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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

Bo¤a Clò D�Amato (MEF) price vs quantity under uncertainty May 09, 2012 1 / 42

Roadmap

Introduction to EU climate policy and ETS

Aim of the research

Literature Review

Model presentation

Discussion of the results

Policy applications


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.



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)



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



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



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)



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)


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


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.


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)


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


Literature Review

slope MAC < slope MD ! High variability in price

slope MAC > slope MD ! High variability in emissions


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


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


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


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)



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



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).



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



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


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


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.


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


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


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


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


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


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


∂εa= 0,

∂E (πna)∂εa

< 0! ∂F∂εna

> 0


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


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)


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)


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)


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


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


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)


Fixed cap case

Case with �rms initially symmetric (before adoption)

when �rm 2 does not adopt, �rm 1 adopt if


∂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)


Fixed cap case

Given that �rm 2 adopts, �rm 1 adopts when


∂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)


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


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


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


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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