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A NOTE ON ENVIRONMENTAL
INNOVATION
Jean-Jacques Laffont
Jean Tirole
95-10
June, 1994
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139
\
A NOTE ON ENVIRONMENTAL
INNOVATION
Jean-Jacques Laffont
Jean Tirole
June, 1994
95-10
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
MAR
2 9 1995
LIBRARIES
95-10
A
Note on Environmental Innovation*
and
Jean- Jacques Laffont^
June
16,
Jean Tirole*
1994
Abstract
The purpose
of this exploratory note
to alert the reader
is, first,
to the negative impact of allowance markets on environmental inno-
some improvements. Stand-alone spot
markets enable the government to expropriate an innovation by offervations and, second, to suggest
ing a competing "technology" (pollution permits) and putting an arbitrary
downward
pressure on the licensing price.
reduce expropriation but
still
Advance allowances
create very suboptimal incentives for
They have the further drawback that permits are ineffiused when the innovation occurs. In this respect, options to
innovations.
ciently
pollute at a given striking price fare better than allowances because
they create private incentives to phase out pollution in case of innovation.
The note then
studies
government procurement. Surprisingly ex-
post licensing by the innovator to the government
may
yield a higher
licensing fee than an ex-ante contract.
"The authors are
grateful to Carlo Carraro
and Paul Joskow
for helpful discussions
to Fondazione Eni Enrico Mattei for financial support.
tIDEI and
GREMAQ,
Toulouse, France
*IDEI, Toulouse, France;
CERAS,
Paris;
and M.I.T., Cambridge,
1
MA USA
and
Introduction
1
companion paper (1994) we analyze the impact
In a
of spot
and futures markets
tradeable pollution permits on the potential polluters' compliance decisions.
there
on the individual incentives
is
to adopt pollution
abatement devices.
The
for
focus
In contrast, this
exploratory note considers technological innovation, namely the invention of substitutes or
pollution abatement devices that can be used by
The
all polluters.
innovation
therefore
is
a public good, while the investments considered in the companion paper are purely private.
The model
2
There are two dates,
tional simplicity,
t
=
1,2,
and a continuum of agents/potential
we assume no
consider first-period pollution.
rights
N(-)
given by n
is
=
Without
The
demand curve
agents'
N(p), where p
decreasing. Unlike in our
is
discounting.
is
polluters.
loss of generality,
we
For nota-
also
do not
for second-period pollution
The
the (second-period) spot price.
companion paper, we do not allow agents
to
function
make
indi-
vidual investments in pollution abatement (although this could be incorporated into the
analysis). So, the
demand
function
Let D(n) denote the social
ment
faces a
+
society $(1
shadow
is
fixed.
damage
where D'
of pollution,
cost of public funds A
>
0;
that
is,
>
0,
D" >
The
0.
govern-
money
raising $1 of public
costs
A) because of distortionary taxation.
We model innovation in a simple way. There is one potential innovator, who at private
cost C(x) incurred at date 1 (C(0) = 0, C'(0) = 0, C'(l) = +oo,C > 0, and C" >
for
x
>
0) innovates with probability
x at the beginning of date
2.
The
a pollution-free perfect substitute for the existing polluting good, or else
abatement device that can be
all
installed at
is
is
a pollution
no cost on any existing equipment and eliminates
We will consider two cases depending
potential innovator before she performs R
pollution (we will use this second interpretation.)
on whether a contract can be signed with the
&
innovation
D.
If
such an ex ante contract can be signed (as in section
the innovator
is
protected by limited liability (or, equivalently,
income
It
will
of the
zero).
R&D
innovator
is
become
process.
clear that
When
we could
consider
no ex ante contract
is
simply granted a patent on her innovation.
1
5),
is
we
will
assume that
very risk averse under
more sophisticated
descriptions
signed (sections 3, 4 and 6), the
Spot market
3
This section assumes that the government issues pollution permits in period 2 after observing whether the innovation occurs.
innovator invents or not;
(iii)
The second-period timing
is
as follows:
(i)
the government sets a price p for pollution permits
(ii)
2
;
the
and
the innovator sets a price i on licenses.
Let us
first
analyze the pricing game.
In the absence of innovation, the regulator
chooses price p so as to solve:
r N(x)dx +
roo
max'{
(1
+
X)pN(p)
Jo
Letting
= — J.J
T)(p)
the standard
Ramsey
denote the elasticity of demand for pollution permits, we obtain
formula:
p
where D'/(l
+ A),
- D(N( P ))}.
i
damage expressed
the marginal
Ki
+ AiHp)*
in
monetary
units,
is
the marginal cost
of "producing the 'good pollution'".
In case of innovation, the inventor,
who has
a lower cost (namely 0) of enabling agents
produce than the regulator (who has marginal cost D'/(l
to
slightly the price for pollution permits.
Welfare
is
+
A)), always undercuts
therefore equal to / °° N(x)dx. 3
p
The
regulator therefore chooses:
p
Because the innovator does not make a
chooses not to perform
R&D
(x
=
=
0.
(2)
profit in either state of nature, she rationally
0).
Advance allowances
4
This section shows that, while spot markets destroy incentives for innovation (see section
3), futures
markets bring limited improvement, even
issue permits in order to exert
rights to pollute
if
the regulator can commit not to
downward pressure on the
license fee.
both substantially discourages innovation and
may
Granting advance
induce a suboptimal
adoption. In case of innovation, the spot price adjusts downward so as to allow permits to
compete with the innovation.
2
By
exerting price pressure on the licenses of the innovation,
We
could alternatively allow the government to choose the number of permits instead of their
treatment
of this case would follow the lines of the analysis in section 4.
The
3
This expression holds as long as the price does not exceed the inventor's monopoly
clearly inefficient to set a price above the monopoly price.
price.
price.
But
it is
allowances substantially devalue the innovator's property right and reduce the incentive
to innovate.
To
illustrate this simple point, consider the following
potential polluters and n advance permits sold in period
price falls to zero
and so does the price of
rationally chooses not to perform
the n units of pollution and
is
R
k,
D
1.
extreme example: There are n
In case of innovation, the spot
licenses sold to the
=
(i
0),
n
polluters.
The
innovator
even though the innovation eliminates
awarded a patent.
Advance permits have a second perverse
example, but does occur more generally.
that need not occur in this extreme
effect,
Let us
assume that the innovator
first
is
not
allowed to trade on the permits market. Unless the equilibrium price for pollution control
(through either a license from the innovator or a permit)
equal to zero (in which case
is
the innovation does not take place anyway), the existing n permits are used ex post even
though the innovation could completely eradicate pollution. Let N(p) denote the secondperiod
demand
curve, with inverse
the innovation occurs:
> P(n) and no
Either p
innovator); or p
< P(n) and
the
same as
more
allows
Let us
The number
consider the following timing after
innovator sets a license price p, (b) then the market for
a) the
permits clears.
for permits.
demand P{n). And
license
sold (which
is
is
not optimal for the
the innovator de facto picks the price on the spot market
of licenses sold
in the absence of innovation.
is
then [N(p)
The only
—
n].
So, the level of pollution
positive effect of innovation
is
that
is
it
potential polluters to produce.
now analyze the
innovator's choice of pricing and
R&D
intensity.
Let pm
denote the constrained monopoly price for the innovator:
p
m
\p
is
m
maximizes
actually a slight misnomer.
{p[N(p)
The permits
—
n] }
(3)
.
play the role of a competitive fringe, and,
by a standard revealed preference argument, force the innovator to charge a lower license
price
p
m
that she would charge in their absence.] Let
The innovator chooses
m denote
the resulting maximand.
R&D level x so as to solve:
i
To summarize, the
II
sale of
maximizes
{xll
m — C(x)}
(4)
.
advance permits has two perverse
effects here:
First, the
permits partially prevent the adoption of a superior, pollution-free technology. Second,
they further reduce the innovator's incentive to innovate (this incentive
is
already subop-
timal in the absence of permits because the innovator does not internalize the increase in
"consumer surplus" brought about by the innovation.)
Let us
now
allow the innovator to trade on the permits market.
of licensing costs, the innovator's profit
is
In the absence
independent of the number of permits she
purchases.
purchasing n
np and has
n), pays
still
When
quite low. But,
n
=
n, the
permits, she faces residual
— h]. The
p[N(p)
profit
if
< h
demand curve N(p) — in —
innovator's incentives are unchanged and are
n units of pollution are eradicated, and welfare
than when the innovator does not trade
in
is
higher
the permits market.
Unfortunately, the innovator's (weak) willingness to buy permits on the market in case
of innovation disappears
The
innovator's profit, (p
of the
number
has then no
The crux
when she
—
an arbitrarily small marginal cost
faces
e)[N(p)
—
— n)] —pn,
(n
is
now a
strictly decreasing function
of repurchased permits n. Allowing the innovator to trade on the market
effect.
of the matter
is
that none of the market participants (polluters, innovator)
internalizes the social cost of pollution of the leftover permits.
To induce market
pants to phase out the wasteful permits in case of innovation, one possibility
these permits to pollute by options with a striking price
ing cost
t
of licensing.
e
of the innovator.
is
partici-
to replace
exceeding the marginal licens-
tj
In contrast with final sales of permits, sales of options have
the desirable property that they provide incentives to
therefore to retire previous rights to pollute.
make
full use of the
They furthermore have a
innovation and
beneficial
impact
on the incentive to innovate as they restore some of the innovator's monopoly power
lost
with the issuance of permits.
Alternatively the government, which internalizes the social cost of pollution of the
over permits, could respond to innovation by buying back some permits.
could also purchase the innovation from the innovator (see section
The government
6).
Procurement
5
By
left-
opposition with the market-oriented approach of the previous section, this section con-
siders the ideal planning solution.
We make
the strong assumption that the government
can ex ante identify the potential innovation and designs an incentive contract
for the
innovator so as to maximize social welfare.
The government
optimally issues no advance permits at date
purchase the innovation at some price
property rights on the innovation,
free technology,
namely the
Once the government
q.
it sells
the license at the
1.
Rather
it
promises to
acquires the (exclusive)
Ramsey
price for the pollution-
price that solves:
-—
\
r-^-rh-
(5)
p
Let
W R denote the associated social welfare.
there
is
no innovation and the government
Similarly
sells
let
WR denote social welfare when
the corresponding optimal
number
of
permits in period
—
{xq
2.
4
The innovator
reacts to incentive q by choosing x so as to
maximize
C(x)} or
C'(x)
The optimal procurement
=
q.
(6)
policy consists in choosing
q,
or equivalently x, so as to maxi-
mize:
xW R + (1
We
- x)W R -
+
(1
+
\)xq
-
[xq
C{x))
= xW R +
(1
- x)W R -
-
C(x)
\xC'{x).
obtain:
W R - WR =
+
(1
A)C'(x')
+
Xx*C"(x
For instance, in the case of a quadratic cost function (C"(x)
q
Because
it is
Ex
6
computed
xC"(x)), one has
'
1+2A
costly to leave rents to the innovator, the prize q'
social value of the innovation
(7)
).
WR-W R
_
m
=
m
at the
shadow
=
C'(x')
is
lower than the
cost of public funds
tv
(
1
7J^
)•
post licensing to the government
Suppose now that no contract between the potential innovator and the government can be
signed at date
in
but that the government can purchase the innovation at date 2 and, as
1,
the previous subsection, license
move bargaining between
date
The government
2.
agreed with the innovator
following period
1).
The
it
to the agents.
We
assume
frequent-offer, alternating-
the government and the innovator starting at the beginning of
issues short-term pollution permits as long as
(so,
we
are
now
it
has not yet
treating "period 9" as an infinite-horizon
reader will check that the licensing- fee
by the Nash bargaining solution with reservation value
W
R
is
game
equal to the one given
for the
government
(as in
Binmore- Rubinstein- Wolinski (1986)): 5
W R -WR
q
A
£>()
5
WR
and
WR
are equal to the
=
and
£>{•)
=
Let
u^ =
(1
—2A—
=
(8)
maximal values of {-D(N(p))
+
(I
+
A)pAT(p)
+ /"
N(x)dx}
for
£>(•), respectively.
R
R
denote the discount factor corresponding to the bargaining periods, w = (\ — 0)W and
— /3)W R denote the per-period welfares, and qt and g,- denote the equilibrium offers when the
P
government and the innovator make the
offer.
Then:
qt
w R -Xqi
= fa, and
= w R -0\qa
.
Note that
(as
may seem
surprising in view of the asset specificity literature, which emphasizes the role
is
for instance the case for quadratic cost functions) q
of long-term contracts in reducing expropriation by the buyer
by the supplier through the promise of a high transfer
price.
may
exceed
q'.
This
and encouraging investment
There are two differences with
the asset specificity literature. First, the buyer (the government) here partly internalizes
more importantly, the
the seller's welfare. Second, and
seller faces limited liability.
are then not quite transferable, and a long-term procurement contract does not
utilities
maximize
The
total surplus of the two parties.
innovator's rent.
6
The
public funds.
licensing fee
is
reduced so as to limit the
possibility that ex post bargaining yield
than (ex ante) procurement
is
The government
nicely illustrated
is
a higher licensing price
by the case of a very low shadow cost
But
would never agree ex
it
ante to such a price because this would give excessive incentives for
case in which q
>
of
then willing ex post to accept almost an infinite licensing
price in order not to delay the adoption of the innovation.
The
The
q* actually raises several issues. First,
it is
R&D.
not in the interest of
the innovator to sign ex ante a contract with the government. Second, as in Hart-Moore
(1992), an innovator
to force
it
who has
to raise the price
signed an ex ante contract might blackmail the government
from
q* to q to
complete the research,
if
she
is
indispensable
for its completion.
Last,
we have assumed
that the innovator does not
while bargaining with the government.
parties
more
The
sell
short-term licenses to the agents
possibility of short-term licenses
patient in the bargaining process.
We
makes both
have not yet studied the net
effect.
Summary
7
The purpose
of this exploratory note has been,
first,
to alert the reader to the negative
impact of allowance markets on environmental innovations and, second, to suggest some
improvements. Stand-alone spot markets enable the government to expropriate an innovation by offering a competing "technology" (pollution permits) and putting an arbitrary
downward pressure on the
still
licensing price.
Advance allowances reduce expropriation but
create very suboptimal incentives for innovation.
that permits are inefficiently used
when the innovation
They have the
further drawback
occurs. In this respect, options to
pollute at a given striking price fare better than allowances because they create private
incentives to phase out pollution in case of innovation.
The note then
studied government procurement. Surprisingly ex post licensing by the
innovator to the government
6
cost
may
yield a higher licensing fee than
In a private context, the licensing fee
C
is
concave (convex).
is
an ex ante contract.
higher (lower) under a long-term contract
if
the marginal
MIT LIBRARIES
Ml
III
3 9080 00922 5183
The
Limited scope of this note has
of a futures
market as a guide
left
many
issues unexplored. For
for the agents' individual
example, the role
investments in pollution-abating
technologies and the issues of agent rent extraction (that are the focus of our companion
paper) were
more
left
here out of the analysis. Another desirable extension would describe in
detail the microstructure of the innovation process (see Aghion-Tirole (1993))
examine how financing, control
rights
on the process, property
and return from licensing would be optimally
split
among
government, users of the innovation and financiers.)
consider
more complex
incentive
futures markets, procurement,
rights
and
on the innovation
the several actors (innovator,
Last,
it
would be very useful to
mechanisms than the simple ones (stand-alone markets,
and ex post licensing to the government) analyzed
here.
References
Aghion,
P.
and
J.
Tirole [1993]
"On
the
Management
of Innovation"
,
forthcoming, Quar-
terly Journal of Economics.
Binmore, K., Rubinstein, A. and A. Wolinsky [1986] "The Nash Bargaining Solution
Economic Modeling", The Rand Journal of Economics, 17:176-188.
Hart, 0. and J. Moore [1992]
Capital", mimeo.
"A Theory
of
Debt Based on the
Inalienability of
in
Human
and J. Tirole [1994] "Pollution Permits and Compliance Strategies", Fondazione Eni Enrico Mattei Discussion Paper.
Laffont, J.- J.
!i906