Abstract
Recent attempts at explaining the energy-efficiency gap rely on considerations related to organizational and behavioral/cognitive failures. In this paper, we build on the strategic delegation literature to advance a complementary explanation. We show that strategic market interaction may encourage business owners to instill a bias against energy efficiency in managerial compensation contracts. Since managers respond to financial incentives, their decisions will reflect this bias, resulting in a lack of investment.
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Notes
Or, to be more specific, liquidity constraints, risk, and losses of future options.
For a recent survey of the strategic delegation literature, see Kopel and Pezzino [24].
We assume decreasing returns to investment in energy efficiency. Indeed, energy efficiency solutions are neither perfectly substitutable nor perfectly complementary. Consequently, further investments lead to duplication of effort and cannibalization effects. In this simple model, if we assume increasing returns, owners’ and managers’ objectives become convex in investment so that the game has no interior equilibrium.
This assumption is made for convenience only. The results would not change if firms were assumed to participate in an energy buy-back program whereby any surplus energy is purchased by the energy supplier. In order to cover this case, we need only replace the energy bill \(B(q_{i},\gamma _{i},r)=r\left (q_{i}-\gamma _{i}\right )\) in Eqs. 1 and 2 by the energy revenue \(R(q_{i},\gamma _{i},s)=s\left (\gamma _{i}-q_{i}\right )\) where s is the price at which the supplier buys back excess generated power. After making this substitution, we obtain exactly the same expressions for managerial compensation and business owners profits as in Eqs. 1 and 2, except that the energy rate r has been replaced by the feed-in tariff s. Therefore, this change to the model does not alter the trade-offs that managers and business owners face when defining their strategies.
Since managerial compensation is intended to secure the participation of managers, it will be equal to their respective (exogenously defined) reservation incomes. Consequently, from an owner’s perspective, maximizing profit net of compensation is the same as maximizing profit. For more on this point, see Kopel and Pezzino [24].
For surveys of the experimental evidence on loss aversion, see Kahneman et al. [21] and DellaVigna [10]. Greene [17] argued that loss-averse people are more likely to ignore cost-effective energy efficiency investment opportunities. This claim has received empirical support by Heutel [18] and Schleich et al. [27].
The assumption that \(\frac {a}{b}-q_{i}\geq 0\) ensures that firm i’s strategy set (i = 1, 2) is compact. This condition has obvious economic meaning. It says that manager i would not select a quantity leading to a negative price when firm i is the only active firm in the market.
If r = r2, then region III reduces to the point (1,1).
We omit the expression of this threshold because it is very lengthy.
The reader is referred to [2] for a full comparison and discussion of these two alternative specifications.
Let \(K:\gamma _{i}\rightarrow \frac {k}{2}{\gamma _{i}^{2}}\) and \(A:\gamma _{i}\rightarrow \sqrt {\frac {2}{k}\gamma _{i}}\). Note that \(K\left (\sqrt {\frac {2}{k}\gamma _{i}}\right )=A\left (\frac {k}{2}{\gamma _{i}^{2}}\right )=\gamma _{i}\). Then, by the definition of the inverse function, we have A(γi) = K− 1(γi).
A similar equivalence result between AJ and KMZ R&D models was shown by Amir [2] under the assumption that there are no innovation spillovers.
These follow the same logic as earlier proofs and are available from the authors.
Consider a representative consumer with utility given by \(U\left (q_{1},q_{2}\right ):=a\left (q_{1}+q_{2}\right )-\frac {1}{2}b\left ({q_{1}^{2}}+2\theta q_{1}q_{2}+{q_{2}^{2}}\right )+m,\text { with }a,b>0\text { and }\theta \in [0,1]\). The demand system (34) can be derived as the solution to the problem: \(\max \limits _{(q_{1},q_{2})}U(q_{1},q_{2})-{\sum }_{i=1}^{2}p_{i}q_{i}\). Namely, it follows from the first-order conditions pi = ∂U/∂qi, i = 1, 2.
In the quantity-setting version of our model, reaction functions are downward sloping since \(\frac {\partial ^{2}M_{i}}{\partial q_{i}\partial q_{j}}=-b\theta <0\).
In the price-setting version of our model, reaction functions are upward sloping since \(\frac {\partial ^{2}M_{i}}{\partial p_{i}\partial p_{j}}=\frac {\theta }{b\left (1-\theta ^{2}\right )}>0\).
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Acknowledgments
We thank anonymous reviewers for their helpful comments and suggestions. We also thank the participants of the 18th International Symposium on Dynamic Games and Applications, 11th Workshop on Dynamic Games in Management Sciences, 6-ème Journées de l’innovation “Jinnov,” and the seminar participants at Center for Environmental Economics–Montpellier and the University of Valladolid for helpful discussions. The usual disclaimer applies.
Funding
The authors acknowledge the financial support of the French Agence Nationale de la Recherche (ANR). Mabel Tidball received funding from the project GREEN-Econ (ANR-16-CE03-0005) and the LabEx Entreprendre (ANR-10-LABX-11-01). Denis Claude received funding from the project RILLM (ANR-19-CE26-0008-01).
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Appendices
Appendix 1: Proof of Lemma 1
Let BRi(x) denote the set of decisions that are best-responses to a decision x for player i, i = 1, 2. Let \((\delta _{i}^{\text {c}_{k}},\delta _{j}^{\text {c}_{k}})\) be any pair of managerial incentives from region II(k), k = 1, 2. Assume that \((\delta _{i}^{\text {c}_{k}},\delta _{j}^{\text {c}_{k}})\) is an equilibrium point. Then, \(\delta _{j}^{\text {c}_{k}}\in \text {BR}_{j}(\delta _{i}^{c_{k}})\) where \(\text {BR}_{j}(\delta _{i}^{c_{k}})=[\ell _{j}(\delta _{i}),1]\). Since the game is symmetric, it must be the case that \(\delta _{i}^{\text {c}_{k}}\in \text {BR}_{i}(\delta _{j}^{c_{k}})\) where \(\text {BR}_{i}(\delta _{j}^{c_{k}})=[\ell _{i}^{-1}(\delta _{i}),1]\). Now, observe that \(\text {BR}_{i}(\delta _{j}^{c_{k}})\cap \text {BR}_{j}(\delta _{i}^{c_{k}})=\emptyset \) since these two sets lie on opposite sides of the 45∘ line. We conclude that \((\delta _{i}^{\text {c}_{k}},\delta _{j}^{\text {c}_{k}})\) are not mutual best responses. To complete the proof, observe that the same holds for any point \((\delta _{i}^{\text {c}_{k}},\delta _{j}^{\text {c}_{k}})\) in Region II(k), k = 1, 2.
Appendix 2: Proof of Proposition 3
The idea of the proof is illustrated in Fig. 6.
Consider any \(\delta _{j}\in \left [\tilde {\delta },1\right ]\). Then, δi is a best reply to δj if \(\pi _{i}^{\text {III}}\geq \pi _{i}^{\text {II}_{(j)}}(\delta _{i})\). Observe that firm i’s profit function is continuous in \(\tilde {\delta }\). Indeed, we have: \(\lim _{\delta _{i}\rightarrow \tilde {\delta }}\pi _{i}^{\text {II}_{(j)}}\left (\delta _{i}\right )=\pi _{i}^{\text {III}}\left (\tilde {\delta }\right )\). Now, observe that owner i’s profit function is strictly concave since:
and reaches a maximum for
Hence, \(\pi _{i}^{\text {III}}\geq \pi _{i}^{\text {II}_{(j)}}(\delta _{i})\) if \(\delta _{i}^{\star \star }\geq \tilde {\delta }\) or, equivalently, if
The proof is completed by noting that condition (48) holds provided that r ≥ r4.
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Claude, D., Tidball, M. A New Rationale for Not Picking Low-Hanging Fruits: the Separation of Ownership and Control. Environ Model Assess 26, 985–998 (2021). https://doi.org/10.1007/s10666-020-09735-5
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DOI: https://doi.org/10.1007/s10666-020-09735-5