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When Does Eco-Efficiency Rebound or Backfire? An Analytical Model

R´ egis Chenavaz

Kedge Business School, Aix-Marseille School of Economics

Stanko Dimitrov

University of Waterloo

Frank Figge

Kedge Business School, Macquarie University

11th Workshop on Dynamic Games in Management Science Montr´ eal, Canada

Introduction Model Argument Results Take Away Motivation Literature

Motivation

Different firms worry about environmental issues Huppes (2005), Picazo-Tadeo (2012), Sheffi (2018)

Coca-Cola, Nestl´ e, and AB InBev (beer) focus on water use Siemens makes efforts on the use of energy Apple, Tesco (retailing) and Chiquita (bananas) examine their carbon footprint

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 2 / 26

Introduction Model Argument Results Take Away Motivation Literature

Motivation

Eco-efficiency is doing business using natural resources more efficiently World Business Council for Sustainable Development (2002) Eco-efficiency offers profitable opportunities Sheffi (2018)

Diminish the environmental burden

Lower (variable) cost

Please the consumer

More sales

Mitigate the risk of eco-litigation

Less NGO complaint and consumer boycott

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 3 / 26

Motivation

Eco-efficiency appears financially wise... Bank (2002), Wall Street Journal (2016) ... but, is it always environmentally wise?

Introduction Model Argument Results Take Away Motivation Literature

Literature

There is a rebound effect when eco-efficiency does not reduce the resource use as expected Khazzoom (1980), Wirl (1996), Sorrel et al. (2008, 2009), Jacobs and Subramanian (2012), Agrawal and Bellos (2017), Benjaafar et al. (2018)...

Increased automobile fuel efficiency leads to more driven miles, and more net fossil consumption than expected Jenkins Jr. (2018) In the US, the rebound effect cancels out 10% of CO2 savings from greater car efficiency Van Benthem and Reynaert (2015) Rebound effect with eco-efficient appliances such as LED lights Mc Ginty (2014), Zink and Geyer (2016)

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 5 / 26

Introduction Model Argument Results Take Away Motivation Literature

Literature

Extreme cases of rebound

There is a backfire effect (over rebound) when eco-efficiency even increases the total resource use Also known as Jevons paradox (1866) There is a reverse rebound (super conservation) when eco-efficiency makes more environmental savings than expected Surveys of Greening et al. (2000) and Saunders (2008)

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 6 / 26

Introduction Model Argument Results Take Away Motivation Literature

Literature

Example: an increase of eco-efficiency of 10% leads for the total resource use (=ressource use per unit*demand) to

an increase = ⇒ backfire effect demand must increase “strongly” with eco-efficiency no change = ⇒ total rebound a decrease of less than 10% = ⇒ partial rebound a decrease of 10% = ⇒ zero rebound a decrease of more than 10 % = ⇒ reverse rebound demand must decrease with eco-efficiency

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 7 / 26

Introduction Model Argument Results Take Away Motivation Literature

Literature

Survey of Saunders (p. 2203, 2008) Super-conservation (reverse rebound) is a highly counter-intuitive phenomenon. How can, say, a 1% increase in fuel efficiency result in a 2% decline in fuel use? The answer lies in the fact that profit maximization in response to a change in τ invokes a host of complex interactions: cross-substitutions among factors, changes in their marginal productivities (and therefore prices), changes in the way prices affect the cost function, and changes in the cost function itself. In their impact on rebound some of these will be negative, some positive.

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 8 / 26

Introduction Model Argument Results Take Away Motivation Literature

Literature

Rebound effect: the cost effect explanation Surveys of Greening et al. (2000), Sorrell and Dimintropoulos (2008), Saunders (2008)

Improved eco-efficiency for a product decreases the cost and thus the price of that product, which increases the demand Greater demand offsets the reduction in resource use

Reverse rebound: no explanation Survey of Saunders (2008)

What, but not why Parametric functions for demand and cost

Yield strong but specific results Cancel out some of the effects at play

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Introduction Model Argument Results Take Away Motivation Literature

Approach and Contribution

Dynamic pricing and eco-efficiency investment policies of a firm within an optimal control framework Joint consideration of supply- and demand-sides in the firm’s dynamic behavior with general (opposing parametric) demand and cost functions We measure the known cost effect on the supply-side and the intermediary role of price We find two new effects on the demand-side, which influence the rebound

What and why of the reverse rebound

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Introduction Model Argument Results Take Away General Formulation

General Formulation: Main Variables

Dynamic behavior of a firm in a monopoly situation t ∈ [0, T] continuous time pt price - decision (control) variable ut investment in eco-efficiency - decision (control) variable et eco-efficiency level - state variable ηx/y =

• ∂x

∂y y x

• = elasticity of x with respect to y

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Introduction Model Argument Results Take Away General Formulation

General Formulation: Eco-Efficiency Dynamics

det dt = E(ut, et) Investment increases eco-efficiency with diminishing returns Eco-efficiency decays autonomously over time ∂E ∂u > 0, ∂2E ∂u2 < 0, ∂E ∂e < 0 Parametric example: det dt = √ut − δet Similar to Saha et al. (2017) and Zhang et al. (2017)

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 12 / 26

Introduction Model Argument Results Take Away General Formulation

General Formulation: Demand

Consumer are sensitive to price and to eco-efficiency (greenness) Eurobarometer (2013), Laroche et al. (2001), Nielsen (2014) D = D(pt, et) Demand decreases with the price and increases with eco-efficiency Consumers are marginally less price sensitive for greener products ∂D ∂p < 0, ∂D ∂e 0, ∂2D ∂p∂e 0 Parametric example: D = a0 − a1pt + a2et Dai and Zhang (2017), Saha et al. (2017), Zhang et al. (2017)

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Introduction Model Argument Results Take Away General Formulation

General Formulation: Resource and Cost

Resource is an environmental input that disappears in the production process, like raw material, water, or energy Sheffi (2018) The resource use per unit produced decreases with eco-efficiency R = R(et), dR de 0 The unit production cost increases with the resource use C = C(R), dC dR 0 Consequently, the unit cost decreases with eco-efficiency C = C(R(et)), dC de = dC dR dR de 0

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Introduction Model Argument Results Take Away General Formulation

Objective of the Firm

π = π(pt, ut, et) profit π = [pt − C(R(et))]D(pt, et) − ut Intertemporal profit maximization max

p0,u0

T e−rtπdt subject to det dt = E(ut, et)

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 15 / 26

Introduction Model Argument Results Take Away Profit Maximization Impact of Eco-Efficiency on Price Effects at Play

Profit Maximization

C(R(e)) D(p, e)

✻ ❄ ✻ ❄ ✲ ✛

D∗ p∗ Profit Cost Markup Sales

D p, C There is an optimal relationship between price and investment ...and thus between price and eco-efficiency: p = p(e) The profit-maximizing price trades-off

Markup p − C(R(e)) Sales D

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 16 / 26

Impact of Eco-Efficiency on Price

C(R(e′)) D(p, e′)

✏ ✏ ✶ ❄

e′ > e D∗ p∗

1

D∗

1

p∗ = p∗

2

D∗

2

p∗

3

D∗

3

D p, C

dp de ∈ R effect of eco-effiency on price (assuming p = p(e))

Cost effect - Known Markup effect + New Sales effect - New

dD de ∈ R total effect of eco-efficiency on demand

D∗

3 : Rebound (partial or backire effect)

D∗

2 : Rebound

D∗

1 : Reverse rebound

Zero rebound: special case

Introduction Model Argument Results Take Away Profit Maximization Impact of Eco-Efficiency on Price Effects at Play

Effects at Play

Remark 1: p = p(e) implies D = D(p(e), e) The total effect of eco-efficiency on demand writes dD de = ∂D ∂e

• +

+ ∂D ∂p

• −

dp de

• +/−

The total effect of eco-efficiency on demand dD

de is ambiguous

Reverse rebound case dD

de < 0 ⇔ dp de >> 0

Distinction between

Assumption on the direct effect ∂D

∂e 0

Result on the total effect dD

de < 0

Intermediating role of price ∂D

∂p dp de

Examining dp

de is a first step to investigate further dD de

R´ egis Chenavaz When Does Eco-Efficiency Rebound or Backfire? GERAD 2019 18 / 26

Impact of Eco-Efficiency on Price

General demand formulation D = D(p, e) dp de =

−

dC dR dR de +

−

D

∂2D ∂p∂e ∂D ∂p 2 + +

ηD/e ηD/p p e 2 − D

∂2D ∂p2 ∂D ∂p 2

• +

Proposition 1 The impact of eco-efficiency on price depends on the cost (-), sales (-), and markup (+) effects Parametric example D = a0 − a1p + a2e − a3pe

Subclasses of the General Demand Formulation

Additive separability D = h(p) + l(e) dp de =

−

dC dR dR de +

+

ηD/e ηD/p p e 2 − D

∂2D ∂p2 ∂D ∂p 2

• +

Corollary 1 The impact of eco-efficiency on price depends on the cost (-) and markup (+) effects; the sales (-) effect disappears Parametric example D = a0 − a1p + a2e

Subclasses of the General Demand Formulation

Multiplicative separability D = h(p)l(e) dp de =

−

dC dR dR de 2 − D

∂2D ∂p2 ∂D ∂p 2

• +

Corollary 2 Price decreases with eco-efficiency = ⇒ no reverse rebound The sales (-) and markup (+) effects cancel each other out; only the cost (-) effect remains Parametric example D = a0p−a1ea2

Impact of Eco-Efficiency on Demand: Reverse Rebound ⇔ dD

de < 0

Demand D = D(p, e) dD de = ∂D ∂p

• −

−

dC dR dR de +

+

ηD/e ηD/p p e +

−

D

∂2D ∂p∂e ∂D ∂p 2

2 − D

∂2D ∂p2 ∂D ∂p 2

• +

+ ∂D ∂e

• +

Proposition 2 A strong “enough” markup (+) effect is required for the reverse rebound Consumers must be “green”

Impact of Eco-Efficiency on Total Resource: Backfire Effect ⇔ dRD

de > 0

Total resource use RD = R(e)D(p, e) d(RD) de = dR de

• −

D + R             ∂D ∂p

• −

−

dC dR dR de +

+

ηD/e ηD/p p e +

−

D

∂2D ∂p∂e ∂D ∂p 2

2 − D

∂2D ∂p2 ∂D ∂p 2

• +

+ ∂D ∂e

• +

            Proposition 3 Strong “enough” sales (-) effect and demand sensitivity to eco-efficiency are required for the backfire effect Paradox of demand sensitivity to eco-efficiency

Summary of Results

Kind of Rebound Proposition 1 Proposition 2 Proposition 3 Backfire

dp de < 0 dD de > 0 d(RD) de

> 0 i > 100 Implication Implication Condition Total Rebound

dp de < 0 dD de > 0 d(RD) de

= 0 i = 100 Implication Implication Condition Partial Rebound

dp de ∈ R dD de > 0 d(RD) de

< 0 0 < i < 100 Implication Condition Condition Zero Rebound

dp de > 0 dD de = 0 d(RD) de

< 0 i = 0 Implication Condition Implication Reverse Rebound

dp de > 0 dD de < 0 d(RD) de

< 0 i < 0 Implication Condition Implication Index of total resource use RDi = 100 Conditions are necessary and sufficient

Managerial Implications

Mark-up High Differentiation focus

dp de > 0

Partial, zero, and reverse rebounds Luxury products Differentiation

dp de ∈ R

All rebounds Branded mass products Low Cost focus

dp de ∈ R

All rebounds Non-branded corner stores Cost leadership

dp de < 0

Partial and total re- bounds and backfire Commodities Niche Mass market Cost and Sales (Market size)

Table: Relationship between price and eco-efficiency in a Porter matrix

Willingness to pay more: reverse rebound Willingness to buy more: backfire effect

Introduction Model Argument Results Take Away

Take Away

All eco-efficiency rebounds simply explained

Direct and total eco-efficiency effects on demand Intermediating role of price

Solution to the puzzle of the reverse rebound

Demand-side Markup effect

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