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R&D, ENDOGENOUS SUBSTITUTIO AND CLIMATE CHANGE
[Youngho Chang, Division of Economics, HSS, Nanyang Technological University, +65-65138107, [email protected]]
[Yang Tang, Division of Economics, HSS, Nanyang Technological University, +65- 67906115, [email protected]]
[Di Yin, Division of Economics, HSS, Nanyang Technological University, +65-93556224, [email protected]]
Overview
This study aims to examine how R&D in fossil fuels and backstop resources and resulting technology progress
influence resource use, economic grwoth and climate change in the world economy. The technology progress is
expected to lead to the endogenous substitution among different energy resources (Chakravorty et al, 1997 and 2005)
and affect the speed of carbon dioxide accumulation in the atmosphere. The endogenous substitution governs the
timing of resource use in which a resource with lower costs is used first in each sector. R&D in fossil fuels and
backstop resources accelerates the substitution among fossil fuels by accumulating the knowledge stock of using
fossil fuels and at the same time it eventually helps the economy switch to the backstop resources as zero extraction
cost and the accumulation of knowledge stock of backstop resources make the cost of using backstop resources
competitive to fossil fuels (Nordhaus, 1994, 2000 and 2002; Popp, 2004 and 2006). This study constructs an
economic growth model with two sectors (Uzawa, 1961 and 1963) and multiple resources, incorporating
environmental constraints from climate change models such as general circulation models (GCMs). The model is
expected to suggest two switching points: R&D and resource switching points. A fossil fuel with the lowest
conversion cost is to be used first and over time it is replaced by another fossil fuel with the next lowest conversion
cost. With the accumulation of knowledge stock on backstop resources, fossil fuels will be eventually replaced by
backstop resources as their costs become lower and competitive to fossil fuels thanking to no or little extraction cost
and decreases in conversion costs. The resource switching point comes after the R&D switching point. This study
also shows that the level of carbon emissions and the corresponding temperature change, which reflect how
technological change and R&D influence climate change. The derived optimal trajectory of carbon tax rate indicates
the cost of adapting to climate change.
Methods
This study constructs an economic growth model with two sectors (capital goods producing and consumption goods
producing sectors) and multiple resources, incorporating environmental constraints from climate change models. The
key question is how technological change via R&D in fossil fuels and backstop resources affects the substitution
among different resources and the accumulation of knowledge stock.
The seminal difference between endogenous resource substitution and exogenous resource substitution is that the
endogenous resource substitution takes conversion costs into account. For the fossil fuels, the energy cost contains
not only an extraction cost discussed in the literatures but also a conversion cost that can decrease follwoing the
accumulated knowledge stock on fossil fuels. For the backstop resources, the energy cost only has the conversion
cost that will decline thanking to the increasing knowledge stock on the backstop resources. The key equations are as
follows.
p jt  z jt  c j , j  {P,W , G}
pBt  zBt
where p j,t is the energy cost for petroleum (P), coal (W), gas (G), backstop resource (B) at time t. c j is the extraction
cost for fossil fuels, which is a constant for a certain type of fossil fuels. z j,t is the conversion cost depending on the
refining and converting process that changes the primary resource to the delivered resource. An increase in
knowledge stock is expected to decrease the conversion cost.
z jt 
v j0
H Ft
, j {P,W , G}
zBt 
vB 0
H Bt
where vj,0 is the initial conversion cost for resource j. HF,t and HB,t are the knowledge stocks on fossil fuels and
backstop resource in time period t.
The progress of technology increases the knowledge stock for energy via the investment of R&D. Here, R m,t is the
R&D expenditure on fossil fuels and backstop resources. The following equation implies that the knowledge stock
on resources depends on the expenditure on R&D and the existing knowledge stock.
H m ,t  (1   H ) H m,t 1  Rm,t / a; m  F , B
Multiple resources appear to substitute with each other following the premise that the cheapest-cost resource is used
first. The simulation analysis is conducted by General Algebraic Modeling System (GAMS).
Results
The simulation analysis presents the energy use patterns in the two sectors – the capital goods producing sector and
the consumption goods producing sector. For the consumption goods producing sector, the sequence for energy use
appears to be gas, oil, coal and a backstop resource, while for the capital goods producing sector, it appears to be oil,
coal and a backstop resource. Natural gas appears to be too costly to be used in the consumption goods producing
sector. The simulation also shows various resource switching points that are associated with technological progress
in harnessing energy resources vis-à-vis the concentration level of carbon in the atmosphere.
The simulation analysis also presents an optimal trajectory of carbon tax rate that is derived from an optimal
trajectory of carbon emissions and temperature changes. The carbon tax rate lasts at least until the year 2185. The
temperature change reaches a maximum in the year 2315 and then declines.
Conclusions
This study examines how technological change via R&D in fossil fuels and backstop resources affects the resource
use, economic growth, and climate change in a framework of economic growth model with environmental constraints.
It constructs a model with key factors such as an efficiency factor, an energy price and the knowledge stock for
energy and illustrates how the endogenous substitution among different resources influences the trajectory of carbon
emissions, economic growth and climate change. The simulation analysis of the model presents that the energy use
pattern in the consumption goods producing sector is gas, oil, coal, backstop resource while for the capital goods
producing sector is oil, coal, backstop resource. With the optimal carbon tax rate, the temperature change reaches a
maximum in 2315 and then declines. The energy knowledge stock appears to lower the peak of the temperature
change and shorten the year in peak.
References
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Warming. Journal of Political Economy, 105 (6): 1201-1234.
[2] Chakravorty, U., D. Krulce and J. Roumasset, 1997. Specialization and non-renewable resources: Ricardo meets
Ricardo. Journal of Economic Dynamics and Control, l 29: 1517–1545.
[3] Nordhaus, W. D., Managing the Global Commons: The Economics of the Greenhouse Effect, MIT Press,
Cambridge, MA, 1994.
[4] Nordhaus, W.D. and J. Boyer, Warming the World: Economic Models of Global Warming, MIT Press,
Cambridge, MA, 2000.
[5] Nordhaus, N.D., Modeling induced innovation in climate-change policy, in: A. Grubler, N. Nakicenovic, W.D.
Nordhaus (Eds.), Technological Change and the Environment, Resources for the Future, Washington, DC, 2002, pp.
182–209.
[6] Popp, D., 2004. ENTICE: endogenous backstop technology in the DICE model of global warming. Journal of
Environmental Economics and Management, 48 (1): 742–768.
[7] Popp, D., 2006. ENTICE-BR: The effects of backstop technology R&D on climate policy models. Energy
Economics, 28 (2006): 188–222.
[8] Uzawa, H., 1961. On a Two-Sector Model of Growth I. Review of Economic Studies. 29: 40-47.
[9] Uzawa, H., 1963. On a Two-Sector Model of Growth II. Review of Economic Studies. 30: 105-118.