlier version of this paper was presented at the 16th Annual Conference of the European Association of Environmental and Resource Economists (EAERE), and received very valuable comments from the participants. Finally, the authors are indebted to an anonymous referee of the Journal of

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Bioeconomics and to Janet T. Landa. If there are any errors in our work, it is solely the responsibility of the authors.

Appendix: Sufficient conditions The necessary conditions derived in Sect. 2 two of this paper are also sufficient if the functions f 0 = U (st ), U (s, ct ), f 1 = r (st ) − ct , f 2 = f (kt , σt ) − ct are concave at c, σ, k and s. To check the concavity of f 0 , the quadratic form associated to the Hessian must be negatively defined or semi-defined. The Hessian is: ⎛

Ucc ⎜ Uσ c ⎜ ⎝ Ukc Usc

Ucσ Uσ σ Ukσ Usσ

Uck Uσ k Ukk Usk

⎞ ⎛ Ucs u 1ct ct + u 3αα αct αct + u 3α αct ct ⎜ Uσ s ⎟ 0 ⎟=⎜ Uks ⎠ ⎝ 0 Uss 0

0 0 0 0

⎞ 0 0 0 0 ⎟ ⎟ 0 0 ⎠ 0 u 2ss

The quadratic form associated to the Hessian is negatively semi-defined so the utility function is concave in its four variables. The Hessian for the case of function f 1 will be: ⎛

f 1cc ⎜ f 1σ c ⎜ ⎝ f 1kc f 1sc

f 1cσ f 1σ σ f 1kσ f 1sσ

f 1ck f 1σ k f 1kk f 1sk

⎞ ⎛ f 1cs 0 ⎜0 f 1σ s ⎟ ⎟=⎜ f 1ks ⎠ ⎝ 0 f 1ss 0

0 0 0 0

⎞ 0 0 0 0 ⎟ ⎟ 0 0 ⎠ 0 rss

Once again the quadratic form associated with the Hessian is negatively semi-defined so the self-renewing function of the resource is concave in its four variables. Finally, we check the degree of concavity of function f 2 , with the Hessian: ⎛

f 2cc ⎜ f 2σ c ⎜ ⎝ f 2kc f 2sc

f 2cσ f 2σ σ f 2kσ f 2sσ

f 2ck f 2σ k f 2kk f 2sk

⎞ ⎛ f 2cs 0 ⎜0 f 2σ s ⎟ ⎟=⎜ f 2ks ⎠ ⎝ 0 f 2ss 0

0 fσ σ f kσ 0

0 fσ k f kk 0

⎞ 0 0⎟ ⎟ 0⎠ 0

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