Environmental groups in monopolistic markets

Transcription

1 Environmental groups in monopolistic markets Pim Heijnen and Lambert Schoonbeek Department of Economics University of Groningen The Netherlands Abstract We examine a market on which a monopolistic firm supplies a good. The production of the good causes damage to the environment. Consumers are heterogeneous with respect to their disutility of the environmental damage. An environmental group can enter the market and set up a campaign in order to influence consumers preferences. We characterize the equilibrium of the resulting entry-deterrence game and investigate its social welfare properties. In equilibrium social welfare is largest if the monopolist deters entry of the EG by selecting a clean-enough production technique. JEL classification: L1, Q2. Keywords: environmental group, environmental quality, monopolist, entry deterrence, social welfare. 1 Introduction Environmental groups (EG s) use campaigns in order to convey information to consumers. One of the goals of such campaigns can be to discourage people from buying certain goods, because the production process of these goods generates too much pollution to the environment. For example, it can happen that consumers are aware of the environmental damage caused by the consumption of a certain good and dislike this detrimental effect. Yet, a campaign launched by an EG could increase the level of guilt felt by them if they purchase the good in question. On the other hand, it can also happen that consumers underestimate the actual level of pollution caused by a product and that a campaign of Corresponding author: Pim Heijnen: Department of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands. addresses: P.Heijnen@eco.rug.nl and L.Schoonbeek@eco.rug.nl, respectively. Fax: Phone: (Heijnen) and (Schoonbeek). We thank Marco Haan and Peter Kooreman for useful remarks on an earlier version of the paper. 1

2 an EG informs them about the full amount of damage that results from their consumption behaviour. 1 This paper investigates a model that can be used to study the effects of such a campaign of an EG. In our model we consider a profit-maximizing monopolistic firm that supplies a good on a market. The production of this good causes damage to the environment. The monopolist can control the environmental damage generated per-unit production by choosing an appropriate production technique. However, the use of a cleaner technique also implies that the per-unit production cost becomes higher. Utility-maximizing consumers dislike environmental damage, but they are heterogeneous in this respect. The key feature of the model is that an EG can decide to enter the market and expend effort in a campaign aimed at increasing each consumer s disutility of the environmental damage that results if he or she consumes the good. The ultimate goal of the EG is to minimize the aggregated environmental damage plus the costs of their campaign. Our model is a three-stage game in which first the monopolist selects the level of environmental damage per-unit production, next the EG decides whether it will enter and expend effort in a publicity campaign, and finally the monopolist chooses the price of its product and the consumers decide whether to buy the good. We derive the (subgameperfect Nash) equilibrium of the model and discuss social welfare properties associated with this equilibrium. More particularly, we demonstrate that the monopolist and EG are involved in a so-called entry-deterrence game (for a general discussion of such games, see Tirole [9]). That is, in equilibrium we can have a situation with either blockaded entry, or entry deterrence or entry accommodation between the monopolist and EG. We characterize in terms of the size of the model parameters which of these three situations is relevant in equilibrium. Moreover, we prove that in equilibrium social welfare is largest if we have a situation with entry deterrence, i.e. if the monopolist deliberately selects a 1 For example, Greenpeace organizes campaigns about the environmental damage caused by different consumer products, see under campaigns at 2

3 production technique that is so clean that it is not profitable for the EG to enter and start a campaign. 2 Our model is closely related to the vertical product differentiation model with environmentally conscious consumers presented by Arora and Gangopadhyay [1] and Moraga- González and Padrón-Fumero[8]. Further references that elaborate on the latter type of model are Bansal and Gangopadhyay[3],and Cremer and Thisse[4]. We remark here that these studies focus on the effectiveness of traditional tax and regulatory measures a government might use in order to reduce environmental pollution and increase social welfare. Non-governmental organizations like an EG do not play any role in these studies. Instead, our study focuses precisely on the effect of this type of organization. The mentioned references further consider duopoly models, whereas we limit attention to a model with a monopolistic firm in order to obtain tractable results. We can make three further remarks concerning related literature. First, Liston-Heyes [6] also examines a model in which a monopolistic firm and an EG have conflicting interests. However, different from our approach, in her model the firm needs permission from the government for a project which, if approved, yields profit to the firm but damage to the environment. The EG is opposed to the project. The decision by the government is binary: either the firm is allowed to carry out its plan, or the permission is denied. The situation is modelled as a rent-seeking contest in which both players lobby at the government in order to increase the probability of a decision which is favourable from their own perspective. Related to the approach in our model, Liston-Heyes [6] assumes that the EG wants to minimize the expected environmental damage plus lobbying expenditures. For a similar model, see also Heyes [5]. Second, Maxwell et.al. [7] discusses a three-stage model in which identical Cournot 2 It is interesting to observe here that on June 11, 2004, the electronics company Samsung announced that it will replace toxic chemicals (like brominated flame retardants) in some of its products by safer alternatives. This decision was made after initial talks with Greenpeace (see We can interpret Samsung s behavior as an attempt to deter a campaign by this EG. 3

4 oligopolists face the possibility of mandatory pollution abatement regulation by the government. The firms first select a voluntary abatement level. Next, the consumers observe this abatement level and determine whether to enter a so-called influence game. Finally, the firms play a Cournot production game. If the consumers enter the influence game, then they as well as the firms exert pressure on the government in order to induce it to prescribe a level of abatement that is desirable from their own perspective, respectively, and in turn the mandatory abatement policy is determined by the government. It turns out that, just like in our model, in equilibrium there are circumstances such that the firms deter entry of the influence game by selecting an appropriate (high-enough) voluntary abatement level. However, contrary to Maxwell et.al. [7], governmental regulation does not play a role in our model. Third, we observe that our analysis is related to the theoretical industrial organization literature on advertising models, see Bagwell [2] and Tirole [9]. In particular, we mention here [10] which elaborates on a model of persuasive advertising in a market with heterogeneous consumers. Recall that in the case of persuasive advertising, a firm attempts to influence consumers preferences in favour of its own product. Clearly, from a formal point of view, we can consider a campaign of an EG as a kind of negative persuasive advertising. Notice that in contrast with the advertising literature, we have an outsider (the EG) which is the actor that advertises. The paper proceeds as follows. In Section 2 we introduce the model. In Section 3 we derive the equilibrium of the model, and in Section 4 we examine social welfare implications of the equilibrium. Section 5 concludes. 2 The model Consider a market with a profit-maximizing monopolistic firm which supplies one good. The production of each unit of the good generates a damage, d > 0 say, to the environment. The actual size of d depends on the production technique chosen by the firm. Once this 4

5 technique has been chosen, the marginal (production) cost for the firm is constant and given by the function c(d) > 0. We assume that c (d) < 0 and c (d) > 0 for all d. If a good is produced such that more environmental damage is caused, it also becomes cheaper to produce this good, but this effect diminishes for larger d. The firm has no fixed cost. Consumers buy either one unit of the good or do not buy it. They are uniformly distributed on the line [0, θ] with mass one, where θ > 0 is given. A consumer θ [0, θ] receives a utility U = V θd p if he buys the good and zero otherwise. The good is only bought if U 0. The term V > 0 denotes the intrinsic utility of the good, θd is the disutility experienced by consumer θ as a consequence of the environmental damage generated by the production of the good, and p is the price of the good. Note that consumers are heterogeneous in the disutility they experience from environmental damage. An EG has the option to enter this market, i.e. it can set up a campaign in which it exerts effort to change consumers preferences by making consumers more aware of the environmental damage caused by the good. Denoting the EG s effort as x, we have x > 0 if the EG enters and x = 0 otherwise. We assume that as a result of a positive effort x, the preference parameters shift from θ to θ + x for all θ, i.e. the disutility of environmental damage rises with xd (see von der Fehr and Stevik [10, p.117] for a similar approach in a standard advertising model). For the EG, it is costly to exert effort; the corresponding cost function is given by s(x), with s(x) > 0, s (x) > 0 and s (x) > 0 for all x > 0, and s(0) = s (0) = s (0) = 0. We call s(x) the publicity cost of the EG. The EG also has to pay a sunk entry cost F 0, but only if x > 0. The entry cost can be viewed as the nonrecoverable fixed cost of, for example, establishing contact with the media or recruiting volunteers, i.e. all things necessary to set up a campaign. The EG tries to minimize its total costs. If it enters, these costs are given by γqd+s(x)+f, where q denotes the demand for the firm s good, qd is total aggregated environmental damage caused by the market demand, and the parameter γ > 0 converts environmental damage 5

6 to its monetary value. If the EG does not enter, its total costs are equal to γqd. We now consider a game with the following timing: in t = 1 the firm chooses d (by selecting a corresponding production technique); in t = 2 the EG chooses whether to enter or not. After entry the EG chooses x > 0, otherwise x = 0; in t = 3 the firm selects p and next the consumers decide whether to buy the good or not. In the next section we will derive the equilibrium of the game by using backward induction. We assume that there always must be some consumers who are willing to purchase the firm s good, even if the EG has entered and exerted effort. Basically, this means that the EG is not so influential that it can completely sweep away the firm s demand. On the other hand, we also assume that there are always some consumers who are not willing to buy the good. In other words, the market is never covered, even if the EG does not enter. If the market would be covered in that case, then it is likely that the market would remain covered for small values of x, which would imply that then total demand remains constant. In this sense, a covered market is a barrier to entry since the EG has to exert considerable effort to have a minimal impact on demand. This would complicate our analysis without adding additional insight. The assumption of an uncovered market is standard in the literature, see e.g. also Moraga-González and Padrón-Fumero [8]. Finally, if below a specific functional form for c(d) or s(x) is needed, then we choose, respectively, c(d) = α/d 2 and s(x) = βx 2, with α > 0 and β > 0. We notice that this specification for c(d) is also used by Moraga-González and Padrón-Fumero [8]. It turns out that we do not need these specific functional forms in the analysis of stages 2 and 3; however, we do need them in our analysis of stage 1 and in our discussion of the social welfare properties of the equilibrium. 6

7 3 The equilibrium of the model 3.1 Stage 3 To begin with, suppose that the EG has entered and that x > 0 as well as d > 0 are given. We now want to solve for the corresponding optimal price in stage 3. Observe first that in this case the consumers are located on the line [x, θ + x]. The indifferent consumer is found by solving U = 0 for θ, which gives θ = (V p)/d. As a result, demand is given by q = V p θd x θ, (1) and profit equals [ V p Π = [p c(d)] x θ ]. (2) θd The first-order condition of profit-maximization reads dπ dp = V p x θ p c(d) = 0, (3) θd θd which gives the optimal price p e = V + c(d) xd, (4) 2 where the superscript e denotes that we consider the case of entry. Notice that d 2 Π/dp 2 = 2/( θd) < 0, which shows that p e indeed gives a maximum. We now easily obtain the following expressions for, respectively, the indifferent consumer, demand and profit in the case of entry: θ e V c(d) + xd =, 2d (5) q e V c(d) xd =, 2 θd (6) Π e [V c(d) xd]2 =. 4 θd (7) We assume throughout the paper that, given x and d, demand is positive and the market not covered. A necessary and sufficient condition for this to hold is: Assumption 1. 0 < V c(d) xd < 2 θd. 7

8 Notice that Assumption 1 also guarantees that the firm s profit Π e is positive. The consumers surplus in the case of entry is defined as CS e = 1 θ θ e x [V θd p e ]dθ = [V p e ]q e d 2 θ [ (θ e ) 2 x 2]. (8) Using (4), (5) and (6), we obtain CS e = 1 4 θd [V c(d) + xd][v c(d) xd] d ( ) 1 2 θ 4d 2 [V c(d) + xd]2 x 2 = 1 8 θd [V c(d)]2 1 1 [V c(d)]xd + 4 θd 8 θd (xd)2 [V c(d) xd]2 =. (9) 8 θd Hence, consumers surplus is half of firm s profit in the case of entry. Concluding our discussion of the case of entry, we notice that, in fact, p e, θ e, q e, Π e and CS e are functions of x and d. In order to simplify the notation, we do not mention this dependency explicitly. Next, let us turn to the case where the EG has not entered (and thus x = 0), and suppose that d > 0 is given. In order to find for this case with no entry the optimal price, and the corresponding indifferent consumer, demand, profit and consumers surplus, we can simply substitute x = 0 in the results derived above for the case with entry. Using obvious notation, we then obtain from, respectively, (4), (5), (6), (7) and (9) the following expressions: p ne = V + c(d), 2 (10) θ ne = V c(d), 2d (11) q ne = V c(d), 2 θd (12) Π ne [V c(d)]2 =, 4 θd (13) CS ne [V c(d)]2 =. 8 θd (14) Observe that Assumption 1 is sufficient to guarantee that 0 < q ne < 1. Also notice that 8

9 p ne, θ ne, q ne, Π ne and CS ne are functions of d. Again, we do not mention this dependency explicitly in our notation. 3.2 Stage The decision of the EG Turning to stage 2, suppose that d > 0 is given. The EG now has to choose between two options: either it enters and chooses an effort level x > 0, or it does not enter (and then x = 0). In making its decision, the EG takes into account the subsequent behaviour of the firm and consumers in stage 1 as discussed above. First, suppose that the EG enters. The EG then has to determine its optimal effort x by minimizing its total costs γq e d+s(x)+f with respect to x. This leads to the first-order condition s (x) = γd 2 θ, (15) which has a unique solution, x e > 0 say, given the assumptions we made with respect to the function s(x). The second-order condition for a minimum is satisfied, since s (x) > 0 for all x > 0. Clearly, x e is a function of d, i.e. in fact x e = x e (d). However, in order to save on the notation, we simply write x e unless it is more convenient to do otherwise. We implicitly also assume that V c(d) x e d > 0, i.e. Assumption 1 must be satisfied. Remark that in the special case with s(x) = βx 2, we have x e = γd/(4β θ). It is obvious now that the EG will decide to enter if and only if γq e d + s(x e ) + F < γq ne d, (16) where q e follows from (6) by substituting x = x e. We can present the following result. Proposition 1. Assume that d > 0 is given. Then there exists an ˆF (d) > 0 such that for all 0 F < ˆF (d) the EG enters, whereas for all F ˆF (d) the EG does not enter. Moreover, ˆF (d) is increasing in d. Proof See Appendix A. Hence, the EG only enters if F is smaller than a unique and positive threshold ˆF (d). 9

10 For the special case with s(x) = βx 2, we can find an explicit expression for ˆF (d), by noting that in this case ˆF (d) = γxe d 2 θ s(xe ) = γ ( γd 2 θ 4β θ ) d β ( ) 2 γd 4β θ = γ2 d 2 > 0. (17) 16β θ A digression on a socially optimal effort level In the previous subsection we have seen that after entry the EG chooses the effort level x e. Let us now compare, as an interesting sidestep, the effort chosen by the EG with the effort that would be chosen if instead the government would choose to inform the public. In order to ease the exposition, we assume in this subsection that the entry cost of the EG is zero, and that the government has zero entry cost as well. We further assume that the publicity cost and effects on the consumer s preferences of a campaign organized by the government are identical to those of a campaign organized by the EG. However, the goal of the government is different in the sense that it also takes into account the firm s profit and consumers surplus. That is, the government will choose x in order to maximize social welfare given by SW = Π e + CS e γq e d s(x) = 3 8 θd [V c(d) xd]2 γ [V c(d) xd] s(x). (18) 2 θ Observe that dsw dx = 3 γd [V c(d) xd] + 4 θ 2 θ s (x). (19) On the RHS of (19) we see the effects of a marginal increase in x. The first term shows the (negative) effect on the firm s profit and consumer s surplus (follows from Assumption 1), the second term shows the (positive) effect on the damage to the environment, and the third term is the negative effect on the publicity cost. We will denote an effort level that, given d, maximizes SW as a socially optimal effort level x soc 0. Clearly, x soc depends on d, but we do not denote this explicitly in order to simplify the notation. 10

11 We now can present the following result. Proposition 2. Assume that d > 0 is given. Then a socially optimal effort level x soc exists and, moreover, such an x soc is strictly smaller than x e. Proof See Appendix A. The proposition above states that although it can be beneficial to society as a whole if the public is informed, the EG excessively informs them. 3.3 Stage 1 Turning again to the original model, let us now consider the firm s choice of d in stage 1, given the subsequent behaviour analysed above for stages 2 and 3. In order to obtain tractable results, we use from now on the specific functional forms c(d) = α/d 2 and s(x) = βx 2. In stage 1, the firm has to choose d while facing possible entry of the EG. In fact, it turns out that the following three things can happen: blockaded entry, entry deterrence and entry accommodation. In the first two cases entry is barred, but for different reasons. If the firm would ignore the threat of entry, then it would set environmental damage such that its profit were maximized given x = 0. In the case of blockaded entry it can simply ignore the EG without further consequences. In the case of entry deterrence, however, the threat of entry is real and if the firm does not lower its level of environmental damage, the EG would enter. The firm does lower environmental damage (because in this case it is profitable to do so) and discourages the EG to enter. In the case of entry accommodation, the firm could possibly still deter entry, but it is more profitable to let the EG enter and anticipate this entry. We will subsequently calculate the optimal d for the cases of blockaded entry, entry deterrence and entry accommodation. In the case of blockaded entry, the firm maximizes Π ne with respect to d. The firstorder condition is dπ ne dd = 2[V c(d)][ c (d)d] [V c(d)] 2 4 θd 2 = 0. (20) 11

12 Observe that this equation is satisfied if d is chosen such that V c(d) = 0. However, such a choice of d would result in zero profit and conflict with Assumption 1, and hence is not relevant. As a result, we can reduce (20) to V c(d) + 2c (d)d = 0, (21) from which we obtain the corresponding unique optimal d, i.e. d block 5α V. (22) Using (21), it can be shown that the second-order derivative of Π ne with respect to d evaluated in d = d block is negative if and only if 2c (d)d + c (d) > 0 for d = d block. The latter inequality holds, since in the special case with c(d) = α/d 2, we have for any d > 0 that 2c (d)d + c (d) = 12α d 3 2α d 3 = 10α > 0. (23) d3 Hence, the second-order condition for a maximum is satisfied in d = d block. i.e. Substituting d block into (17), we obtain the corresponding threshold of the entry cost, F block 5αγ2. (24) 16βV θ 2 Concluding, if F F block, then there is blockaded entry. That is, the EG s entry cost is so high that the firm can simply choose the profit-maximizing value d block it would also choose if the EG would not consider entry at all; in turn, given d block, it is indeed optimal for the EG to choose no entry. 3 Considering the case of entry deterrence, then the firm deliberately lowers the environmental damage to a point where the EG does not enter. Recalling (17), remark that if both F < ˆF (d block ) and the firm ignored the possibility of entry and would set d = d block, then the EG would enter, i.e. entry is not blockaded. The firm could, however, try to lower the environmental damage d such that F ˆF (d), because in that case the EG has no 3 In Appendix B we present condition (B.1), which guarantees that Assumption 1 is satisfied in the case of blockaded entry. 12

13 reason to enter. Since d block is the global (and unique) maximum of the profit function Π ne (d), this means that deviating from d block lowers Π ne (d). In fact, the further d is from d block, the lower is the firm s profit. This implies that the firm will lower d to the point where ˆF (d) = F, making the EG just indifferent between entering and not entering. We denote this level of environmental damage as ˆd(F ), and observe that it is given by 16βF ˆd(F ) θ 2 γ 2. (25) Notice also that ˆF ( ˆd(F )) = F, and that for F < F block we have ˆd(F ) < d block. Of course, this behavior should be profitable for the firm, i.e. accommodating entry should give a lower profit. Whether this indeed is the case, depends on the magnitude of F. Before deriving the exact range of values of F for which the firm will deter entry, it is convenient to consider first the case of entry accommodation. In the case of entry accommodation, the firm maximizes Π e with respect to d. The first-order condition reads dπ e dd = 4d[V c(d) xe d][ c (d) (γd)/(4β θ)] [V c(d) x e d] 2 4 θd 2 = 0. (26) This equation is satisfied if d is chosen such that V c(d) x e d = 0. However, this choice of d would result in zero profit and conflict with Assumption 1, and hence is not relevant. Thus, we can reduce (26) to 5α d 2 = V + 3γd2, (27) 4β θ which can be rewritten as a quadratic equation in d 2. From this one can verify that (27) has a unique positive solution, which we denote as d acc > 0. After a straightforward calculation it can be shown that the second-order derivative of Π e with respect to d evaluated in d = d acc is negative if and only if 2c (d)d + c (d) + 3γd > 0 (28) 2β θ for d = d acc. Recalling (23), it follows directly that this is true, and we thus know that the second-order condition for a maximum is satisfied in d = d acc. Remarking that d block solves 13

14 5α/d 2 = V, it follows from (27) that 5α/(d block ) 2 < 5α/(d acc ) 2, and thus d acc < d block. Concluding, the firm chooses d acc if it accommodates to entry of the EG. Whether this behaviour is indeed optimal for the firm, depends on the size of F. Therefore, let us now analyse for which values of F either entry deterrence or entry accommodation is optimal for the firm. We make a number of observations. First, using (7) and (13), it follows that Π e (d) < Π ne (d), i.e. given d, the firm s profit always decreases if the EG enters (of course, assuming that Assumption 1 holds). Second, we define d 0 > 0 according to Π ne (d 0 ) = 0. Using (13), it follows that d 0 = α/v. Given d 0 and using (17), we next define F 0 ˆF (d 0 ), and notice that F 0 = αγ 2 /(16βV θ 2 ). Remark that if the firm chooses d = d 0, then it is able to deter entry of the EG for F F 0, and in that case its profit is just equal to zero. Third, observe that Π ne (d 0 ) = 0 < Π e (d acc ) < Π ne (d block ). The last inequality follows since, while taking d = d block, our first observation implies that Π ne (d) evaluated in its global maximum must be larger than Π e (d) evaluated in any d. Fourth, Π ne (d) is a continuous and strictly increasing function on the interval [d 0, d block ]. Fifth, combining results, we see that there exists a unique, d deter say, such that both d 0 < d deter < d acc and Π ne (d deter ) = Π e (d acc ). Remark that the firm is indifferent between choosing d = d deter (in which case there is entry deterrence) and d = d acc (in which case there is entry accommodation). Given d deter and using (17), we define F deter ˆF (d deter ), and notice that F 0 < F deter < F block. It follows now that for the firm, it is profitable to deter entry if F deter F < F block, whereas it is profitable to accommodate entry if 0 F < F deter. 4 Summarizing our discussion, we obtain the following proposition. Proposition 3. There exist F deter and F block, with 0 < F deter < F block, such that for all F the following holds in the equilibrium: (i) If 0 F < F deter, then the firm chooses d = d acc, and the EG enters. 4 In Appendix B we present conditions (B.2) and (B.4) which guarantee that Assumption 1 is satisfied in the case of entry deterrence, and condition (B.12) which guarantees that Assumption 1 is satisfied in the case of entry accommodation. 14

15 (ii) If F deter F < F block, then the firm chooses d = ˆd(F ) and entry of the EG is deterred. (iii) If F F block, then the firm chooses d = d block and entry of the EG is blockaded. Proposition 3 characterizes for each possible value of F, the corresponding unique equilibrium value of the environmental damage chosen by the firm in stage 1, and the subsequent entry decision of the EG in stage 2. Remark that for each case the subsequent unique equilibrium choice of the EG s effort in stage 2 and the firm s unique equilibrium price in stage 1 follow in a straightforward way. It is also useful to present the following corollary in which we compare the magnitudes of the different equilibrium values of d mentioned in Proposition 3. Corollary 1. The following holds for the environmental damage levels of Proposition 3: (a) d acc < d block. (b) If F deter F < F block, then ˆd(F ) < d block. (c) If F deter F < F block, then there exists an F (F deter, F block ) such that ˆd(F ) > d acc if and only if F ( F, F block ). Proof See Appendix A. Part (b) of Corollary 1 shows that if F [F deter, F block ), then the firm deters entry by lowering d relative to d block. Moreover, part (c) shows that for F [F deter, F ), the firm deters entry by lowering d relative to d acc. Thus, in the latter case, there is less environmental damage per product sold than under entry by the EG. 4 Social welfare In this section we examine for the equilibrium derived above, for all possible values of F, the properties of the firm s profit, the consumers surplus and the total costs of the EG. Based on these properties, we are able to present a social welfare result. Throughout this section, we focus on the special case with c(d) = α/d 2 and s(x) = βx 2. It is convenient to 15

16 introduce here the following notation. First, q acc denotes the firm s demand if it accommodates entry of the EG, i.e. it is obtained by substituting d = d acc and x = x e (d acc ) in (6). Second, q block is the demand in the case of blockaded entry, i.e. it is found by substituting d = d block in (12). Third, ˆq(F ) represents the demand if the firm deters entry of the EG by setting d = ˆd(F ), i.e. ˆq(F ) is obtained by substituting d = ˆd(F ) in (12). Fourth, we denote the total equilibrium costs of the EG as γq acc d acc + s(x e (d acc )) + F if 0 F < F deter, (F ) γ ˆq(F ) ˆd(F ) if F deter F < F block, γq block d block if F F block. (29) Now we can present the following proposition. Proposition 4. In the equilibrium of the model the following holds: (i) If 0 F < F deter, then the firm s profit and consumers surplus are constant, while the EG s total costs are increasing in F. (ii) If F deter F < F block, then the firm s profit and consumers surplus but also the EG s total costs are increasing in F. (iii) If F F block, then the firm s profit, consumers s surplus and EG s total costs are constant in F. (iv) (0) > (F deter ). (v) The firm s profit and consumers surplus are continuous functions of F, while (F ) is a continuous function of F except in the point F = F deter where it jumps downward. Proof See Appendix A. The interpretation of Proposition 4 is straightforward. As argued in its proof, total aggregated environmental damage is constant in the situations of part (i) and (iii), whereas in the situation of part (ii) it turns out to increase as a function of F. Part (iv) demonstrates that the EG s total costs are smaller in the entry deterrence case with F = F deter than in the entry accommodation case (even) with F = 0. Part (v) shows that the EG s total costs 16

17 make a downward jump if F crosses the point F = F block, i.e. if the situation switches from entry accommodation to entry deterrence. Let us now define social welfare in the equilibrium as the summation of the firm s profit and the consumers surplus minus the total costs of the EG corresponding to the equilibrium. Proposition 4 allows us to make the following claim about social welfare in the equilibrium, considered as a function of F 0. Proposition 5. Social welfare in the equilibrium is maximal for some F [F deter, F block ). Proof See Appendix A. Proposition 5 shows that the threat of entry by the EG can be more effective than the actual entry from a social welfare point of view. The maximum of social welfare is achieved in a case with entry deterrence, where the firm deliberately lowers the environmental damage such that the EG does not enter. Therefore, loosely speaking, we can say that the EG is needed in order to keep the pressure on. In order to understand the forces behind this social welfare result in a more intuitive way, let us compare entry deterrence with blockaded entry. Under entry deterrence the firm s profit, and hence also the consumers surplus, are smaller than under blockaded entry. On the other hand, the EG s total costs (which now only consist of the cost of total aggregated environmental damage) are also smaller under entry deterrence than under blockaded entry. Apparently, the loss in terms of the profit and consumers surplus are outweighed by the gain in terms of the EG s total costs. Next, let us compare entry deterrence with entry accommodation. Under entry deterrence the firm s profit, and hence also the consumers surplus, are larger than under entry accommodation. The EG s total costs might be larger under entry deterrence than under entry accommodation (notice that under entry deterrence, the EG incurs no entry cost and no publicity cost). Still, under entry deterrence, the possible increase in the EG s total costs apparently can be 17

18 more than compensated by the increase of the firm s profit and consumers surplus. 5 Conclusion This paper has analysed a market on which a monopolistic firm supplies an environmentally unfriendly good. The firm can influence the amount of pollution generated per-unit production of the good by choosing an appropriate production technique. However, a cleaner product also implies that the per-unit production cost becomes higher. Consumers of the good dislike the environmental damage caused by the good, but they are heterogeneous with respect to the size of the associated disutility. The key feature of our analysis is that we assume that an EG can enter the market and set up a campaign in order to increase each consumer s disutility of the environmental damage caused by the consumption of the good. Thus, instead of analysing the effectiveness of traditional regulatory measures (like taxes on polluting goods or unit-emission standards, etcetera) imposed by a government, we focus here on the impact on the market outcome of the presence of a non-governmental organization like an EG. We have derived the characteristics of the equilibrium of the resulting entry-deterrence game between the firm and EG and discussed the welfare properties of this equilibrium. It turned out that in equilibrium social welfare is maximal in a situation in which the EG s nonrecoverable entry cost are such that the firm deters entry of the EG by selecting a clean-enough production technique. Hence, the threat of entry (instead of the actual entry) by the EG is most useful in this case. Let us denote the entry cost associated with the (presumably unique) equilibrium welfare optimum as F. Our analysis then suggests that it might be useful for a government to commit itself prior to stage 1 of the game to the following policy measure towards an EG with entry cost F : (a) if F > F, then the EG receives a subsidy equal to F F in case it actually sets up a campaign; (b) if F < F, then the EG has to pay a tax equal to F F in case it actually sets up a campaign. Observe that under this policy measure, in equilibrium the monopolist actually 18

19 always deters entry of the EG. Hence, in equilibrium the government never has to pay a subsidy and never receives a tax, i.e. the measure is always budget neutral. As a final remark, we mention that we have focused on a monopolistic market in order to obtain tractable results. In future research it might be interesting to generalize our analysis to oligopolistic markets. 19

20 References [1] S. Arora, S. Gangopadhyay, Toward a theoretical model of emissions control, Journal of Economic Behavior & Organization 28 (1995) [2] K. Bagwell, The economics of advertising, Working Paper, Columbia University (2003); also forthcoming in M. Armstrong, R.H. Porter (Eds.), The Handbook of Industrial Organization Volume 3, North-Holland, Amsterdam. [3] S. Bansal, S. Gangopadhyay, Tax/subsidy policies in the presence of environmentally aware consumers, Journal of Environmental Economics and Management 45 (2003) [4] H. Cremer, J.-F. Thisse, On the taxation of polluting products in a differentiated industry, European Economic Review 43 (1999) [5] A. G. Heyes, Environmental regulation by private contest, Journal of Public Economics 63 (1997) [6] C. Liston-Heyes, Setting the stakes in environmental contests, Journal of Environmental Economics and Management 41 (2001) [7] J.W. Maxwell, T.P. Lyon, S.C. Hackett, Self-regulation and social welfare: the political economy of corporate environmentalism, Journal of Law & Economics 43 (2000) [8] J.L. Moraga-González, N. Padrón-Fumero, Environmental policy in a green market, Environmental and Resource Economics 22 (2002) [9] J. Tirole, The Theory of Industrial Organization, MIT Press, Cambridge MA, [10] N.-H. von der Fehr, K. Stevik, Persuasive advertising and product differentiation, Southern Economic Journal 65 (1998)

21 Appendix A: Proofs Proof of Proposition 1 Remark first that if F = 0, then the EG will enter because we know that x e > 0. Next, notice that x e does not depend on F. Therefore, the LHS of (16) grows linearly in F while the RHS is constant. This implies the existence of ˆF (d) > 0. Clearly, ˆF (d) γ(q ne q e )d s(x e ) = γx e d/(2 θ) s(x e ). Since x e is the solution of s (x) = γd/(2 θ), we have d ˆF (d) dd = γxe 2 θ + γd 2 θ dx e dd ds dx e dx dd = γxe 2 θ > 0. (A.1) which completes the proof. Proof of Proposition 2 Assumption 1 implies that we must restrict ourselves to effort levels with x < (V c(d))/d. Define now, for the moment, the interval I [0, (V c(d)/d] and consider SW defined in (18) as a function of x on this interval. Since this function is a continuous function on the compact interval I, we know that there exists at least one point where it attains a maximum on I. Let I 1 I be the nonempty set of points where this maximum is achieved. Because 0 < x e < (V c(d))/d and, moreover, x e is the unique solution of s (x) = γd/(2 θ), we obtain that dsw dx = γd x=(v c(d))/d 2 θ s ((V c(d))/d) < 0. (A.2) Hence, a small decrease of x starting from the point x = (V c(d))/d increases SW, and hence this point is not an element of I 1. We thus know that SW attains a maximum on the interval [0, (V c(d))/d). Observe now that any point in I 1 is a socially optimal effort level. If x soc I 1, then we have either (i) x soc = 0, or (ii) 0 < x soc < (V c(d))/d. In case (i), obviously x soc < x e. In case (ii), x soc must satisfy the first-order condition s (x) = γd 2 θ 3 [V c(d) xd], 4 θ (A.3) 21

22 and using Assumption 1 it directly follows that we have x soc < x e. Proof of Corollary 1 Parts (a) and (b) are already discussed in the main text. In order to prove part (c), notice first that if F = F deter, then ˆd(F ) = d deter < d acc. Next, if F = F block, then ˆd(F ) = d block > d acc. Since Π ne (d) is a continuous and strictly increasing function of d on the relevant interval, F must exist, which completes the proof. Proof of Proposition 4 In order to prove part (i), let 0 F < F deter. For these values of F, the firm accommodates entry and sets environmental damage equal to d acc. The EG reacts by setting x = x e (d acc ) = γd acc /(4β θ). The firm s profit and consumers surplus are the same for all F. The EG, however, has to pay the entry cost F, and (F ) therefore increases on the relevant region for F. In order to prove part (ii), let F deter F < F block. Now the firm deters entry by setting environmental damage equal to ˆd(F ), which is an increasing function of F. Recall from Corollary 1 that ˆd(F ) < d block. Since d block is the unique and global maximum of Π ne, the firm s profit must be an increasing function of F in the relevant region for F. Using (13) and (14), we conclude that the same must hold for the consumer s surplus. Using (12), we see that the total costs of the EG in this region are equal to (F ) = γ ˆq(F ) ˆd(F ) = γ(v c( ˆd(F )))/(2 θ). We next observe that this (F ) is increasing in F because d (F ) df = γ 2 θ [ ] d df (V c( ˆd(F ))) = γ 2 θ [ c ( ˆd(F ))] > 0. (A.4) In order to prove part (iii), let F F block. Now we have blockaded entry. That is, the firm sets environmental damage equal to d block and the EG does not enter. Clearly, in the relevant region for F, the firm s profit, consumers surplus and (F ) are all constant. Turning to part (iv), recall from subsection 3.3 that Π ne (d deter ) = Π e (d acc ). From this 22

23 and (7) and (13), we obtain d [V c(d acc ) x e (d acc )d acc ] = [V c(d deter acc )] d deter. (A.5) Remarking that part (c) of Corollary 1 implies that d deter < d acc, we thus have [V c(d acc ) x e (d acc )d acc ] > [V c(d deter )]. (A.6) Using (6) and (12), we can conclude that (0) > (F deter ). Turning to part (v), let us consider the continuity properties of the functions associated with the firm s profit, consumers surplus and EG s total costs. Observe that there are only two points where these three functions possibly can be discontinuous: in F = F block where the firm shifts from entry deterrence to blockaded entry, and in F = F deter where the firm shifts from entry accommodation to entry deterrence. In F = F block, we have by definition Π ne ( ˆd(F )) = Π ne (d block ) and (F ) = γ ˆq(F ) ˆd(F ) = γq block d block. Thus, in F = F block all three functions are continuous. Next, recall that F deter = ˆF (d deter ) where Π ne (d deter ) = Π e (d acc ). Using this we obtain that the firm s profit and consumers surplus are also continuous in F = F deter. In order to see that (F ) is not continuous in F = F deter, recall from (iv) of this proposition that (0) > (F deter ). The costs (0) correspond to the case of entry accommodation with F = 0. For F (0, F deter ) we still have entry accommodation, but obviously the EG s total costs increase linearly in F. Hence, (F ) jumps downward in the point F = F deter. Proof of Proposition 5 Using (i) of Proposition 4, we first notice that social welfare is decreasing as a function of F if F [0, F deter ). Combining this with (iv) and (v) of Proposition 4, we see that social welfare cannot be maximal for F [0, F deter ). Second, (iii) of Proposition 4 implies that social welfare is constant as a function of F if F [F block, ). Hence, on this interval we can focus on the case with F = F block. 23

24 Third, denoting social welfare in case the EG does not enter as SW ne (F ), observe that for F [F deter, F block ), the derivative of social welfare with respect to F can be written as dsw ne df = [ d ( Π ne + CS ne γ ) ] dd 2 θ (V c(d)) d ˆd(F ) df. (A.7) Using this, let us examine the left-derivative of SW ne in F = F block. Because d dd d d block (Π ne + CS ne ) = 0, (A.8) it follows that dsw ne df F F block = γ 2 θ c (d block ) d ˆd(F ) df F F block < 0. (A.9) This implies that the maximum of social welfare must be to the left of F block ; social welfare can be increased by lowering F slightly from F block. 24

25 Appendix B: Details regarding Assumption 1 In deriving the equilibrium of the game, we have acted so far as if Assumption 1 simultaneously holds for d block (blockaded entry), ˆd(F ) (entry deterrence) and d acc and x e = x e (d acc ) (entry accommodation). In this appendix we will show that there indeed exist combinations of parameters of the model for which our approach is justified. We will examine the three cases one by one. Again we use c(d) = α/d 2 and s(x) = βx 2, with α > 0 and β > 0. Blockaded entry It has to be shown that there exist parameters such that V c(d) > 0 and V c(d) < 2 θd for d = d block. Substituting (22), it follows that the first inequality is always satisfied whereas the second inequality is satisfied if and only if α > 4V θ 2. (B.1) Entry deterrence We have to demonstrate that there exist parameters such that V c(d) > 0 and V c(d) < 2 θd for d = ˆd(F ). Substituting (25), we see that the first inequality is satisfied if and only if 2 16βF V θ α < γ 2. (B.2) Next, taking arbitrary d > 0 and substituting c(d) = α/d 2, we can rewrite V c(d) < 2 θd as 2 θd 3 V d 2 + α > 0. (B.3) Clearly, (B.3) is satisfied if d is close enough to zero and if d becomes infinitely large. Furthermore, the LHS of (B.3) has a minimum at d = V/(3 θ). Substitution shows that condition (B.3) evaluated in this minimum is satisfied if and only if α > V 3 27 θ 2. (B.4) Clearly, (B.4) is sufficient to guarantee that V c(d) < 2 θd for d = ˆd(F ). 25

26 Accommodation We have to show that V c(d) xd > 0 and V c(d) xd < 2 θd for d = d acc and x = x e = x e (d acc ). Observe that d acc is defined as the solution of 2c (d)d = V c(d) + 3x e d, which can be rewritten as V c(d) x e d = 2c (d)d 4x e d = 4α d 2 γd2 β θ. (B.5) (B.6) Therefore, instead of showing that V c(d) x e d > 0 for d = d acc, we can also show that (d acc ) 2 < Next, recall from (27) that d acc is the solution of 4αβ θ γ. (B.7) 3γ 4β θ d4 + V d 2 5α = 0, (B.8) which is a quadratic equation in d 2. Solving this equation for d 2, and picking out the positive solution, we obtain that (2β ) 2 θv (d acc ) 2 = + 3γ 60αβ θ 9γ The aim is now to show under which conditions we have (2β ) 2 θv + 3γ 60αβ θ 9γ 2β θv 3γ < 2β θv 3γ. (B.9) 4αβ θ γ. (B.10) Therefore, define A 2β θv/(3γ), B 20β θ/(3γ) and C 4β θ/γ, where B > C. Using these definitions and applying straightforward manipulations, we can rewrite (B.10) as which is equivalent with α < 4A2 C (B C) 2, (B.11) α < β θv 2. (B.12) γ Finally, we need to show that for d = d acc we have V c(d) x e d < 2 θd, which, using (B.5), is equivalent with 2c (d)d < 2 θd + 4x e d. Using d block > d acc, it follows 26

27 that c (d acc ) > c (d block ) > θ. The latter inequality follows since d block is defined by (21) and, moreover, we know that V c(d block ) < 2 θd block. Using c (d acc ) > θ, we have 2c (d acc )d acc < 2 θd acc, and thus certainly 2c (d acc )d acc < 2 θd acc + 4x e d acc. Conclusion There are four restrictions, namely (B.1), (B.2), (B.4) and (B.12). Two of these are lower bounds on α and the other two are upper bounds on α. Remark that all restrictions are satisfied if, for example, we take β or θ large enough, or γ small enough. Hence, the restrictions are not contradictory. 27