Sustainable growth with renewable and fossil fuels energy sources

Carlo Andrea Bollino, Silvia Micheli

30th USAEE/IAEE North American Conference October 9-12, 2011 - Washington, DC

The aim of the paper

• Showing the effectiveness of a carbon tax and a flow of public

capital which captures intensity of government long term

commitment to support new technology developments instead

of a subsidy to the price of renewables

Outline

• Introduction

• Background

• The model

• Main results

• Conclusions

Introduction• There is an ongoing debate on the effectiveness of

environmental policies to tackle climate change

• In a business-as-usual scenario, fossil fuel use is projected to grow, and the dirtiest fuel, i.e. coal, is expanding its share to face the rising in energy demand driven by countries

• The current European response to climate change is the so-called 20-20-20 climate and energy package

EU’s 20-20-20 targets

• 20% cut in EU’s greenhouse gases emissions (or 30% as part of an international agreement) by 2020;

• 20% energy share from renewables (wind, solar, biomass, etc.) of total energy production by 2020, including a 10% biofuel target for transport;

• 20% increase in energy efficiency in relation to projected 2020 levels

The tools to deliver the targets

1) A revision and strengthening of the Emission Trading System (ETS), the EU’s key tool for cutting emissions cost-effectively

2) An “Effort Sharing Decision” governing emissions from sectors not covered by the EU ETS, by binding national emission limitation target for 2020 which reflects its relative wealth. These targets range from an emissions reduction of 20% by the richest Member States to an increase in emissions of 20% by the poorest

The tools to deliver the targets

3) Binding national targets for renewable energy which collectively will lift the average renewable share across the EU to 20% by 2020 (more than double the 2006 level of 9.2%)

4) A legal framework to promote the development and safe use of carbon capture and storage (CCS)

The importance of investment

• Having established that we need a decisive effort to promote new investment and new lifestyle behaviors, the crucial question today is how can we achieve a new period of development, and be able to de-couple economic growth from increasing energy and carbon usage

Background• A large strand of literature (Acemoglu et al., 2009; Bosetti et

al., 2009; Grimaud et al., 2010; Nordhaus, 2008) states that we need two economic instruments to correct for the two types of market failures: an environmental tax and a research subsidy

• The environmental tax is needed because governments have to increase the cost of pollution in order to reduce pollution generation

• Subsidies to renewable energy sector are needed to spur investment and encourage innovation in green technologies

The reasons for public intervention are then straightforward • The model we propose gets underway from the one proposed

by Grimaud et al. (2010)

The model

• The economy is made up of four production sectors: - final output (sector 1);- energy services (sector 2);- fossil-fuel sector (sector 3);- renewable sector (sector 4).

• There is research only in the renewable energy sector

• There are two market failures: pollution and research spillovers

The model

• We construct two variants since we take into account two different production functions:

1. The first variant (variant A) evaluates a production function where a stock of public capital enters the production function as an input

2. In the second variant (variant B), the quantity of renewable energy depends on investment and a stock of knowledge

The model

• We model the effective value of an innovation paid to the inventor as an incentive for doing research in renewable energy in order to lower production costs and make it competitive in the energy market

• The effective value of the patent for innovation in the two variants proposed changes according to the production function of renewable energy

The modelThe final output sector (sector 1)

• The final output Y is produced using not-skilled labor and energy services

• The profit of the representative producer is:

• The FOCs are:

where Fx is the derivative of F with respect to x.

,

Y Yt t t t E t tY w L p E

0Y tLY w

, 0E E tY p

The model The energy services sector (sector 2)• Expected profit is:

where is the CO2 cut due to energy efficiency technologies

is the quantity of fossil fuels is the quantity of renewables

• The FOCs lead to

• The pollution tax τ depends upon the effort made by the representative firm to reduce CO2 emission

, , , , ( )EE t E t t EF t ER t t t t tp E p EF p ER I EF Z

( )Et tZ Z I

(1 ) 0E EF EF EFp E p Z 0E ER ERp E p

1 0EIZ

1

EIZ

tEF

tER

The model The fossil fuel sector (sector 3)• The representative fossil fuel producer maximizes

subject to the amount of resources extracted from time t:

• The FOCs are as follows:

• Working on the above equations, we get the classical Hotelling rule that is

EF EFt EF tp EF I

0

t

t s t tS EF ds S EF

1 0EF EFEF I t Ip EF EF

tEF S t Sp EF EF

2EFI

EF EF SI

EFp p EF

EF

The modelThe renewable energy sector (sector 4)• Because of the nature of innovation, the price received by the inventors is

different from the social value of innovation

• The instantaneous social value of innovation is defined as

that is the sum of the marginal profitability in the renewable sector plus the marginal profitability in the R&D sector

• So the optimal value of a patent is

, , ,ERER H

ER t ER t ER ta a a

, ,

s

x

t

r dx

ER t ER s

t

A a e ds

The model - The renewable energy sector (sector 4)

• The effective value of an innovation iswhere is a share of the effective value which is effectively paid to the innovator and

• The intertemporal effective value is

and differentiating the equation above with respect to time, we get:

that is the rate of return of the innovation on the financial market equals the rate of return of R&D activities

,, ER tER t ERa aER

0 1ER

, ,

s

x

t

r dx

ER t t ER s

t

A A a e ds

t tt

t t

A ar

A A

The model - The renewable energy sector (sector 4)

• The profit function in the R&D sector is

where is the knowledge production function

• Finally the marginal profitability of innovation in the R&D sector, that is equal for both variants of the model, is

ERH ER ERt t t tA H I

,ER ER ERt t tH I H

ERHER

ER

ER

ER

HH

ER tER HI

Ha AH

H H

The model - The renewable energy sector (sector 4)The variant A

• We consider that the renewable energy production function is made up of three inputs: investment in renewables IER, stock of existing knowledge HER and public capital Gt. The production function is

with ER increasing and concave in each argument.

• Gt is the cumulated government effort to support renewable energy in the long run and it includes both the actual value of policy commitment in monetary resource and the shadow value of the regulatory legislation, which creates a favourable administrative framework for investment decisions

( , , )ER ERt tER ER I G H

The model - The renewable energy sector (sector 4)The variant A• The profit function is:

and the first-order conditions yields:

• The effective value of the innovation in variant A (when G enters the renewables production function), given by the combination of the FOCs, is:

( , , )ER ER ER ERER tp ER I G H I

,H

A G HER t ER

I I

ER Ha

ER H

10 1 0

ER

ER

ER

ER I ERI

p ER pI ER

0ER

GER G

I

ERp ER

G ER

The model - The renewable energy sector (sector 4)The variant B

• Renewables production function is made up of two inputs: investment in R&D activities IER and the stock of knowledge HER so that:

with ER increasing and concave in each argument.

• The government intervention is modelled as a subsidy σ to investment, which is set:

( , )ER ERt t tER ER I H

0 1

The model - The renewable energy sector (sector 4)The variant B• The profit function is:

and the first-order conditions are:

• The effective value of an innovation in variant B (when governments subsidize investments through a subsidy σ) given by the combination of the FOCS is:

( , ) (1 )ER ER ER ERt ERp ER I H I

,

1ER ER

ER tER ER

ERB H H

ER ER

I I

ER Ha

ER H

0 (1 ) 0ER

ER Ip ERI

0ER

ER Hp ERH

Main results• First we find the condition for :

that is if

• We get a better effect of the capital stock G instead of σ when the productivity of the public stock (ERG) is relatively stronger than the productivity effect of knowledge stock (ERH)

• If σ = 0, than a better effect of the capital stock is granted if the lhs is > 1• If σ = 1, it suffices a very small positive ERG to satisfy the condition above

(1 ) 0G H H HER

F I I I

ER H ER H

ER H ER H

(1 )0G H

I

ER ER

ER

(1 )G

H

ER

ER

, ,A BER t ER ta a

Main resultsWe study the change of the effective value of innovation with respect both toG and σ that yields respectively to:

• Both the expressions above are negative, i.e. an increase in public subsidy reduces the effective value of innovation, because firms will adopt existing technologies in the presence of the subsidy σ

• Comparing both equations we see that the effect of the subsidy is less harmful in the first equation than in the second one, if

• G is less likely than σ to incur in the risk of choking innovation with over subsidization

GG HER ER

AGGER

ERI

ERa

G ER

BER H

ERI

a ER

ER

Conclusions

• The effective value of an innovation paid to inventors of new green technologies varies according to the renewables production function: the policy is more effective when the flow of public capital enters the production function as a public stock (variant A) compared to the monetary subsidies to energy prices (variant B)

• A possible fruitful approach to encourage the adoption of renewable energy should take into account that investors react positively to a stock of public capital which captures intensity of government long run commitment, instead of a direct subsidy to the price of renewables