Strategic Corporate Social Responsibility in an
Oligopoly Model with Managerial Delegation
A.W.P. Hiddink, s2096528
10 June 2019
Abstract
This thesis investigates the case of strategic corporate social responsibility (CSR) in an oligopolistic context with vertical product differentiation. Al-truistically motivated owners can hire CSR oriented managers to whom they delegate the CSR and market decision. Depending on the size of the altruistic preferences, equilibria can range from zero to full CSR situations with ambigu-ous effects on prices, quantities and profits. Owners take both the altruistic and strategic components of the model into account when hiring their manager.
Jel Classification: D43; D64; L22; M14
1
Introduction
According to Colleoni (2013), a vital component of Starbucks’s business strategy is their awareness for the environmental consequences of their production activities and their responsbility in local communities. Over the years, Starbucks invested large amount of resources in order to minimize the damage of their production activities on the environment. Furthermore, Starbucks provides direct support to local farmers in Rwanda and Costa Rica in the form of farmer support centers. Amongst other things, these farmer support centers assist the farmers in reducing the cost of produc-tion and reduce fungus infecproduc-tions. In addiproduc-tion, these farmers receive a fair price for their products. As a result, Starbucks won the world’s most ethical company award in late 2017. Note that the example of Starbucks is not an exception, but is common practice in the business world.
During the last few decades, there has been a growing concern among human kind that firms should do more than just serve the interests of their main shareholders (make profits). In contrast, it is nowadays believed that firms should also take into consideration how their activities affect all agents dealing with the firm. Examples of such agents can be employees, consumers, business partners and the environment. Over time, the view of the economic science on firms shifted more and more away from pure profit-maximization and started moving towards a view in which firms fo-cus on all stakeholders instead of shareholders only. As a result, the term corporate social responsibility was born (CSR). As will be discussed in the literature review, no exact definition of CSR exists, as the concept is too broad to be captured in a single definition. Broadly speaking, CSR can be seen as a model of business that is based on self-regulation. It assists firms in being socially accountable to its stakeholders, the public and itself.
awareness). Although social ratings are not linked to a firm’s financial performance directly, it is possible that it has an indirect effect. If the firm neglects the environ-ment, for example, its social rating will decrease and, thereby, damages its image. This may have negative effects on the profitability of the firm.
As more firms realize that it is possible to financially benefit from CSR activities, many firms have adopted so-called strategic CSR plans in their business strategies. The paper of Rangan, Chase, and Karim (2012), from the Harvard Business School, even argues that each firm needs a strategic CSR plan. These plans are mainly con-cerned with making trade-offs between the benefits and costs of CSR.
The main task of this thesis will be to analyze the effects of CSR on market outcomes, such as prices, quantities and profits, in a game theoretic framework under duopolis-tic competition. The analysis of the thesis formally conceptualizes the premise that engaging in CSR activities builds a competitive advantage over the rival firm, by creating a more socially friendly image. The model tries to explain why companies like Starbucks adopt extensive CSR strategies. In the model, there are socially con-cerned consumers who are homogeneous with respect to the physical characteristics of the good, but heterogeneous with respect to CSR activities. In other words, in this model CSR effort can be seen as an example of vertical product differentiation. In line with the discussion above, more socially conscious consumers will have a higher willingness to pay and are, therefore, willing to pay a premium to firms engaging in CSR activities.
In addition, owners of firms need to hire a CSR oriented manager if CSR effort is desired. In the business world, it is considered common practice to delegate CSR decisions to a CSR oriented manager. By hiring a CSR oriented manager with past recordings of CSR activities, the owners can credibly signal their CSR intentions to the consumers. There are different managers available for hiring who differ in their CSR valuation. The owners also delegate the competition decisions to the CSR ori-ented manager.
Section 4 concludes.
2
Related Literature
2.1
Defining CSR and traditional theories
com-panies integrate social and environmental concerns in their business operations and in their interaction with their stakeholders on a voluntary basis”. To sum up, CSR can be conceptualized as all the actions taken by a firm to improve social welfare beyond all its standard economic and legal objectives.
Having defined the concept of CSR, it is important to investigate why firms engage in CSR. According to the literature on business, there are four main theories on CSR, which are mainly verbal in nature. The first theory is based on agency theory and due to Jensen and Meckling (1976). According to agency theory, firms engage in CSR to overcome information asymmetries. Agency theory is based on the premise that the interests of shareholders and managers are not necessarily aligned. It is argued that CSR reports are used to overcome these information asymmetries, as agents are better equiped to verify the principal.
In addition, other academics have presented the stakeholder theory as an engine of CSR. An example of such a paper is Freeman (2010). The theory’s main argument is that a firm should not only take into account the interest of shareholders when developing their business plans, but rather focus on all parties involved with the firm. In the literature, these parties are referred to as stakeholders. Freeman (2010) defines a stakeholder as: ”a person or group that can affect or is affected by the performance of the organization’s objectives”. Customers, governments, suppliers, employees, and local communities are some examples of stakeholders. Freeman and McVea (2001) claim that stakeholders are important to the financial performance of a firm, since they can punish undesirable behavior. According to their view, it can be argued that issuing, for example, sustainability reports can be used to shape the opinions of stakeholders in a positive manner.
some-thing that can be achieved by institutions. Hence, this theory predicts that CSR effort by firms is ultimately driven by institutions expecting CSR behavior. Note that this theory differs from the two theories discussed above, as agency theory and stakeholder theory are based on the firm itself, whereas institutional theory is based on the environment of the firm.
The last theory explaining CSR is the legitimacy theory. This theory is mainly based on the ethics of society as a whole. Campbell (2007) argues that firms should operate in the market, taking the perceptions of society into account. Violation of this claim could imply that firms lose their legitimacy. Moreover, Marcus and Goodman (1991) write that losing legitimacy means losing support from society and the media. Hence, according to this theory, firms engage in CSR to live up to the ethical considerations of society. Otherwise, public support could be at stake, which can be detrimental to the firm’s survival.
2.2
Strategic CSR
feelings or are responding to threats and profit-maximization also important drivers of CSR? An important task of this thesis is to construct a theoretical model of CSR that is able to distinguish between altruistic and strategic CSR.
2.3
Empirical relation between CSR and Financial
Perfor-mance
The previous sections made clear that there exist multiple theoretical views towards CSR. However, the relationship between CSR and the profitability of the firm is not immediately clear. Take the work of Baron (2001) for example. CSR based on altruism has a potential negative effect on profits, whereas CSR based on profit-maximization increases profits. In case of an ambiguous theoretical prediction, an econometric estimation of the relationship should give clarity. In fact, estimating the relationship between CSR and financial performance is one of the most researched problems in this literature. Not only because of the academic considerations above, but also because the answer is useful for firms and policy makers. Unfortunately, estimating the relationship between financial performance and CSR has proven diffi-cult and has led to mixed results. For example the early works of Cochran and Wood (1984), Waddock and Graves (1997) and Russo and Fouts (1997) found positive rela-tionships between financial performance and CSR. In later years, Lin, Huang, Chen, and Ke (2011) confirmed this result for a sample with Chinese firms. However, the works of Wright and Ferris (1997) and L´opez, Garcia, and Rodriguez (2007) found a negative relationship between CSR and financial performance.
positive relationship and little evidence for a negative relationship. In a more recent study, Endrikat, Guenther, and Hoppe (2014) found an overall positive relationship between CSR focused on the environmental dimension and financial performance. In conclusion, the meta studies seem to suggest a positive relationship between CSR and financial performance.
The literature identifies several reasons why research on the relationship between CSR and financial performance has led to mixed results. The first cause is that the empirical studies on CSR and financial performance suffer from endogeneity prob-lems. As with virtually all empirical studies, there is a large probability that the estimated relations suffer from the endogeneity problem. The endogeneity problem occurs if there is measurement error, omitted variables or reverse causality and re-sults in biased estimators. For example, the paper of Wokutch and Spencer (1987) found that the causal relation between CSR and financial performance runs the other way round, which would imply that better financial performance causes CSR. An example of a study that addresses this issue is the work of Jo and Harjoto (2011). These researchers use an IV-estimation to overcome the endogeneity problem. As an instrument, the authors choose the age of the firm, as it highly correlates with CSR, but not with financial performance.
2.4
Modeling CSR
Before the main model of this thesis will be presented, it is insightful to first review some papers that have attempted to model CSR in a mathematical economic model. The first discussed paper is the work of Alves and Santos-Pinto (2008). These authors model CSR in the context of a two stage oligopoly model with two firms. The CSR ef-fort in their paper is that both firms can contribute a fixed amount per unit of output to social causes, which makes their product more desirable in the eyes of the con-sumer. The authors show the existence of a symmetric CSR equilibrium if consumer value CSR effort sufficiently high and if the degree of product substitutability is not too high. Prices, quantities and profits are all higher in the CSR equilibrium than under regular Cournot competition. A different approach is taken by Baron (2001) who focuses on private politics. In his paper there are activist consumers who can put pressure on the firms to adopt more environmentally friendly policies. Neglecting the environment could potentially cause consumer boycots. The main result of the paper is that the strategic position of the firm is determined by CSR and private politics. The model of McWilliams and Siegel (2001) provides theoretical foundations for a neutral relationship between CSR and financial performance. Their analysis is based on supply and demand theory and uses cost-benefit analysis to determine the CSR level that maximizes profits and satisfies the demand for CSR of the stakeholders. Their main result is that the financial performance of the CSR undertaking firms are identical to the financial performance of firms that do not undertake CSR.
manufacturers to engage in CSR activities, whereas from a profits perspective the reverse is optimal.
The work on which the model of this thesis is most inspired is the work of Man-asakis, Mitrokostas, and Petrakis (2007). Their work is similar to the work of Alves and Santos-Pinto (2008) in the way CSR is modeled. A major difference is that in order to have CSR activities in their model, the owners of the firm need to hire a socially responsible manager that has a long history of engaging in CSR activities. The managers maximize an objective function that consists of firm profits and total CSR activities. The managers differ with respect to the valuation put on total CSR activities. The owners hire a manager such that total profits are maximized. The authors show that it a dominant strategy for both owners to hire a socially respon-sible manager. The intuition for this result is that hiring a CSR oriented manager builds a competitive advantage over the rival firm. Therefore, in order to prevent losing demand to the rival, it is optimal for both owners to hire a CSR oriented man-ager. Prices, quantities, profits and social welfare all increase compared to standard Cournot competition. In addition, Manasakis, Mitrokostas, and Petrakis (2015) also investigate strategic CSR in the setting of international markets and multinationals. The main objective of the paper is how CSR efforts differ if foreign markets are served via exports or foreign direct investment (FDI). The main result is that multinationals serving foreign markets via FDI will engage more in CSR than multinationals serving foreign markets through exports.
3
The Model
3.1
Main Ingredients of the Model
zero. The demand side of the market is formed by a unit mass of consumers. These consumers are assumed to be identical regarding their valuation towards the physical characteristics of the good. However, the consumers are heterogeneous regarding their valuation towards the CSR effort undertaken by the firms. This heterogeneity is captured in the model by the parameter β. The utility function of a type β consumer is given by: U (xi, xj, M ) = (α + βυi)xi+ (α + βυj)xj− 1 2(x 2 i + x 2 j + 2γxixj) + M (1)
Where xi, i = 1,2 corresponds to the quantity of good i, bought by the consumer of
type β and M can be interpreted as the money spent on all other goods. As can be observed from (1), the utility function is of the quasi-linear type. This type is chosen, because this specific functional form produces linear demand functions for xi and xj.
It also makes sure that changes in the prices of xi and xj only cause substitution
effects and no income effects, provided that the income of the consumer is sufficiently high. The total willingness to pay of a type β consumer can be decomposed in a val-uation towards the physical characteristics and a valval-uation towards CSR effort. The parameter α measures the valuation of the consumer regarding the physical charac-teristics of the good and is identical across consumers.
The parameter υi ∈ [0, ¯υ] measures the CSR effort undertaken by the firms, where ¯υ
can be interpreted as an upper boundary on CSR effort. It is assumed that α > ¯υ. Another assumption is that the cost of CSR is proportional to output. The CSR effort can be interpreted in different ways. For example, it can be interpreted as a donation to charity per unit of output, where ¯υ is the maximum amount per unit of production that the firm is able to donate to charity. The CSR effort can also be interpreted in an environmental dimension. If, for example, the production of the firms pollutes the environment, υi can be seen as the per unit abatement cost.
If the firms set υi equal to ¯υ, the best possible technology for reducing pollution is
consumers might appreciate that the suppliers of this input receive a fair price for the input. The υi parameter then represents the extra amount that the firms pay to
the suppliers of the input. For input prices beyond ¯υ consumers do not build extra appreciation for the firm’s CSR effort, as they might consider ¯υ a reasonable price. In the remainder of this thesis, the general term CSR effort will be used, unless stated otherwise.
As previously mentioned, the parameter β ∈ [0, 1] measures the valuation of a con-sumer regarding the CSR effort of the firms and is heterogeneous across concon-sumers. Essentially, β measures how socially conscious a consumer is and determines by how much the total willingness to pay of a consumer increases after a CSR effort increase. For a consumer that is not socially conscious at all (i.e. β = 0), a CSR effort increase has no effect on the total willingness to pay, whereas for a consumer with type β = 1, the willingness to pay and CSR effort change one for one. This thesis will assume that β is distributed according to a cumulative distribution function F (β) and density function f (β), where β ∈ [0, 1] . Hence, we know that the average consumer type, ¯β, is given by: ¯ β = Z 1 0 βf (β)dβ
The parameter γ ∈ [0, 1] measures the degree of substitutability between xi and xj. A
γ value of zero belongs to the case of independent goods and a γ value of 1 corresponds to homogeneous goods.
The paper of Manasakis et al. (2007) argues that the set-up discussed so far suffers from a credibility problem. Consider the case where consumers have been convinced that firm i has stated publicly that it donates a certain amount per unit of output to charity. (i.e. a strictly positive υi value). As a result, the maximum willingness to
pay for firm i’s product has increased. As firm i realizes that the willingness to pay for its product has increased, it is not in firm i’s interest anymore to actually donate υi per unit of output to the charity, since this is a costly affair. Ultimately, consumers
effort will be undertaken in equilibrium. This implies that firms will not engage in any CSR activities in equilibrium.
To solve this problem, it will be assumed that if a firm wants to engage in CSR activities, it has to hire a so-called CSR manager. This manager will have detailed recordings of past CSR activities and is, therefore, capable of credibly signaling CSR activities to the consumers. Hence, in this set-up there will be separation of ownership and management. If a manager is hired, he will make both the CSR and competition decision for the owner. It is important to note that the manager will maximize his own objective function, which will differ from pure profit maximization. It will be assumed that the manager will not only maximize profits, but rather a weighted sum that includes total expenditure on CSR activities (υiqi). Different types of managers
will be available for hiring and their type is captured through a µ parameter. A higher µ value corresponds to a manager that puts greater emphasis on total CSR expenditures. The utility function of the manager of firm i is given by:
Vi = πi+ µiυiqi (2)
Where qi is equal to firm i’s market demand and πi represents firm i’s profits. The
second term of (2) measures the utility generated by CSR activities, which enters the utility function linearly by assumption. With respect to the utility function of the owner, an important change is made compared to the work of Manasakis et al. (2007). Their paper assumes that the owners are pure profit-maximizers. This thesis deviates in that aspect and postulates a utility function for the owner that incorporates altruistic behavior. The utility function of owner i is given by:
Mi = πi+ iυiqi (3)
The objective function specified in (3) is similar to the managers’ objective function. The parameter πi are the profits of owner i and iυiqi measures the generated
util-ity from engaging in CSR activities. The parameter i is exogenously determined
A higher i corresponds to a more altruistic owner that puts higher weight on CSR
activities. The fact that this thesis considers these alternative objective functions for managers and owners contributes to the literature that researches this topic. The most famous paper in this literature is the paper of Fershtman and Judd (1987). The model analyses a sequential game with 3 stages. The timing of this game with perfect information is as follows:
Stage 1: The owners of the firms will simultaneously and optimally choose what type of manager they want (set µi);
Stage 2: the managers will simultaneously and optimally set their CSR effort (set υi);
Stage 3: The managers will simultaneously and optimally set prices on the market (Bertrand competition)
The model is solved by backward induction. With regard to the mode of competition, this thesis also differs from Manasakis et al. (2007) who assumed Cournot competi-tion in the third stage.
The main objectives of this thesis’ model is to derive which types of CSR equilibria exist (symmetric vs asymmetric), what the drivers of strategic CSR are, how equi-librium manager types interact with the strength of the altruistic type of the owner and, finally, what the effects of strategic CSR with altruistic owners are on market outcomes (prices, quantities, profits).
3.2
The Market Demand Function
type β for good i.
pi = α + βυi− xi− γxj (4)
The regular individual demand function of a type β consumer for good i can be found by inverting the system of equations given by (4):
xi(β) =
α(1 − γ) + β(υi− γυj) − pi+ γpj
1 − γ2 (5)
The market demand function is found by aggregating across all consumers. This is done by solving the following integral:
qi =
Z 1
0
α(1 − γ) + β(υi− γυj) − pi+ γpj
1 − γ2 f (β)dβ (6)
Solving the integral above yields the market demand function for good i is:
qi(pi, pj) =
α(1 − γ) + ¯β(υi− γυj) − pi+ γpj
1 − γ2 (7)
For simplification purposes, it is assumed that β is uniformly distributed in [0, 1]. Hence, the density function is f (β) = 1 for all β ∈ [0, 1]. This implies that ¯β is 12. Using this result into (7):
qi(pi, pj) =
α(1 − γ) + 12(υi − γυj) − pi+ γpj
1 − γ2 (8)
As a last step, the market inverse demand function for good i can be derived, by inverting the system given by (8). This yields:
pi(qi, qj) = α +
1
2υi− qi− γqj (9)
addition, if firm j increases CSR effort the opposite effect holds, namely an inward shift of firm i’s demand curve. Hence, the CSR choice leaves the owners of the firms with a trade-off. On the one hand, increased CSR effort by firm i implies an outward shift of its demand function and, thereby, boosting sales. On the other hand, however, CSR effort is costly and will take away resources of firm i that firm i could have spent elsewhere. Another worth-mentioning result is that the market demand function corresponds to the demand function of the average consumer with type ¯β.
3.3
Building Intuition: the Monopoly Case
After having derived the market demand function in the previous section, it is now possible to work through the model by backward induction. Before the more compli-cated case of oligopoly is studied, it is instructive to study the easier monopoly case first. The model easily allows for monopolies by assuming that γ is equal to zero. In that case, the goods are entirely independent. As a result, the situation of both firms can be studied separately. Substituting γ = 0 into (8) and dropping the subscripts simplifies the market demand function to:
q = α + 1
2υ − p (10)
Assume that a manager with type µ has been hired in stage 1 that made the CSR decision υi in stage 2. In the third stage of the game, the manager of the firm
maxi-mizes (2) by setting the price appropriately. Substitution of (10) into (2) and solving the first-order condition yields the equilibrium price of the manager, conditional on its CSR decision and type:
p = 2α + 3υ − 2µυ
Substitution of (11) into (10) gives the manager’s equilibrium quantity, conditional on its CSR decision and type:
q = 2α − υ + 2µυ
4 (12)
Substitution of (11) and (12) into (2) yields an expression for the manager’s utility function: V = 2α + (2µ − 1)υ 2 16 (13)
In the second stage, the manager sets υ such that (13) is maximized. The first-order derivative of V with respect to υ is given by:
∂V ∂υ =
2(2µ − 1)(2α + (2µ − 1)υ) 16
Unfortunately, the second-order condition of this maximization problem is not satis-fied, as the second-order derivative is strictly positive, which means that the objective function of the manager is convex in υ:
∂2V
∂υ2 =
2(2µ − 1)2
16 > 0
This implies that the solution to the manager’s optimization problem can be found on the corners of the υ interval. Inspection of (13) reveals that if µ > 12, CSR effort is positively related to the manager’s utility level. Therefore, it is utility-maximizing to set CSR effort as high as possible (i.e. set υ = ¯υ). If µ < 12, CSR effort is negatively related to the manager’s utility level. Hence, utility-maximization requires CSR effort to be set as low as possible (i.e. set υ = 0). If µ = 12, CSR effort disappears from (13) and, therefore, any CSR effort choice is optimal.
collapses to the textbook monopoly outcome. If µ > 12, managers set CSR effort equal to ¯υ, which means that owners need to hire a manager. The exact manager type can be derived, by substituting (11), (12) and υ = ¯υ into (3). The first-order condition for this problem can be derived by taking the first-order derivative of M with respect to µ:
∂M ∂µ =
4¯υ − 4¯υµ
8 = 0
Solving the first-order condition above for µ yields the utility-maximizing manager type for a monopolist owner:
µ = (14)
Since it was assumed that µ > 12, it is required that > 12. The expression given by (14) gives rise to the following proposition:
Proposition 1. Under monopoly, a utility-maximizing owner hires a manager equal to his own altruistic type, .
3.4
Solving the Model under Bertrand Oligopoly: Behavior
of Managers
In this section, the model moves away from monopoly by assuming γ > 0. This ensures strategic interaction between the firms. Similarly to the monopoly case, the analysis starts in the third stage, where managers simultaneously set prices to max-imize their utility functions given by (2). Substituting the market demand function given by (8) into (2) and solving the first-order condition yields manager i’s best-response function: pi = α 2(1 − γ) + 1 4(3 − 2µi)υi− γ 4υj + γ 2pj (15)
This function plots manager i’s utility-maximizing price, given the price set by man-ager j. As the best-response functions are upward sloping, the standard Bertrand result holds that predicts that prices are strategic complements with heterogeneous products. The effect of an increase in CSR effort by manager i on the best-response function depends on the manager hired in the first stage of the game. Relatively profit-oriented managers (i.e. if µi < 32), perceive CSR effort mainly as a costly
en-deavor and, therefore, treat CSR effort similarly to a marginal cost increase. To save the profit margin as much as possible, the manager will, therefore, set prices more aggressively given the price of manager j. This is reflected by a outward shift of the best-response function.
A relatively CSR oriented manager (i.e. if µi > 32), behaves differently compared
to the relatively profit-oriented manager. As the weight on CSR expense (υiqi) is
functions given by (15):
pi =
2α(1 − γ)(2 + γ) + (6 − 4µi− γ2)υi + (1 − 2µj)γυj
2(4 − γ2) (16)
Substituting (16) into (8) yields the corresponding equilibrium quantities of the man-agers:
qi =
2α(1 − γ)(2 + γ) − (2 − γ2)(1 − 2µ
i)υi+ (1 − 2µj)γυj
2(4 − γ2)(1 − γ2) (17)
Essentially, the comparative statics effects of ∂pi
∂υi and
∂qi
∂υi reveal three classes of
man-ager behavior in the third stage. The first class of manman-agers are characterized by µi < 12 and are managers with a strong emphasis on profits. According to the partial
derivatives of piand qi with respect to υi, these managers increase the price and lower
the quantity after a CSR effort increase. The reason for this is similar to the intu-ition developed above. Relatively profit-concerned managers like to protect the firm’s profit margin as much as possible. Therefore, the effect on the price can be treated as a marginal cost increase, which leads to a higher price. However, the sign of ∂qi
∂υi is
affected by two opposing effects. The first effect is the traditional price effect, which puts a negative force on the quantity in this case, as the manager has increased the price after the CSR effort increase. The second effect of engaging in CSR is a market effect, which makes firm i’s product more attractive, as socially conscious consumers appreciate CSR. This competitive advantage over the rival has a positive force on the quantity. For profit-oriented managers, characterized by µi < 12, the price effect
outweighs the market effect, as the sign of ∂qi
∂υi is negative.
The second class of managers are located on the interval 1
2 < µi < 3 2− 1 4γ 2. This class
represents intermediate types, who have relatively balanced preferences between prof-its and CSR. According to the signs of ∂pi
∂υi and
∂qi
∂υi, these managers increase the price
However, the size of this price increase is less than the price increase of the profit-oriented managers, as there is more weight on CSR activities. Therefore, the price effect is now dominated by the market effect such that the quantity also increases. The last class of managers are characterized by µi > 32 − 14γ2 and are managers with
a strong emphasis on CSR. Since their utility is mainly derived from CSR activities, it is vital for this manager group to have the quantity as high as possible. Therefore, managers from this group find it utility-maximizing to lower the price, despite the fact that CSR effort increases marginal cost. As the price effect and market effect now work in the same direction, the quantity increases.
Note that if the products become relatively more homogeneous (i.e. a higher value of γ), the intermediate manager group becomes smaller and the CSR manager group becomes larger. The intuition for this is that a higher γ parameter means a more elastic demand function. In such an environment, increasing the price results in a higher demand loss. As a result, the trade-off between profits and CSR becomes more extreme and more managers will behave as group 3 managers and prioritize the quantity. The truly profit-oriented managers in group 1 are unaffected by γ and will protect the profit margin at all cost.
The last step of the third stage is substituting the expressions for the price and quan-tity into (2). This yields the utility function of manager i, conditional on its CSR decision and type:
Vi =
2α(1 − γ)(2 + γ) − (2 − γ2)(1 − 2µi)υi+ (1 − 2µj)γυj
2
4(4 − γ2)2(1 − γ2) (18)
In stage 2, managers simultaneously set υi such that the expression in (18) is
The analysis and intuition is identical to the monopoly case with the only difference that the analysis now involves two players. If µi > 12, it is utility-maximizing for
manager i to set υi = ¯υ. If µi < 12, utility-maximization for manager i requires to set
υi = 0. All in all, this leads to four cases in stage 1 that need to be considered one
by one.
There are two symmetric cases and two asymmetric cases. The first case represents a symmetric equilibrium configuration, where neither firm will undertake CSR activities in equilibrium. This case occurs if both owners hire a manager in the domain µ < 12. The second case is a symmetric CSR scenario, where both owners hire a manager that undertakes CSR activities in equilibrium. This case occurs if both owners hire a manager in the domain µ > 12. Finally, there are two asymmetric CSR scenarios, where one owner hires a manager that engages in CSR, whereas the other owner does not. This case occurs if µi > 12 and µj < 12.
3.5
Optimal Manager Selection with µ
i<
12: textbook Bertrand
Competiton
The first case is relatively straightforward, since the owners rationally anticipate that in this case the managers will not engage in CSR activities in stage 2. Substitution of υi = υj = 0 into (16) and (17) reveals that the µ parameters vanish from the
price and quantity expressions. Consequently, the utility functions of the owners are independent of µi. Intuitively, not engaging in CSR activities implies that managers
with µi < 12 lose their ability to influence the price and quantity through their type.
As a result, all managers with µi < 12 behave as managers that are fully
profit-oriented. Mathematically, any µi ∈ [0,12) is utility-maximizing for the owners in
stage 1. However, since all managers located on this interval mimic the behavior of a manager that only cares about profits, it is most intuitive and natural to argue that both owners will hire a manager with µi = 0 in this scenario. Hence, this scenario
price and quantity for this scenario are given by:
pBERTi = 2α(1 − γ)(2 + γ)
2(4 − γ2) (19)
qBERTi = 2α(1 − γ)(2 + γ)
2(4 − γ2)(1 − γ2) (20)
Multiplying (19) and (20) yields the utility function of owner i as a function of only exogenous variables:
MiBERT = α
2(1 − γ)
(2 − γ)2(1 + γ) (21)
3.6
Optimal Manager Selection with µ
i>
12: Symmetric CSR
As previously mentioned, in the first stage, the owners of the firms set µi such that
the utility function specified in (3) is maximized. Consider the problem of owner i. Owner i rationally anticipates the events that will occur in stage 2 and 3 and knows that the hired managers will set υi = υj = ¯υ. Substituting this information and (16)
and (17) into the utility function of owner i and taking the first-order derivative with respect to µi leads to the following first-order condition for owner i:
∂Mi ∂µi = −γ 2υ(1 − γ)(2 + γ)(2α − ¯¯ υ) − 8¯υ2(2 − γ2)µ i+ 2¯υ2(4 − γ2)(2 − γ2)i+ 2γ3υ¯2µj 2(4 − γ2)2(1 − γ2) = 0
Note that the second-order condition is satisfied, as: ∂2M i ∂µ2 i = −4¯υ 2(2 − γ2) (4 − γ2)2(1 − γ2) < 0
Solving the first-order condition for µi yields the best-response function of owner i:
The interpretation of (22) is similar to the best-response function with prices derived in stage 3. However, the strategic variable is now the manager type, instead of the price. This means that equation (22) plots owner i’s utility-maximizing manager type, given the manager type hired by owner j. Note that the owners perceive manager types as strategic complements, as the best-response functions are upward sloping. The utility-maximizing manager types can be derived by solving the system of best-response functions, given by (22):
µCSRi = 2¯υ(4 − γ
2)(2 − γ2)(4(2 − γ2)
i+ γ3j) − γ2(1 − γ)(2 + γ)(2α − ¯υ)(γ3+ 4(2 − γ2))
2¯υ(16(2 − γ2)2− γ6)
(23)
A few remarks regarding (23) are in order. Compared to the monopoly case, where utility-maximizing owners selected managers equal to their own altruistic type, it can directly be observed that this result breaks down under duopoly (µCSR
i 6= i).
Al-though (23) may not seem intuitive, it offers two reasons why the monopoly result is distorted. The first reason is a competing owners effect that is represented by the first term of (23). This term reveals that under duopoly, not only an owner’s own altruistic type is taken into account, but also the altruistic type of the rival. With oligopolistic owners, the owners rather use some weighted average of their altruistic types instead of only their own type when making their manager decision, with γ be-ing the weightbe-ing factor. Changbe-ing the rival’s altruistic type or the weightbe-ing factor γ induces the owner of firm i to hire a different manager type, even if his own altruistic type remained constant.
The second reason is a consumer valuation effect. Note that the total valuation re-garding the goods consist of a physical component (α) and a CSR component (¯υ). If α increases, the physical characteristics become relatively more important compared to the CSR characteristics. Investing in CSR is then relatively less important and there is less scope to build a competitive advantage over the rival. Consequently, a utility-maximizing owner requires a manager that is less CSR oriented.
rela-tively more important. As there is more scope to build a competitive advantage over the rival, a utility-maximizing owner will hire a manager that is more CSR oriented to take advantage of the new situation. Both reasons can potentially cause µCSRi to be higher than i, which is an indication of strategic CSR.
Another implication of Proposition 1 was that an increase in is reflected one to one in µ. This result also breaks down in the duopoly case. The effect of an increase of i on µCSRi is still positive, but less than 1. The intuition is that hiring a more
CSR oriented manager will decrease the price. However, due to upward sloping best-response functions, the rival owner will hire a more CSR oriented manager as well. This will decrease the price even further. Therefore, rational owners do not fully update their utility-maximizing manager type deliberately. By being more careful in their manager choice, the owners ensure that the price in the third stage will not fall too low, relative to their altruistic types.
If the value of γ is higher, the effect of an increase of ion µCSRi becomes smaller. This
is logical, as stronger market interactions between the goods of firm i and j make the effects of more CSR oriented managers on the price more severe. As a result, owners need to be even more careful in environments with large strategic interactions. The developed intuitions regarding µCSR
i can be summarized with Proposition 2 and 3:
Proposition 2. Under duopoly with symmetric CSR, both owners engage in strategic CSR, as µCSR
i 6= i
Proposition 3. Under duopoly with symmetric CSR, the comparative statics effect
∂µCSR i
∂i ∈ (0, 1) and is decreasing in γ
The proof of Proposition 3 can be found in the appendix. In addition, (23) was derived under the assumption that both owners selected a manager in the domain µi > 12. To make sure that (23) is consistent with this assumption, a condition on
inequality µCSRi > 12 yields the following consistency constraint, CCiCSR(j): i > γ2(2 + γ)(1 − γ)(2α − ¯υ)(γ3+ 4(2 − γ2)) + ¯υ(16(2 − γ2)2− γ6) 8¯υ(4 − γ2)(2 − γ2)2 − γ3 4(2 − γ2)j (24)
The next step is to find a closed-form solution for the price. This is done, by substi-tuting (23) into (16). This results in the following expressions:
pCSRi = pBERTi + Φ − Ω (25)
Where Φ and Ω are defined as:
Φ ≡ (2 + γ) γ2(2 + γ)(1 − γ)(2α − ¯υ)(γ3+ 4(2 − γ2)) + (3 − γ)(16(2 − γ2)2 − γ6)¯υ 2(4 − γ2)(16(2 − γ2)2 − γ6) Ω ≡ 2¯υ(4 − γ 2)(2 − γ2) 4(2 − γ2)(2 i+ γj) + γ3(2j + γi) 2(4 − γ2)(16(2 − γ2)2− γ6)
Substituting (23) into (17) yields an expression for the equilibrium quantity:
qCSRi = qiBERT + ∆ − K (26)
Where, ∆ and K are defined as:
∆ ≡ 2¯υ(2 − γ2)(4 − γ2) 4(2 − γ2) (2 − γ2)i− γj + γ3 (2 − γ2)j − γi 2(4 − γ2)(1 − γ2)(16(2 − γ2)2− γ6) K ≡ (2 + γ)(1 − γ) γ2(2 + γ)(1 − γ)(2α − ¯υ)(γ3+ 4(2 − γ2)) + (16(2 − γ2)2− γ6)¯υ 2(4 − γ2)(1 − γ2)(16(2 − γ2)2− γ6)
The analysis of the equilibrium quantity is similar to the price analysis above. There are two effects why the equilibrium quantity under symmetric CSR deviates from the quantity under Bertrand competition. The parameter K is again a collection of structural market parameters and is strictly positive, whereas the ∆ parameter measures the effect of altruistic owners. The sign of ∆ depends on the difference between i and j. If for example the rival owner’s altruistic type is significantly
larger, he will hire a manager that is significantly more CSR oriented, relative to owner i’s manager.
Subsequently, this rival manager will set a lower price, relative to manager i’s price. If this price difference is large enough, it is theoretically possible that owner i loses demand to the rival, despite the fact that owner i engaged in CSR activities. This would be represented by a negative sign of the ∆ parameter. Of course, ∆ has a positive sign if owner i is sufficiently more altruistic relative to owner j. Since K and ∆ can potentially operate in opposite directions, the net effect on the quantity is ambiguous. From the analysis on pCSR
i and qiCSR, it can be concluded that the net
effect on profits, πi, is uncertain as well. This leads to the following proposition:
Finally, by substituting (25) and (26) into (30), owner i’s utility function can be derived, as a function of only exogenous variables:
MiCSR = A + 2¯υ(2 − γ2)(4 − γ2) 4(2 − γ2) (2 − γ2)i− γj + γ3 (2 − γ2)j − γi 2 2(2 − γ2)(1 − γ2)(4 − γ2)2(16(2 − γ2)2− γ6)2 (27)
Where A is defined as:
A ≡ (2 + γ)(1 − γ)(2α − ¯υ)(16(2 − γ2)2− γ6− γ2(2 + γ)(1 − γ)(γ3+ 4(2 − γ2))
3.7
Optimal Manager Selection with µ
i>
12and µ
j<
12:
Asymmetric CSR
The analysis for owner j is similar to the analysis developed in section 3.5. The pa-rameter µj vanishes from owner j’s optimization problem, as owner j hires a manager
that does not deliver CSR effort in equilibrium (e.g. υj = 0). Conform the discussion
in section 3.5, owner j will hire a manager with µj = 0.
In contrast, owner i hires a manager that delivers the maximum CSR effort in equi-librium (e.g. υi = ¯υ). In order to derive owner i’s utility-maximizing manager type,
it is required to substitute (16), (17), υi = ¯υ and υj = 0 into (3) and taking the
first-order derivative of Mi with respect to µi. This leads to the following first-order
condition: ∂Mi ∂µi = −2γ 2α¯υ(1 − γ)(2 + γ) − 8¯υ2(2 − γ2)µ 1+ ¯υ2(2 − γ2)(γ2+ 2(4 − γ2)i) 2(4 − γ2)2(1 − γ2) = 0
The utility-maximizing manager type can be found, by solving the first-order condi-tion for µi: µcsr∗i = (2 − γ 2)¯υ γ2+ 2(4 − γ2) i − 2γ2α(1 − γ)(2 + γ) 8¯υ(2 − γ2) (28)
Similarly to the previous section, (28) clearly confirms the result that µcsr∗
i 6= i in
duopoly models. Hence, the asymmetric CSR case is also able to predict strategic CSR. The intuition for this result is similar to the intuition behind (23). In addi-tion, the result that an increase in altruistic owner type is not fully reflected in the manager type holds in the asymmetric case as well. Although the propositions are almost identical to the symmetric CSR case, they are repeated below for completeness purposes:
Proposition 5. Under duopoly with asymmetric CSR, the owner of the CSR under-taking firm engages in strategic CSR, as µcsr∗
i 6= i
Proposition 6. Under duopoly with asymmetric CSR, the comparative statics effect
∂µcsr∗ i
∂i ∈ (0, 1) and decreasing in γ
The proof of Proposition 6 is identical to the proof of Proposition 3 and, therefore, omitted. Note that (28) was derived under the assumption that µi > 12. To ensure
that (28) is consistent with this assumption, the following consistency constraint (CCcsr∗
i ) is in order:
i >
4¯υ(2 − γ2) + γ2 2α(1 − γ)(2 + γ) − (2 − γ2)¯υ
2¯υ(2 − γ2)(4 − γ2) (29)
Substitution of (28), υi = ¯υ and υj = µj = 0 into (16) yields the price of the owner
that engages in strategic CSR:
pcsr∗i = 2α(1 − γ)(2 + γ) + (2 − γ
2)¯υ(3 − 2 i)
This price is easier to analyze if it is rewritten as:
pcsr∗i = pBERTi + B + C (31)
Where B and C are defined as:
B ≡ (2 − γ 2)(4 − γ2)¯υ(3 − 2 i) 4(2 − γ2)(4 − γ2) C ≡ 2γ 2α(1 − γ)(2 + γ) 4(2 − γ2)(4 − γ2)
Equation (31) shows that pcsr∗i deviates from pBERTi , because of two parameters. In the same vein as the previous section, C is a strictly positive constant that collects structural market parameters. B measures the altruistic owner effect. This parameter is positive if i < 32 and negative if i > 32. As a result, only if i < 32, it can
unambiguously be claimed that the CSR owner in the asymmetric case sets a higher price. If i > 32, the net effect is uncertain. The quantity of the CSR owner can be
found, by substituting (28), υi = ¯υ and υj = µj = 0 into (17):
qcsr∗i = 2α(2 + γ)(1 − γ) + (2 − γ
2)¯υ(2 i− 1)
8(1 − γ2) (32)
The quantity can also be written as:
qcsr∗i = qiBERT + D − E (33)
Where D and E are defined as:
Using similar intuition as above, the parameter E is a strictly positive constant, containing structural market parameters and puts a downward pressure on qcsr∗
i ,
relative to qiBERT. The altruistic owner effect measured by D is positive if i > 12 and
negative if i < 12. Only if the altruistic strength is sufficiently large, it will positively
contribute to the quantity sold of the CSR engaging owner. All in all, the net effect on the equilibrium quantity of the CSR engaging owner is uncertain. From this analysis, it can be concluded that it must hold that the effects on the profits are uncertain as well. The following proposition summarizes:
Proposition 7. Under duopoly with asymmetric CSR, the net effects on the price, quantity and profits for the CSR engaging owner are ambiguous.
The utility function of the CSR owner in the asymmetric CSR case is given by:
Micsr∗= 2α(2 + γ)(1 − γ) + (2 − γ2)¯υ(2 i− 1) 2 32(2 − γ2)(1 − γ2) (34)
The analysis also needs to be applied to owner j who fully focused on profit-maximization. The price and quanity set by owner j are given by:
p∗j = 2α(1 − γ) γ 3 + 4(2 − γ2) + γ ¯υ(2 − γ2)(2 − γ)(1 − 2 i) 8(2 − γ2)(2 − γ) (35) qj∗ = 2α(1 − γ) γ 3+ 4(2 − γ2) + γ ¯υ(2 − γ2)(2 − γ)(1 − 2 i) 8(2 − γ)(1 − γ2)(2 − γ2) (36)
Using the same method as above it can be verified that if i > 12, the ultimate effect
on the price and quantity is ambiguous and if i < 12, the price and quantity for owner
j are higher than under Bertrand competition. Owner j ultimately benefits from the CSR activities of owner i if owner i’s type is relatively low. This is summarized with the following proposition:
owner are ambiguous.
The final step of this section is deriving the utility function of owner j, by multi-plying (35) and (36): Mj∗ = 2α(1 − γ) γ3+ 4(2 − γ2) + γ ¯υ(2 − γ2)(2 − γ)(1 − 2i) 2 64(2 − γ2)2(2 − γ)2(1 − γ2) (37)
Note that the case with µi < 12 and µj > 12 is the mirror image of the case just
discussed and, therefore, omitted.
3.8
Determining the Subgame Perfect Nash Equilibria
The last section derived the outcomes of all possible scenarios in stage 1. However, it is still unknown which scenario is actually selected in the subgame perfect Nash equilibrium. In order for a scenario to be part of a subgame perfect Nash equilibrium, it should also be a Nash equilibrium in stage 1. As always, the requirement for a Nash equilibrium is that both owners should not have an incentive to deviate from their selected strategy, given the strategy of the rival owner. In the context of the model, owner i’s manager choice should be a best response to owner j’s manager’s choice and vice versa. This section will derive conditions on i and j for which the four
cases can be sustained in a subgame perfect Nash equilibrium. The analysis starts by determining whether the textbook Bertrand equilibrium with heterogeneous products is a potential equilibrium candidate.
Using the terminology above, the Bertrand equilibrium is a Nash equilibrium of the first stage, if both owners have an incentive to hire a manager that is completely focused on profit-maximization, given that the rival owner hires a manager that is fully profit-oriented as well. In terms of the model, this occurs if: Mcsr∗
i < MiBERT.
The solution to this inequality yields a condition on i:
This condition is called the incentive constraint (ICiBERT). If the constraint in (38) is satisfied, both owners have an incentive to hire a fully profit-oriented manager, given that the rival owner hires a manager that is completely focused on profit-maximization as well. This implies that the textbook Bertrand equilibrium with no CSR is a Nash equilibrium of the first stage. Together with the incentive constraint ICiBERT, the details of this equilibrium are given in section 3.5. The following Proposition summarizes the result:
Proposition 9. The Bertrand equilibrium with heterogeneous products and no CSR activities can be sustained in a subgame perfect Nash equilibrium if the incentive constraint in (38) is satisfied.
The next step is to determine whether the symmetric CSR case can be sustained as a Nash equilibrium in the first stage. This is the case, when both owners prefer to hire a CSR oriented manager, given that the rival owner hired a CSR oriented manager as well. This the case in the model if MiCSR > Mi∗. The solution of this inequality yields an incentive constraint on i, as a function of j (ICiCSR(j)):
i > X + γ (2 − γ2)(2 + γ)(2 − γ)p32(2 − γ2) − 16(2 − γ2)2+ γ6 (4(2 − γ2)2− γ4)p32(2 − γ2) j (39)
Where X is defined as:
X ≡ (1 − γ) 2α(γ3+ 4(2 − γ2))(16(2 − γ2)2− γ6 2¯υ(2 − γ2)(2 − γ)(4(2 − γ2)2− γ4)p32(2 − γ2) − (1 − γ) (2α − ¯υ)p32(2 − γ2) 16(2 − γ2)2− γ6− γ2(2 + γ)(1 − γ)(γ3+ 4(2 − γ2)) 2¯υ(2 − γ2)(2 − γ)(4(2 − γ2)2− γ4)p32(2 − γ2) + γ ¯υ(2 − γ 2)(2 − γ)(16(2 − γ2)2− γ6) 2¯υ(2 − γ2)(2 − γ)(4(2 − γ2)2− γ4)p32(2 − γ2)
Admittedly, the expression for ICCSR
i (j) is not elegant, but it can be observed that
the right-hand side of (39) is increasing in j. According to equations (25) and (26), a
utility under symmetric CSR. This makes it harder to solve the inequality MiCSR > Mi∗. Remember from the section on symmetric CSR, it was necessary to derive a consistency constraint on i in order to ensure that expression (23) is consistent with
the assumption that µi > 12. Combining the rationality constraint and the consistency
constraint gives the following final condition on i:
i > max
CCiCSR(j), ICiCSR(j)
(40)
This condition checks both the consistency constraint and the incentive constraint and makes sure i satisfies both constraints simultaneously. If (40) is satisfied, hiring
a CSR oriented manager is a Nash equilibrium of the first stage. Together with (40), the details of the subgame perfect Nash equilibrium with symmetric CSR can be found in section 3.6. The following proposition summarizes the result:
Proposition 10. Under duopoly, the symmetric CSR case can be sustained in a subgame perfect Nash equilibrium, given that i > max
CCiCSR(j), ICiCSR(j)
Finally, the last case this thesis needs to consider is the asymmetric CSR case. In this scenario, the owner of firm i hires a CSR oriented manager with µi > 12, whereas
the owner of firm j hires a manager with µj = 0. Owner i should prefer to hire a CSR
oriented manager, given that owner j hires a manager that is fully focused on profit-maximization and vice versa. In terms of the model, the following two inequalities need to be satisfied. For owner i, it is necessary that Micsr∗> MiBERT and for owner j it is necessary that MCSR
j < M ∗
j. For owner i, the incentive constraint (ICicsr∗) is
similar to (38) and the incentive constraint for owner j (ICj∗(i)) is similar to (39).
Moreover, there is a consistency constraint constraint (CCcsr∗
i ) for owner i, as the
hired manager type for owner i needs to be higher than 12. This consistency constraint is given by (29). The final constraints for owners i and j are given by:
i > max
ICicsr∗, CCicsr∗
j < ICj∗(i) (42)
When (41) and (42) are satisfied, owner i will find it utility-maximizing to hire a CSR oriented manager given that owner j hires a fully profit-oriented manager and owner j will find it utility-maximizing to hire a manager that is completely focused on profits, given that owner i hires a CSR oriented manager. In other words, the asymmetric CSR configuration is a Nash equilibrium in the first stage. Together with (41) and (42), the details of the subgame perfect Nash equilibrium with asymmetric CSR can be found in section 3.7. The following proposition arises:
Proposition 11. Under duopoly, the asymmetric CSR case can be sustained in a subgame perfect Nash equilibrium, given that i > max
ICcsr∗ i , CCicsr∗ and j < ICj∗(i)
In conclusion, each outcome in the first stage can potentially fulfill the require-ments of subgame perfection, by setting i and j appropriately. If both owners are
both sufficiently altruistic, a symmetric CSR equilibrium can be attained, whereas even the textbook Bertrand equilibrium can be reached if the altruistic type of both owners are sufficiently low. Moreover, asymmetric CSR equilibria exist, when owner i’s type is sufficiently high and owner j’s type is sufficiently low.
Note that there also exist parameter configurations for which no consistent subgame perfect Nash equilibrium exists. An example of a parameter configuration without a consistent subgame perfect Nash equilibrium is α = 100, ¯υ = 10 and γ = i = j
= 1
2. It can be verified that with this configuration, the incentive constraints dictate
that the Nash equilibrium in the first stage is for both owners to hire a CSR oriented manager. However, the utility-maximizing manager type for both owner is to play µi = 221. This leads to an inconsistency in the second stage, as managers with type
1
22 will not provide CSR effort in equilibrium. In other words, the parameter
4
Discussion and Conclusions
The model discussed in the previous section established multiple equilibria and propo-sitions. It is interesting to examine how the results of the model relate to the academic literature on this topic. A natural starting point would be to compare the results of this thesis’ model to the results of Manasakis et al. (2007), as their research is closely related to the model of this thesis. The major difference in model specification be-tween the two papers, is the fact that the model of the thesis allowed for owners with altruistic preferences.
A first implication of this is that CSR is solely driven by profit-maximization in the model of Manasakis et al. (2007), whereas CSR in this thesis is the combined result of profit-maximization and altruistic behavior. This causes a number of differences with respect to the results. The most important difference is that the paper of Manasakis et al. (2007) finds that hiring a CSR oriented manager is a dominant strategy, which means that there is only one equilibrium. The findings of this thesis are in contrast with Manasakis et al. (2007), as the optimal strategy of an owner crucially depends on the strength of the altruistic preferences. As a result, this thesis derived conditions that support three different equilibrium types, ranging from no CSR in equilibrium to full CSR in equilibrium.
similarly. The model of this thesis can explain cases as the Dutch food market, based on altruistic preferences of owners. Admittedly, the supermarket case can also be explained by profit-maximization alone. It can be the case that Eko plaza strate-gically targets environmentally conscious consumers and, therefore, offers a product range in line with the preferences of these consumers. Burani and Mantovani (2018) have explicitly attempted to model this situation, in the realm of second-degree price discrimination with non-linear contracts.
In addition, Manaskis et al (2007) obtains the result that market outcomes, such as prices, quantities and profits, unambiguously increase with CSR effort, relative to standard Cournot competition. This sheds light on the empirical debate discussed earlier, regarding the relationship between CSR effort and financial performance. In other words, the paper clearly predicts a positive relationship between CSR and fi-nancial performance. The model of this thesis found for all CSR scenarios ambiguous effects on prices, quantities and profits. As discussed in the model section, this was primarily caused by the fact that the altruistic and market effects operate in opposite directions and that the relative strength determines the effect on the market out-comes. This theoretical explanation can complement the empirical explanation of the mixed results on the relationship of CSR and financial performance (e.g. endogeneity and different methods to quantify CSR).
re-searchers, the model could potentially be the starting point of an empirical analysis that incorporates the altruism motive of CSR. It could also help supporting empirical work that investigates the driving forces behind the selection of managers. A testable hypothesis based on the model is that more altruistically motivated owners hire more CSR oriented managers and that this effect is conditional on the degree of product substitution. In a regression equation, this would be captured by an interaction term between a proxy for altruistic type and degree of product substitution. Moreover, the model could be extended for future theoretical analysis as well. It would be inter-esting to see what happens to the incentive and consistency constraints when policy variables are introduced. A different option for future theoretical research is to extend the analysis to a dynamic setting. Such an environment could allow for reputation building, which can be abused in future periods.
the firms a per unit subsidy, given that the firms engage in CSR activities.
Naturally, every analysis comes with limitations. a significant limitation of this model is the way CSR is conducted. Specifically, there are only two styles of CSR possible: no CSR at all or as large as possible. Remember from the model section that the CSR schedule is horizontal at 0 for types lower than 12 and jumps to ¯υ at type 12. The CSR schedule is horizontal again at ¯υ for types exceeding 12. As a result, this model predicts that the only motive why a CSR manager engages in CSR is his type. The only element that an owner can still decide through manager choice is how severely the CSR manager affects the price and quantity. The model is not capable of explain-ing intermediate CSR, which what is observed in the real world.
The root of this problem lies in the specification of the model. For the manager, the benefits and cost of CSR are both linear in CSR effort, which causes the corner solution in the second stage. An intuitive way of understanding this is to examine the problem of a profit-maximizing firm active under perfect competition with a constant returns to scale technology. Since the revenue and cost function are both linear in the quantity, equating marginal revenue to marginal cost does not work. The solution is to produce as much as possible (at capacity) if the price is higher than average variable cost and 0 otherwise. The same type of argument applies to the CSR prob-lem in this thesis. Assuming a cost function that is quadratic in CSR effort would overcome this problem. As mentioned in section 3.5, an unattractive feature of the corner solution in the second stage is that all managers with µ < 12 behave similarly as a manager that only derives utility from generating profits. The reason for this is that managers who set υ = 0 lose the ability to influence the price and quantity through their type.
Finally, the third limitation is related to the overall usefulness of the model. The model predicts, given the rationality and consistency constraints, three types of equi-libria. In these equilibria, the ultimate effects on the price and quantity are ambigu-ous. While this is not a problem from an intellectual perspective, it is problematic from a practitioners’ point of view. As an economist, the ultimate task is to give policy advice, which is hard to do on a model with many different outcomes. As discussed above, the root of this problem is the presence of altruistic preferences of owners.
In conclusion, this thesis investigated the incentives of owners to engage in strategic CSR under Bertrand duopoly. The owners have the opportunity to hire a CSR ori-ented manager that makes both the CSR and competition decision. These managers maximized a weighted sum consisting the firm’s profit and total CSR expenses. The weight on total CSR expenses represented the manager’s type. The main novelty that this thesis introduced is the presence of altruistic owners. These owners also maximize a weighted sum that consists of profits and CSR effort. Depending on the altruistic strength of owners, equilibria can range from situations with no CSR to situations where both firms provide the maximum amount of CSR.
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5
Appendix
5.1
Proof of Proposition 3
Proof. Differentiating (23) with respect to i:
∂µCSR i ∂i = 4(4 − γ 2)(2 − γ2)2 (16(2 − γ2)2− γ6) Given that γ ∈ [0, 1], ∂µCSR i ∂i > 0
Solving the inequality ∂µCSRi
∂i < 1 yields only one viable solution on the γ interval,
namely:
0 < γ < √2 3 Combining results, it must hold that:
5.2
Deriving the market demand function
The consumers face the following utility maximization problem:
max
xi,xj,M
U (xi, xj, I)
s.t. I = pixi+ pjxj + M
Their utility function reads:
U (xi, xj, I) = (α + βυi)xi+ (α + βυj)xj− 1 2(x 2 i + x 2 j + 2γxixj) + M (43)
Maximizing (43) subject to the budget constraint, gives rise to the following La-grangian. L = (α + βυi)xi+ (α + βυj)xj− 1 2(x 2 i + x2j+ 2γxixj) + M + λ(I − pixi− pjxj− M )
The first-order conditions are: ∂L ∂xi = α + βυi− xi− γxj − piλ = 0 ∂L ∂xj = α + βυj − xj− γxi− pjλ = 0 ∂L ∂M = 1 − λ = 0 ∂L ∂λ = I − pixi− pjxj − M = 0
From the third first-order condition follows λ = 1. Substituting this result in the first two first-order conditions and solving for pi and pj respectively gives the inverse
individual demand functions for a type β consumer for xi and xj:
pi = α + βυi− xi− γxj (44)
