Fixed price vs Fixed Quantity: Incentives to AdoptLow-Carbon Technology under Uncertainty
Federico Bo¤a1 Stefano Clò2 Alessio D�Amato3
1University of Macerata2,3University of Tor Vergata
May 09, 2012Rome, MEF Brown Bag Lunch Seminar
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Roadmap
Introduction to EU climate policy and ETS
Aim of the research
Literature Review
Model presentation
Discussion of the results
Policy applications
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EU Climate Policy: Goals and Instruments
Kyoto: emissions -8% below 1990 by 2012
Climate Package: emissions -20% below 1990 by 2020
Not only climate goal: promoting innovation
Reduce emissions without preventing economic growthpromote innovation and di¤usion of low-carbon technologyGreen economy: new markets and job opportunities
Carbon Emissions: external cost not incorporated in the market price
Need for a market-based instrument to monetize carbon emissionsand increase attractiveness of low-carbon tech.
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EU Climate Policy: Goals and Instruments
Directive 2003/87 establishes the Emissions Trading Scheme (ETS)Cap & Trade scheme
Cap: �x a limit to emissions and distribute an equivalent amount ofemissions allowances among regulated agentsIf emissions > allowances ! reduce emissions internally or acquireallowances in the marketTrade: free bargaining among parties ! abatement at lower marginalcost, allowances allocated where are valued most (Coase Theorem)
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EU Climate Policy: Goals and Instruments
ETS
stimulate technological innovation and a progressive transition towarda low-carbon economy
Carbon emissions are priced for the �rst timefossil fuels tech. more expensive low carbon tech. more attractive
Carbon price varies with uncertaintySupply is �xed (cap), demand of allowances depends on:
GDP trend, energy consumption, power generation fuel mix, fuel priceCarbon price trend re�ects economic and energy markets�variability
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EU Climate Policy: Goals and Instruments
Climate policy has slown downPolitics: unsuccessful international negotiations (EU unilateral policy)
Economics: With economic crisis, ETS lost momentum
Industrial production and energy production decreaseETS carbon emissions decrease (-11,6% in 2009)demand for allowances decreases, supply is rigidSurplus of allowances in the ETSCarbon price decreases (short-term)Carbon price trend lower than expected
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EU Climate Policy: Goals and Instruments
Climate policy has slown down
ine¤ectiveness of the ETS in promoting low carbon technologies.
"A lower carbon price acts as a much less powerful incentive forchange and innovation" (EC 2010)
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EU Climate Policy: Goals and Instruments
Proposals of ex-post adjustments to the ETS insitutional designaimed at increasing the ETS e¤ectiveness in promoting the adoptionof low-carbon technology
Support the carbon price through ex-post cap adjustment to increasethe scarcity of allowancesSet-aside proposal (withdraw allowances)Reduce the emissions target and the ETS capCreate a Carbon Central Bank to adjust the cap in order to �x theprice at a level required to support low-carbon technologiesImpose a carbon price �oor (option adopted in UK)
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Aim of the paper
Some open policy questions
Is the EU strategy of supporting the carbon price through ex-postquantity adjustment e¤ective to promote adoption?Which ETS market design maximizes incentives of adoption wheninvestments are undertaken under uncertainty?
We distinguish between
Cap & trade with quantity control: Fixed quantity (standard scheme)Cap & trade with price control: Fixed price (like a carbon tax)
Focus on the role of uncertainty
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Aim of the paper
Analyze how uncertainty (variation of) impacts di¤erently on expectedpro�ts (marginal bene�ts and costs) depending on the market design
Determine under which market design expected pro�ts and incentivesto adopt are maximized.
Policy applications - Identify which design best �ts:
frameworks with shifts in the generation mix (such as that currentlybeing experienced by Germany);feed-in tari¤s schemes adding to ETS regulations.
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Literature Review
First strand of literature:Choice of market-Based Instruments under uncertainty (Weitzman1974)
Focus on social welfare (MAC and MD)Without uncertainty and under perfect information carbon tax and capand trade are equally e¢ cient to internalize externality (Weitzman1974)
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Literature Review
Under uncertainty:
Carbon tax: price is certain, quantity is notCap and trade: quantity is certain, price is not
Best instrument depends on the slope of MD and MAC
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Literature Review
slope MAC < slope MD ! High variability in price
slope MAC > slope MD ! High variability in emissions
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Literature Review
Second strand of literature:
Market-Based Instruments and technology adoption (not innovation)Focus on investment choice (MB and MC)
Milliam and Prince (1989 and 1992)
Focus on �rm level: cap and trade scheme with auctioning providesmore incentive than taxes (no uncertainty)
Jung et al. (1996)
focus on market-level with heterogeneous �rms compete: auctionedpermits provide the greatest incentives for adoption (no uncertainty)
Parry (1998)
tax and emissions permits have similar e¢ ciency properties (nouncertainty and linear functions)
�ndings criticized by subsequent analyses
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Literature Review
previous literature assumes exogenous price, not consider how a single�rm�s investment decision impacts on the market equilibrium
Denicolò 1999, Requate and Unold 2003
Cap and trade with endogenous price: impact of adoption on carbonprice and free riding e¤ect; asymmetric adoption might take place evenwith symmetric �rms.tax system with �xed carbon price: symmetric adoption with symmetric�rms (at least as many as under cap and trade)incentives for adoption inferior under cap and trade than under taxesNo uncertainty
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Literature Review
We add uncertainty to the literature on technology adoption
Bousquet & Cretì (2010)
how investments under environmental regulation depend on uncertaintyin input price ! price variability leads to an expansion of the existingcarbon intensive capacity.
Pindyck (1991), Chao e Wilson (1993)).
when the convenience of investment depends on the uncertain trend ofresource price, there is an option value associated with delayingadoption ! postpone irreversible investment
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The Model - Assumptions
Two risk-neutral �rms k = i , j
pro�ts expresserd as function of emissions (linear relation betweenemissions and output)
convex cost function
C (ek ) = cmek + dke2k2
cm fuel cost ! linear relation between costs and emissions
dke2k2 convex cost ! accounts for all the other inputs, for the capacity
constraints or decreasing returns to scale
Linear revenue: vekv is the per-unit revenue (willingness to pay)
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The Model - Assumptions
Unregulated pro�t maximization function
maxek
πk = (v � cm) ek � dke2k2
(v � cm) = ck
ck is the per-unit markup
Pro�t maximization FOCek =
ckdk
MB
MC
Q
P
profits
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The Model - Assumptions
Focus on uncertainty
Model uncertainty on the mark-up side but not on the (convex) costside
apply in case of output price volatility (state of the economy) or inputprice volatilitymarkup ck is stochastic
assume uniform distribution ck 2 (εk , ck � εk ) ! εk 2�0, ck2
�εk captures the level of uncertainty, through an inverse relation. largerε implies a smaller degree of uncertaintyEach �rm ex ante knows the distribution, but not the realization, ofboth its own and the rival�s productivity parameter.
Heterogeneous �rms face uncorrelated uncertainty
Homogeneous �rms face the same uncertainty (perfectly correlated asthey use the same technology).
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The Model - Assumptions
After cap and trade is launched, �rms have to buy a permit at a pricep for each unit of emissions e. Pro�t function becomes:
πk = ckek � dke2k2� pek
carbon price shiftes marginal costs
Demand
Marginal Cost
Q
P
A low-carbon technology can be adopted to reduce emissionsAdoption entails an intial investment F
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The Model - Assumptions
Assumptions for consistency
Lower carbon intensityca > cna
Without regulation ! Lower optimal emissions
e�a < e�nacada
<cnadna
Higher marginal costsda > dna
without regulation pro�t from adoption lower than from non-adoption
π�a < π�nac2a2da
<c2na2dna
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The Model - Timing and Setting
2 stages game
At stage 1
each �rm chooses whether to adopt the new technologyBy assumption, the initial investment F must be undertaken underuncertainty, before getting to know the realization of the productivityparameters.Adoption depends on expected pro�ts from adoption and non-adoption,it takes place when
F < E (πa)� E (πna)
At stage 2
Uncertainty is revealedFirms decide how much to produce/emit and how many allowances buyin a auction
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The Model - Methodology
We �rst focus on the Fixed Price case and then on teh Fixed Quantitycase
For each case we determine:
Market equilibrium in the last stageExpected quantity, price and pro�ts in the �rst stageAnalyze how a change in uncertainty impacts on expected pro�ts fromadoption and non adoption
We develop a comparative analysis of the outcome under di¤erentformats.
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Fixed price case
Last stage:
After uncertainty is revealed the authority adjusts the quantity tomaintain the price at a �xed levelGiven the �xed price permits can be acquired according to MC withoutany quantity constraintno interdependency among �rmsOptimal level of emissions:
ek =ck � pdk
Optimal pro�ts
πk =(ck � p)2
2dk
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Fixed price case
First Stage:Under uncertainty �rms decide to adopt according to expected pro�tsExpected level of emissions E (ek )Z ck�εk
εk
ck � pdk
�1
ck � 2εk
�dck =
ck � 2p2dk
Expected level of pro�tsE (πk )Z ck�εk
εk
(ck � p)2
2dk
�1
ck � 2εk
�dck =
c2k � ck εk + ε2k � 3ckp + 3p26dk
Expected emissions and pro�tsdepend positively on ck and negatively on p
∂E (ei )∂ci
> 0,∂E (πi )
∂ci> 0
∂E (ei )∂p
< 0,∂E (πi )
∂p< 0
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Fixed price case
given that da > dna expected emissions and expected pro�ts fromadoption change less rapidly compared to expected pro�ts andexpected emissions from non-adoption ∂E (π)
∂c ,p∂d < 0
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Fixed price case
Lemmaunder �xed price each �rm�s expected pro�ts depend positively only on itsown uncertainty ∂E (πk )
∂εk< 0
when uncertainty increases (εk decreases), expected pro�ts increase
MB (average)
MC
Q
P
Area 2
Area 1
MB 1
MB 2
Pro�t increase (Area 1) higher than pro�t reduction (Area 2)Average of pro�ts higher than pro�ts at the average
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Fixed price case
Corollaryunder �xed price a positive variation of the uncertainty of adoptionincreases the incentives adopt
expected pro�ts from adoption increase
Expected pro�ts from non-adoption do not vary
Adoption threshold increases
F < E (πa)� E (πna)∂E (πa)
∂εa< 0,
∂E (πna)∂εa
= 0! ∂F∂εa
< 0
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Fixed price case
Corollaryunder �xed price a positive variation of the uncertainty of non-adoptionreduces the incentives adopt
expected pro�ts from adoption do not vary
Expected pro�ts from non-adoption increase
Adoption threshold decreases
F < E (πa)� E (πna)∂E (πa)
∂εa= 0,
∂E (πna)∂εa
< 0! ∂F∂εna
> 0
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Fixed price case
CorollaryUnder �xed price, symmetric �rms will make symmetric choices onadoption
Case where �xed cost is higher than the investment threshold
Assume an increase in the uncertainty of adoption
If uncertainty increases expected pro�ts up to a level that investmentthreshold is higher than �xed costs ! all �rms adoptIf uncertainty does not increase expected pro�ts from adoption up to alevel that investment threshold is higher than �xed costs ! no �rmsadopt
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Fixed cap case
Last Stage
each �rm buys allowances, butQuantity constraint: sum of emissions cannot exceed a �xed cap XFirms�choices become interdependent (∑ ek = X )For each of the two �rms we determine the optimal demand for permits(FOC)
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Fixed cap case
First stage
we have to distinguish between asymmetric �rms and symmetric �rms
case with asymmetric �rms
LemmaUnder �xed quantity each �rm�s expected pro�ts depend positively onboth �rms uncertainty ( ∂E (πi )
∂εi< 0 ; ∂E (πi )
∂εj< 0)
This result di¤ers from the �xed price case (expected pro�ts dependonly on own uncertainty)
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Fixed cap case
Lemmauncertainty increases expected pro�ts more under �xed price than under�xed quantity ∂E (π)
∂ε jFP � ∂E (π)∂ε jFQ > 0
price adjusts to mantain emissions �xed! uncertainty impacts onmarginal costs and bene�tspro�t increase lower under FQ (Area 5) than under FP, di¤erence(Area 6) caused by MC increase (high demand increases price)
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Fixed cap case
Pro�t reduction lower under FQ (Area 7) than under �xed price,caused by lower MC induced by lower carbon price (Area 8).
Price variation as counter-balancing e¤ect! impact of uncertainty onexpected pro�ts lower under �xed quantity than �xed price.
FQ: average of pro�ts higher than pro�ts at the average, but lowerthan FP
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Fixed cap case
case with symmetric �rms
Each �rm individually produces half of the emission cap X
Expected pro�ts do not depend on uncertainty ∂E (πk )∂εk
= 0
when uncertainty varies, price adjusts to mantain �xed the quantity
the average pro�t across all states equals the pro�t in the averagestate of the economy
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Fixed cap case
Under �xed quantity a variation of uncertainty impacts on �rms�expected pro�ts only when �rms are asymmetric
�rms have an incentive to be asymmetric in order to exploituncertainty
Requate e¤ect: adoption reduces carbon price, thus loweringincentives to further adoption (asymmetric outcome)
Lemmaan increase of uncertainty increases expected pro�ts only if �rms are nothomogeneous, inducing asymmetric adotion (not in �xed price)
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Fixed cap case
Case with �rms initially symmetric (before adoption)
when �rm 2 does not adopt, �rm 1 adopt if
F < E (πa)� E (πna)∂E (πa)
∂εa< 0,
∂E (πa)∂εna
< 0
∂E (πna)∂εa
= 0,∂E (πna)
∂εna= 0
given that other �rm does not adopt, the incentives to adopt increasewith uncertainty (asymmetric solution)
higher uncertainty increases incentives to adoptasymmetric equilibrium where �rms can exploit hiogher uncertainty andhigehr expected pro�tsHigher uncertainty of non-adoption can promote adoption (not in FP)
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Fixed cap case
Given that �rm 2 adopts, �rm 1 adopts when
F < E (πa)� E (πna)∂E (πa)
∂εa= 0,
∂E (πa)∂εna
= 0
∂E (πna)∂εa
< 0,∂E (πna)
∂εna< 0
given that the other �rm adopts, the incentives to adopt decreasewith uncertainty (asymmetric solution, opposite to FP)
higher uncertainty reduces incentives to adopt (asymmetric equilibrium)If uncertainty decreases, incentives to adopt increase (no reason to staysymmetric)
Higher uncertainty of adoption can promote non-adoption (not in�xed price)
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Fixed Price vs Fixed quantity: Main �ndings
Fixed price
uncertainty impacts positively on expected pro�t independently on�rms degrees of heterogeneityeach �rm�s expected pro�t depends only on its own uncertaintyhigher uncertainty of adoption increases adoption, and vice-versastarting symmetric, �rms end up symmetric
Fixed quantity
uncertainty impacts positively on expected pro�t only if �rms areheterogeneouseach �rms�expected pro�t depends on both �rms�uncertaintyhigher uncertainty of adoption can reduce adoptionstarting symmetric, �rms may end up asymmetric
the impact of uncertainty on expected pro�ts is higher under �xedprice than under �xed quantity
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Policy Applications
LemmaWhen uncertainty related to the low-carbon technology is relatively large,incentives to adopt are maximized under �xed price; the same incentivesare maximized under �xed quantity when uncertainty related to the carbonintensive technology is relatively large
Policy proposals aimed at stabilizing carbon price through capadjustment can be e¤ective
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Policy Applications
German case and nuclear phase outBaseload substition with gas or coal?
Gas price is more volatile than coal price!higher uncertainty relatedto low-carbon technology
Incentives to opt for gas �red-plan are maximized under �xed price
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Policy Applications
Interaction Climate and Energy Policies
Energy goals and policies aimed at increasing renewablesClimate and energy instruments overlap in�uencing ETS e¤ectiveness.Need for coordination
Consider Energy Policy such as feed-in tari¤s
Feed-in tari¤s increase technology return thus increasing marginalbene�ts and the expected pro�ts from adoption (�rst order e¤ect)Feed-in tari¤s reduce uncertainty of adoption, thus reducing expectedpro�ts from adoption (second order e¤ect).
if �rst order > second order
Fixed price: symmetric adoptionFixed quantity: asymmetric adoption to exploit heterogeneity (whenuncertainty of carbon intensive tech is high)
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