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A joint initiative of Ludwig-Maximilians University’s Center for Economic Studies and the Ifo Institute for Economic Research
Area Conference on
Energy & Climate Economics
16-17 October 2009 CESifo Conference Centre, Munich
Announcing Climate Policy:
Can a Green Paradox arise without Scarcity?
Sjak Smulders, Yacov Tsur and Amos Zemel
CESifo GmbH
Poschingerstr. 5
81679 Munich
Germany
Phone:
Fax:
E-mail:
Web:
+49 (0) 89 9224-1410
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[email protected]
www.cesifo.de
Announcing Climate Policy: Can a Green
Paradox arise without Scarcity?
Sjak Smulders, Yacov Tsur, Amos Zemel
Department of Economics, Tilburg University
October 13, 2009
1
Introduction
In a dynamic world, environmental policy making is complex and timeconsuming. Optimal policy needs to take into account that costs and bene…ts
arise at di¤erent points in time and fall on di¤erent countries and generations.
Nevertheless, it is generally felt undesirable to postpone action until all complexities are sorted out. A way to deal with the complexities is to announce
polices well ahead of their implimentation, in order to give involved parties a
chance to prepare for their compliance to the regulation.
There are at least two main aspects of the problem just stated, which we
could label the “leakage aspect”and the “announcement aspect”.
First, the optimal, welfare-maximizing, policy cannot be implemented and
policy makers have to resort to imperfect, i.e. suboptimal, policies. They
might go for a constant tax or cap on emissions, without knowing what the
best level is, let alone how this level should evolve over time. The imperfection
might also relate to participation and coverage of the policy. If not all of
the polluting sectors or countries are subject to the policy, the response of
unregulated sectors and countries could undo some of the pollution reductions
in the regulated sectors and countries. This problem of “carbon leakage” has
been studied extensively. The traditional leakage e¤ect is that the reduction
in one country is partly o¤set by increases in pollution in other countries.
However, negative leakage (with reductions in unregulated countries) has been
shown to be possible, as well as more than 100% leakage (where the reduction
of regulated countries is more than o¤set by increases in other countries –the
co-called green paradox ). See for example Copeland and Taylor (2005), Di
Maria and Van der Werf (2008) for the former, and Sinn (2008) and Eichner
and Pethig (2009) for the latter.
1
The second aspect of the problem is that policy needs to take into account
what is the response of the parties to the announcement before the actual policy is implemented. Two such “announcement e¤ects” can be imagined. The
favourable response would occur when polluters start abating pollution and
accumulating credits, potentially because it is less costly to spread abatement
over time rather than concentrate e¤orts at a short period. The less favourable
reaction – at least in the light of the aim to reduce pollution – would occur
if …rms increase the use of polluting inputs. They might have stocks of polluting inputs that they would like to quickly use before they are no longer
allowed to do so. More subtle, but essentially through the same mechanism,
the total stock of polluting resources might be inelastic in supply, because a
non-renewable resource like oil, gas, or coal is involved. This is why an announcement of carbon taxation may induce resource owners to lower prices
and induce users to burn more fossil fuels. This mechanism is studied in, for
example, Di Maria et al (2008).
This paper studies how announcement of climate change policy a¤ects energy use before and after the actual implementation of the policy. We want
to investigate whether a green paradox or paradoxical announcement e¤ect
(increasing energy use in response to partial regulation or announcement of
regulation, respectively) can occur.
Our approach deviates from the existing literature in three ways.
First, we abstract from scarcity of energy resources, i.e. there is no stock
of energy resources that owners are eager to deplete. While the papers cited
above all rely on the scarcity of the polluting input to generate a paradoxical
announcement e¤ect, we show that scarcity is not required. This situation
seems relevant to abundant resources like coal for which the scarcity rent is
likely to be very small. In our model, fossil energy can be produced at a
constant unit cost. Fossil energy is an input in production, along with other
inputs.
Second, we focus on investment by energy users. We thus shift attention
to the dynamics at the energy demand side, rather than the supply side. The
build-up of capital is time-consuming so that investment behaviour is forward
looking. When climate policy is announced, investment responds and this
a¤ects energy demand before the climate change policy is implemented, as a
result of the change in capacity. The existing literature typically assumes the
resource stock to be the only predetermined stock variable (e.g. Hoel, 2009).
Abstracting from resource scarcity allows us to focus on other investment
decisions without losing tractability.
Third, we allow for competition between conventional energy technologies
and alternative energy technologies. We show that the timing and technological opportunities of these are crucial in determining the paradoxical announcement e¤ects. In particular, we employ the same model structure that Tsur and
2
Zemel (2009) used to study the incentives to build up solar energy capacity,
we further generalize their model, and we extend their analysis to the study
of announced policies. The more general interpretation is that we deal with
investment in productive capacity as well as capital equipment and knowledge
capital for abatement and alternative energy supply. We show that, depending
on the relative cost of both types of investment, a green policy anouncement
may paradoxically result in more pollution.
The conventional view is that, if …rms start investing in abatement capital or alternative energy supply in anticipation of the implementation of the
climate change policy, pollution falls because of the announcement. However,
in our model we …nd that the paradoxical result, with increasing pollution,
is also possible. In this latter case, we assume that the policy takes the form
of an increase in the energy tax at the time of implementation which is announced before. Firms accelerate investment in capital goods before the policy
is implemented. The accumulation of capital raises the demand for energy before implementation since capital and energy are (imperfect) complements.
At the time of implementation, energy use falls so that output is lower. Since
consumers want to smooth consumption, there is a rationale for accelerating
investment. Before the implementation, the acceleration of investment reduces
consumption, while after the implementation, the larger capital stock mitigates
the fall in consumption when energy falls.
The outline of the paper will be as follows.
The model is presented in section 2. Final goods producers produce output
with energy and physical capital as inputs. Energy comes from two sources,
which we call fossil and solar and which are perfect substitutes in production.
Fossil energy is polluting and can be produced at a …xed unit cost in terms
of output. Solar can be produced at zero marginal cost, but there is the …xed
cost of installing capital. Hence the economy can invest in physical capital and
solar capital. Households care about produced consumption goods only. The
government taxes energy use at a constant positive rate > 0 from period T >
0 onwards, while there is no taxation before T . This is called an "announced
policy" and can be contrasted to two alternative policies: the policy without
announcement (with T = 0) and the no-policy case (with = 0). Firms and
households know and fully take into account the announced future increase in
the tax change rate when making their intertemporal investment decisions.
Section 3 presents the results for a simpli…ed version of the model. Assuming a Cobb Douglas production function and assuming that solar energy
is too costly to become competitive at the tax policy, we show under which
conditions energy use is higher with announced policy than without policy or
without announcement. We show that all we need is the production elasticity
of captal to be smaller than the elasticity of marginal utility of consumption.
Since the latter is usually found to be bigger than 1, this condition would be
3
met in any empirically relevant calibration.
The rest of the paper considers how a viable alternative ("solar") energy
technology a¤ects the results and how the results carry over to di¤erent policy
instruments (cap-and-trade instead of taxes, non-constant rates or caps).
2
The Model
There is a single production technology f (x; k), using energy x and capital
k, and with the following usual characteristics:
fkk fxx
fk
fxk fkx
f (0; k)
lim fk
k!1
> 0; fx > 0; fxx < 0; fkk < 0; fxk > 0;
> 0; fk k + fx x < f;
= f (x; 0) = 0
= lim fx = 0; lim fk = lim fx = 1
x!1
k!0
x!0
When useful we may choose a Cobb-Douglas speci…cation:
f (x; k) = F k x
(2.1)
with + < 1 and F > 0.
Production serves as …nal consumption goods c, capital inputs i, and energy
inputs. Production capital is denoted by k. Energy inputs x are fossil energy,
xf , plus solar energy, xs . Fossil energy is bought at a price , or, alternatively
is produced at a unit cost of units of …nal output, where is a time-invariant
parameter until we study announcement e¤ects. Solar energy is proportional
to the installed capacity of solar energy, s. Thus, for solar energy there is no
‡ow cost but a sunk cost only in the form of installing solar capacity (while
the opposite holds for fossil energy). In particular, one unit of solar capacity s
produces a ‡ow of bdt units of solar energy over period dt. Hence, production
can be written as:
f (x; k) = c + i + xf
x = xf + bs
Investment is in production capital and solar capacity:
i = s_ + s + k_ + k
All variables are in principle a function of time, t, which is omitted when no
confusion can arise; dot denote time derivatives. Initial stocks, at time t = 0,
are given, with the stock of solar capital being negligible:
k(0) = k0 ; s(0) = 0
4
Households have a concave utility function over consumption of …nal goods,
u(c), and apply a constant utility discount rate over an in…nite horizon. They
maximize the following intertemporal utility integral:
Z
u(c(t)) exp( t)dt
u0 > 0; u00 < 0
All produced goods are traded in markets with perfect competition. As
a result the planner’s problem and the market equilibrium coincide, so that
it is easiest to study the social planner’s probem. This problem can be now
written as follows
M ax
Z
u(c(t) exp(
s.t. k_ + s_ = f (x; k)
x
bs 0
2.1
(x
bs)
(2.2)
t)dt
(k + s)
c;
E¢ cient production and Investment
We start by discussing the e¢ cient levels of production and the e¢ cient
levels of production capital and solar capacity. By e¢ ciency we mean maximized value added (or GDP) f
xf
G, for given stock of total assets
k + s w. This maximization problem can be formulated as:
max f (x; w
x;s
s)
(x
bs)
s.t. s
0; x
bs
where we can safely ignore the non-negativity constraint on k as the assumption fk (x; 0) = 0 ensures a positive e¢ cient level of production. E¢ ciency
(…rst order) conditions are:
fx
;x
fk
bfx ; s
bs with at least one equality
(2.3)
0 with at least one equality
(2.4)
While this problem is static (with the assumption that the split of total capital w over the two assets k and s is free), it has relevance for our dynamic
setting. First, if k can be costlessly transformed into s and vice versa, the
e¢ cient dynamic economy will maximize static GDP. Second, even with irreversible capital, the e¢ cient dynamic economy can maximize static GDP for
appropriate initial conditions. We will …nd that k and s are nondecreasing in
w, and s = 0 for k < km . Therefore, if the economy starts from s0 = 0 and
k0 < km , the economy can choose (and the e¢ cient economy will choose) to
5
split total investments over the two assets in an e¢ cient way. Hence, in what
follows, we refer interchangebly to the composition of assets (static setting) or
to investment in assets (dynamic setting).
We now derive how e¢ cient capital stocks and fossil input levels depend
on total level of assets (i.e. we derive how k, s, and xf depend on w and )
and how GDP changes with total assets (i.e. we derive G as a function of w
and ). For this it is convenient to de…ne the following functions. First, let X
represents e¢ cient fossil use, for given k and in the absence of solar capital.
Hence, X(k; ) is the level of energy inputs x that solves fx (x; k) = so that
fx (X(k; ); k) = ; Xk > 0; X < 0:
Second, let km represents production capital for which e¢ cient fossil use in
the absence of solar capital generates a return b . Hence km ( ) is the level of
production capital k that solves fk (X(k; ); k) = b , so that
0
fk (X(km ( ); ); km ) = b ; km
( ) < 0:
Third, let S represent the level of solar capital needed for e¢ cient production without fossil energy inputs. Hence, S(w) is the value of s that solves
bfx (bs; (w s)) = fk (bs; (w s)), so that
bfx (bS(w); (w
S(w))); S 0 (w) > 0:
S(w))) = fk (bS(w); (w
Note that if (2.1), then
X = ( F k = )1=(1
)
km = [ ( b= ) F=b ]1=(1
;
)
km ( ) + X(km ( ); ) = [1 + ( = )]1=(1
S=
2.1.1
+
;
)
km ;
w:
Fossil only
First consider the situation in which there is no stock of solar capital and
investment in solar capital is not e¢ cient. In this case e¢ cient production
requires:
fx (x; k) =
(2.5)
bfx (x; k) < fk (x; k)
(2.6)
The equation in (2.5) ensures the e¢ cient level of fossil inputs: marginal product of fossil inputs equals their price. The inequality in (2.6) makes solar
6
investment ine¢ cient: one unit of investment in solar capital allows for the
savings of b units of fossil energy with value fx , so that the return is bfx . However, investing one unit in production capital k earns fk , and if this exceeds
the return to solar investment as in (2.6), solar investment is ine¢ cient. From
these two conditions we immediately …nd the range of capital for which fossil
will be used only:
Lemma 2.1. E¢ cient production entails only fossil energy and no solar capacity, if and only if k < km ( ).
Proof. by construction, we have bfx (X(k; ); k) = b = fk (X(km ; ); km ).
Since fk (X(k; ); k) declines in k, we …nd b = bfx (X(k; ); k) < fk (X(k; ); k)
if and only if k < km . Hence, if fossil only is used, then x = X and k < km .
This proves the "if" part. Now we prove by contradiction that if k < km ,
solar cannot be used. If solar is used, fx
, which requires x
X, since
fx (X; k) = by construction and fxx < 0. Since x
X and k < km imply
fk > b since fk (X(km ; ); km ) = b by construction and fk declines in k and
increases in x. But then fk > b
bfx which implies s = 0 by (2.4). This
contradiction proves the "only if" part.
Because of diminishing returns, when the stock of capital k is low, the
returns to production capital k are relatively high. At the same time, the
returns to solar capital are limited to the marginal product of energy, which are
determined by the carbon price . Hence for su¢ ciently low k, the returns to
production investment exceed the returns to solar investment and the economy
remains a pure fossil economy. With a higher fossil price , the returns to solar
capital increase (as it allows to replaces fossil energy) and solar investment
becomes e¢ cient for lower levels of k.
2.1.2
Simultanous use of fossil and solar
Next consider the situation in which solar and fossil energy are used simultanously. In this case e¢ cient production requires:
fx (x; k) =
bfx (x; k) = fk (x; k)
The …rst equality ensures fossil is used, the second ensures no gains can be
reaped by replacing one asset by another.
Lemma 2.2. If solar and fossil are used simultaneously and production is
e¢ cient, then k = km ( ) and s 2 (0; X(km ( ); )=b).
7
Proof. If solar and fossil are used and production is e¢ cent, we have
bfx (x; k) = b = fk (x; k). Since the …rst equality implies x = X(k; ), the
two equations hold simultanously if b = fk (X(k; ); k), which implies by
construction k = km ( ). If bs > X(km ( ); ), we have fx (bs; km ) < since
fx (X; km ) = and fxx < 0; this would make simultanous use ine¢ cient. If
0 < bs < X(km ( ); ), we have fx (bs; km ) > and fx (x; km ) = for some
x > bs; this implies e¢ cient simultanous use.
Using fossil only, the marginal product of production capacital declines
with investment. When production capital is at km , its marginal product
equals b , and would fall below this level if all investment was used to expand
production capital k beyond km . However, each unit invested in solar capital
reduces fossil energy costs by b . Hence, once production capital reaches level
km , it is e¢ cient to …rst use all investment to replace fossil energy before again
investing in production capacity.
2.1.3
Solar only
Finally, consider the situation in which it is e¢ cient to not use any fossil
inputs. In this case, e¢ cient productions requires:
fx (bs; k) <
, bs > X(k; )
bfx (bs; k) = fk (bs; k)
(2.7)
(2.8)
The inequalities in (2.7) ensure that if no fossil energy is used together with
available solar energy bs, still the price of fossil energy exceeds its marginal
product, so that it is optimal to not use fossil. The equality in (2.8) ensures
equal returns to solar investment and capacity investment, so that total assets
are optimally split between solar and capacity. From these two conditions we
immediately …nd the range of total assets for which solar will be used only:
Lemma 2.3. If w > km ( ) + X(km ( ); )=b
wms ( ), e¢ cient production
requires that no fossil inputs be used (x = bs) and that solar capacity and
production capital are increasing functions of total assets, s = S(w) and
K(w) = w S(w).
Proof. If w > wms , then by lemma (2.1), pure fossil is not e¢ cient, and
by lemma (2.2), simultaneous use is not e¢ cient; hence, e¢ cient production
entails no fossil. S 0 (w) < 0 follows from total di¤erentiation of bfx (bs; (w
s)) = fk (bs; (w s)).
When the total capital stock is high, it does pay to invest part of it in solar
capacity. Suppose everything was invested in k, this implied a low marginal
return to investment in production capital and a large demand for energy.
Diverting away investment from low yielding production capital to producing
energy which is in high demand then improves e¢ ciency.
8
2.1.4
GDP
We can now characterize e¢ cient production (or maximized value added),
G, as a function of total assets, w.
E¢ cient production when fossil is used only is given by
f (X(k; ); k)
X(k; )
G(k; );
while e¢ cient production when solar is used only is given by
f (S; k) = f (S(w); w
S(w))
G(w):
Figure XXX plots G(w; ) and G(w) as well as the line
G(km ; ) + b (w
km ) for w 2 (km ; km + X(km )):
This latter line represents GDP when all capital in excess of km is invested
in solar capacity, up to the point that solar energy provides for all energy use
X(km ). At w = km , the slope of G is b and hence this is the optimal point to
switch to solar. It can be easily checked graphically, that if investment in solar
would start before km, GDP would be lower. See line G(ks ; ) + b (w ks )
with ks < km .
We can now list the properties of G(w):
8
>
<Gw 2 (b ; 1); Gww < 0; G < 0 if 0 < w km
G(w; ) Gw = b ; Gww = 0; G < 0
(2.9)
if km < w wms
>
:
Gw 2 (0; b ); Gww < 0; G = 0 if wms < w
Hence, for …xed carbon price , the GDP function G(:) has almost the same
properties as a standard neoclassical production function, the only di¤erence
being a constant marginal product of capital in the range for which both solar
and fossil are used. It is veri…ed that G and Gw are continuous at the transition
states kw and wms , while Gww is negative during the fossil and solar phases,
vanishing during the coexistence phase and experiencing discontinuous jumps
at both transition states. Furthermore, a higher carbon price depresses GDP,
except in the range over which only solar is used.
Note that if (2.1), then GDP takes the following speci…cation:
8
>
if 0 < w km
<A( )w
G(w) = b (w + w ) if km < w km =
(2.10)
>
:
Qw
if km = < w
where
= =(1
9
) < 1;
(2.11)
(2.12)
+ ;
A( ) = F (1
w
Q
2.2
) (F = )
km (1
=(1
)
(2.13)
;
(2.14)
)= ;
(2.15)
F (b = ) ( = ) :
Optimal consumption and investment
Using the expression for e¢ cient production, we can now rewrite the optimization problem (2.2) as
Z
max u(c(t) exp( t)dt s:t:w_ = G(w; )
w c:
To simplify notation, we suppress the argument when no confusion arises
and write G0 (w) for Gw (w; ). The optimal consumption-saving policy is described by the pair of dynamic equations
w_ = G(w; )
w
(2.16)
c
and
c_ = c (c)[Gw (w; )
(2.17)
]
where
(c) =
u0 (c)=u00 (c)c
(2.18)
is the intertemporal elasticity of substitution. elasticity of marginal utility.
The steady state (w1 ; c1 ) of this system is given by the relations
Gw (w1 ; ) =
and
c1 = G(w1 ; )
w1 =
where
v(w; ) =
(2.19)
+
+
v(w1 )
w1 ;
(2.20)
Gw (w; )w
G(w; )
is the elasticity of GDP with respect to capital (or "capital share" for short).
The following lemma characterizes the steady state.
Lemma 2.4. If b < + , the steady state has fossil only (w1 < km )
and steady state consumption c1 and capital k1 = w1 decline with . If
b > + , the steady state has solar energy only (w1 > wms ) and steady state
consumption c1 and capital w1 are independent of .
10
Proof. follows from (2.9) and (2.19).
For the autonomous system (with constant , i.e. _ = 0) at hand, we can
write c = c(w), hence c_ = c0 (w)w_ and equations (2.16) and (2.17) imply
c0 (w) = c(w)
G0 (w)
G(w)
w
c(w)
(2.21)
:
More precise, we could write c = c(w; ), but we suppress the argument when
no confusion arises and we write c0 (w) for cw (w; ) and G0 (w) for Gw . Combined
with the boundary condition c(w1 ) = c1 , equation (2.21) determines the ( dependent) consumption for every capital stock in [0; w1 ].
We use now equation (??) to study the properties of the c( ) curve. We
…rst characterize the slope of the consumption-capital relationship if we start
with capital below the steady state level.
Lemma 2.5. If (c)v(w) < 1 for 8w 2 [0; w1 ], 8c 2 [0; c1 ] , then 0 < c0 (w)
and c(w) > [( + )=v(w)
]w for 8w 2 (0; w1 ].
Proof. (2.21) implies c0 =
vG (
v wc vG
v(
+ )w
.
+c=w)
Hence, if
v < 1, we have
vG ( + )w
so that a fortiori c0 < c=w if c=w [( + )=v
]. In the
c0 < wc vG
v( +c=w)
0
steady state we have c=w = [( + )=v
], so that c < c=w close to the steady
state and c=w > [( + )=v
] for w slightly below w1 . The inequality holds
for all w < w1 , since c(w) never crosses the line c = [( + )=v(w)
]w,
0
because this would require c (w) > ( + )=v(w)
, which is just shown to
be impossible.
Next we compare the consumption-capital relationship for di¤erent carbon
prices.
Lemma 2.6. Let
following holds:
2 f l;
h
g with
l
<
h
. If (c) < 1= for 8c 2 [0; c1 ], the
1. If b l > + , higher carbon prices shift down the c(w) curve for all w 2
(0; wms ( l )) and leave it una¤ected for w wms , i.e. c(w; l ) > c(w; h )
for w < wms ( l ) and c(w; l ) = c(w; h ) for w wms ( l ).
2. If b h < + , higher carbon prices shift down the c(w) curve for all
w 2 (0; w1 ( l )], i.e. c(w; l ) > c(w; h ) for w 2 (0; w1 ( l )].
3. If b
l
<
+ < b h , then c(w; l ) > c(w;
h
) for w 2 (0; w1 ( l )].
Proof. See appendix for full proof in case of the Cobb-Douglas case. The
easy parts of the proof are given here. To simplify notation, let superscripts l
and h denote dependence on l and h , respectively, so that G0l Gw (w; l ),
l
G0h
Gw (w; h ), Gh
G(w; h ), km
km ( l ). First consider part (i). If
11
b > + , we have w1 > wms . By lemma 2.4 w1 is independent of , and
by (2.9) G and G0 are independent of for w
wms , so that c0 in (2.21) is
l
l
not a¤ected by . For w 2 (km
; wms
), we have Gl > Gh and G0l < G0h so that
0l
0h
c < c which implies (by integration from high to low w) cl > ch . For the
l
, things are more complex because the inequality G0l < G0h is
range w < km
l
h
).
; km
reversed for some w 2 (km
3
Higher carbon prices
We now analyse a once and for all increase in the carbon price . Suppose
initially, that is as of time t = 0, the carbon price is l , while at time T > 0,
when the capital stock is w(T ), the carbon price jumps up from l to h . If
the price change is unexpected, the economy consumes according to cl (t) =
c(w(t); l );as derived from (2.21) and the end condition w1 ( l ); c1 ( l ), from
t = 0 to t = T and then jumps at t = T to ch (t) = c(w(t); h ), which is derived
from (2.21) and the end condition w1 ( h ); c1 ( h ). However, if the price change
is anticipated, because it is announced at an earlier date, consumption will not
jump. Consumption will follow ch (t) = c(w(t); h ) after period T , but before T
it will choose, instead of cl (t) = c(w(t); l ), a path of consumption, say cd , that
still follows (2.21) for = l , but rules out a jump in consumption at time T .
While the change in consumption follows the same rule, viz (2.21), as without
anticipation and announcement, the endpoint at time T is di¤erent. Now from
the phase diagram it is clear that since cl lies above ch , the path cd must be
below cl in order to meet ch at time T . This implies that announcing the price
increase will decrease consumption, as compared to the situation in which the
price increase is not announced and in which consumption cannot anticipate
it. The decrease in consumption has e¤ects on the accumulation of capital
and the use of energy. Before the actual price change, e¢ cient production
conditions as captured by the GDP function G(w; ) have not changed yet,
while consumption is lower. Hence, capital is accumulated at a faster pace.
This means that the capital stock is higher and fossil demand is higher at every
point in time after the announcement (as compared to the situation without
announcement). Hence, we have the following proposition:
Proposition 1. If (c)v(w) < 1 for 8w 2 [0; w1 ], 8c 2 [0; c1 ] , then the
unexpected announcement at time Ta of a higher carbon price at some future
date T > Ta will cause consumption to be lower between dates Ta and T , and
to be higher after T ; and fossil energy use to be higher immediately after date
Ta .
The general intuitioin is as follows. Higher carbon prices reduce e¢ cient
output levels, at least over the period that fossil energy was used at the old
price: essential fossil inputs are more expensive. It might become e¢ cient
12
to introduce solar energy at lower levels of the capital stock, but this is never
going to restore output levels back to the old levels (otherwise solar energy was
introduced in this way also at the old carbon price). Hence, total consumption
possibilities (over the entire horizon) have decreased, which tends to reduce
consumption. This is a "(permanent) income e¤ect". Since it is optimal to
smooth consumption, the expectation of higher carbon prices and thus lower
consumption in future provides a reason to adjust consumption already in the
present and to build up more capital and thus mitigate the fall in consumption
at the time of the higher carbon input price. This is a "anticipation/smoothing
e¤ect". One thing could go against this, which is driven by changes in the rate
of return to investment. Higher carbon prices decrease the rate of return as
long as no solar energy is used: e¢ cient fossil energy use for a given amount
of capital becomes lower so that the marginal product of capital is lower. The
lower retun to investment reduces investment and increases consumption by a
"substitution e¤ect". However, if the elasticity of substitution ( ) is relatively
low, this e¤ect will not dominate. Indeed, < 1=v is a su¢ cient condition.
Note that this condition is an empirically relevant condition, since in general
it is though that < 1.
We could now go through a number of interesting cases. We will provide
a sketch of some aspects; technical details are in the appendix.
3.1
From fossil to fossil
First consider the case in which not the low (old) and but only the high
(new) carbon price makes solar energy e¢ cient in the steady state, i.e. l <
( + )=b < h . Then announcement will cause fossil energy use to be higher
for all t > Ta .
3.2
From fossil to solar
Now consider the case in which both the low (old) and the high (new)
carbon price are too low to make solar energy e¢ cient in the steady state, i.e.
l
< h < ( + )=b. Then announcement will cause fossil energy use to be
higher immediately after Ta , but it might be lower later on. The reason is
that the economy might accumulate capital beyond the old steady state level
w1 ( l ). It could even temporarily introduce solar energy. The reason is that
to avoid a fall in consumption at the time fossil price go up, the economy
builds up additional capital. But if the amount of capital becomes large, the
transition to solar might become attractive.
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3.3
From solar to solar
Now consider the case in which both the low (old) and the high (new)
carbon price are high enough to make solar energy e¢ cient in the steady
state, i.e. h > l > ( + )=b. Then announcement will cause fossil energy use
to be higher immediately after Ta , but it might be lower later on. The reason
is that the economy introduces solar energy earlier on for two reasons: …rst
carbon prices are higher which lowers the threshold value of capital for which
solar starts to be e¢ cient. Second, investment is speeded up so that a given
threshold is reacher sooner.
4
References
References
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[7] Di Maria, Corrado, and Edwin van der Werf, 2008. "Carbon leakage revisited: unilateral climate policy with directed technical change," Environmental & Resource Economics, 39(2), 55-74.
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[7] Eichner, Thomas, and Rüdiger Pethig, 2009. "Carbon Leakage, the Green
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[7] Hoel, Michael. 2009 "Bush Meets Hotelling: E¤ects of Improved Renewable
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[7] Sinn, H.-W. (2008), ’Public policies against global warming’, International
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[7] Tsur,
Yacov,
and
Amos
Zemel
(2009)
"Market
structure and the penetration of alternative energy technologies"
paper
presented
at
the
EAERE
2009
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http://www.webmeets.com/…les/papers/EAERE/2009/625/SolFosBlindJan09.pdf
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