Table 1 Population and life expectancy in ALICE 2.0
2100 1960
1980 2000
2200 2020
2040 2060
2080 11.0
Population WB
a
n.a. n.a.
6.1 7.7
9.0 9.9
n.a. 10.6
11.1 Population ALICE 2.0 ageing
b
n.a. n.a.
6.1 11.1
7.7 9.0
10.0 10.7
11.0 Population ALICE 2.0 no ageing
b
n.a. n.a.
11.3 6.1
7.6 9.0
10.0 10.6
n.a. Life expectancy at birth WB
a
n.a. 63.5
67.4 82.6
71.2 74.7
77.9 80.3
80.0 Life expectancy at birth ALICE 2.0
c
60.0 64.0
68.0 72.0
80.0 76.0
80.0 80.0
a
Population is in billion people and life expectancy in years, calculated from World Bank data WB, 1994.
b
The population at the beginning of period t is taken to be the average population of periods t−1 and t. The population in period t includes the children who enter the model one period later. Both population sequences, with and without ageing, are calibrated
to the WB data.
c
With ageing.
3. Consumers
Generations maximise their lifetime utility uc
t
, b
t
, derived from rival consumption of the consumer good during the life-cycle, c
t
= c
t t
,c
t + 1 t
, c
t + 2 t
, and non-rival consumption of the resource amenity, for convenience referred to as ‘environ-
mental services’, b
t
= b
t
, b
t + 1
, b
t + 2
. We omit the superscript t in the consumption of the resource
amenity to stress that the amenity consumption is the same for all generations alive at period t. By
this definition of utility, an extension is made with respect to conventional IAMs, since the latter
treat climate change damages as if they would constitute merely a decrease of man-made con-
sumer goods. We think that a large part of the damages caused by global warming can be under-
stood as a decrease in the quality and quantity of environmental functions, much more than as a
reduction in the flow of man-made goods. Indeed, the IPCC 1996b, Section 1.3.2 recognises that a
decrease in biodiversity may be one of the major consequences of climate change. Our explicit spe-
cification of a resource amenity provides a means to incorporate this insight into a competitive equi-
librium framework. In order to allow for covering a more complete range of climate change effects,
we would need to model both amenity and pro- ductivity effects. An extension of our model with
respect to these effects is one of the potential fields of future research.
The consumption behaviour of generations from which not all members live three periods is
based on some further assumptions. For any member of a generation, until the beginning of the
third period, only the probability of living three periods is known. At the beginning of the third
period, any member is either alive or not. Each member is supposed to maximise expected life-
time utility. There are no non-intended bequests to future generations resulting from the uncer-
tainty in life-time Hurd, 1989, because there is an intra-generational life insurance company to
which all members of a generation pay their sav- ings in the second period of life. The insurance
company repays the savings to the living members of the generation in the third period. Under this
condition, there is no need to explicitly describe the actions of the insurance company and of
separate consumers; one representative consumer who maximises aggregate utility, subject to one
budget constraint, can describe the generation.
7
The utility function u· employed is a nested CES function of form:
uc
i
, b
i
=
i + 2 t = i
s
t − i
n
t i
c
t i
11 + n
b
t n
1 + n r − 1r
n
r r − 1
, 2
where r = 0.67 is the intertemporal elasticity of substitution, s = 1 is the consumers’ time prefer-
7
The working of an intragenerational insurance company is described, for example, in Blanchard and Fischer 1989.
ence factor,
8
and n = 0.1 is the constant share of the expenditures on the resource amenity relative to the
man-made consumer good: 8
t i
b
t
= n
c
t i
, 3
where 8
t i
are the so-called Lindahl prices for generation i in period t for non-rival consumption
of the resource amenity, relative to the price of the man-made consumer good.
The first generation i = 0 maximises utility sub- ject to its budget constraint:
max{uc , b
c
1
+ 8
1
b
1
5 w
1
l
1
+ c
1
k
1
+ H
1
}, 4
while generations i = 1, … , solve: max{uc
i
,b
i t = i,…,i + 2
b
i t
c
t i
+ 8
t i
b
t
5
t = i,…,i + 2
b
i t
w
t
l
t i
+ H
t i
}, 5
where prices are normalised so that the consumer good has price unity, b
i t
is the price depreciation factor from period i to period t whenever conve-
nient, we also write b
t
for b
t t + 1
, w
t
denotes the price of labour, l
t i
denotes the labour endowment, c
1
is the price of the man-made capital stock k
1
in the first period owned by the first generation, and
H
t i
is the income which generation i receives in period t as its share in the value of the environmen-
tal resource. For generation i, the first order condition for the first choice variable c
i
is given by: u
i
·c
i
= l
i
1,b
i i + 1
, b
i i + 2
. 6
for some scalar l
i
\ 0. Non-rivalry of the demand
for the resource amenity implies that consumers should agree on the provision of the amenity level
and jointly finance them. Thus, Lindahl prices 8
t i
should add up to the production price p
t b
: p
t b
= 8
t t − 2
+ 8
t t − 1
+ 8
t t
, 7
and the first order condition for the choice variable b
i
should satisfy: u
i
·b
i
= l
i
8
i i
, b
i i + 1
8
i i + 1
, b
i i + 2
8
i i + 2
. 8
for the same scalar l
i
\ 0 as in Eq. 6, such that
the budget in Eq. 5 holds.
3
.
1
. Producers ALICE 2.0 includes a simple production sector
for a man-made consumer good y
t
, consisting of one private firm. It uses labour units l
t
, emission units e
t
, and a man-made capital stock k
t
as production factors. The capital stock is itself pro-
duced by this production sector. We therefore assume that the capital stock is made up of the
consumer good, and that it has to be replaced after use in one period. The production structure is based
on a nested function, in which the intermediate good y
t m
is made of a Cobb – Douglas composite of capital and labour:
y
t m
= A
t
k
t a
l
t 1 − a
, 9
where A
t
is a productivity coefficient.
9
The com- posite good y
t m
is used, together with emission units, in a quadratic production function:
y
i
+ k
t + 1
= y
t m
+
1 2
hz
t
e
t
2z
t
− e
t
y
t m
, 10
where h is the maximal CO
2
tax at which net emissions become zero, and z
t
is the maximum emission intensity when no carbon taxes are im-
posed. This becomes clear from the first order condition for emissions:
p
t e
] h
1 − e
t
z
t
y
t m
Þe
t
] 0,
11 where p
t e
is the price of emission units in period t, and the complementarity sign ‘Þ’ denotes that the
left-hand inequality is binding i.e. becomes an equality if emissions are positive. The parameters
h and z
t
are chosen such that the efficient emis-
8
The intertemporal elasticity of substitution, r, and time preference, s, are based on estimates in the literature Davies,
1981; Auerbach et al., 1989; Hurd, 1989. Note that in an OLG model, there is no a priori reason to have a strictly
positive time preference rate, represented through s B 1. Re- placing s = 1 by a value s B 1 would result in higher interest
rates in all scenarios, though qualitatively, results would not change. For a detailed calibration analysis, see Gerlagh
1998b, Section 4.2.3.
9
The value of A
t
is calibrated such that in the first period gross output is equal to 38.4 trillion US per year 1990
market prices, and increases by 3 per year. Output growth is assumed to decrease slowly to zero by the end of the 22nd
century. For a detailed calibration analysis, see Gerlagh 1998b, Section 6.2.
sion levels decrease by 1 percent for every 4 UStC price increase of emission units,
10
and that the maximum emission levels follow the
IS92a scenario IPCC, 1992. The IS92a bench- mark scenario assumes an autonomous decrease
in the emission intensity z
t
, partly based on an autonomous increase in energy efficiency AIEE
and an autonomous expansion of backstop technologies.
Because of constant returns to scale, the value of inputs equals the value of outputs:
y
i
+ k
t + 1
= w
i
l
i
+ c
t
k
t
+ p
t e
e
t,
12 where c
t
is the price for capital in period t. Since capital is produced in the previous period, we
have: c
t + 1
= 1b
t
, 13
for t = 1, …, . After substitution of the value Eq. 12, we have the following first order condi-
tions for labour and capital:
w
t
l
t
= 1 − ay
t
+ k
t + 1
− p
t e
e
t
, 14
and c
t
k
t
= a
y
t
+ k
t + 1
− p
t e
e
t
. 15
3
.
2
. Climate change As noted above, ALICE 2.0 extends the exist-
ing IAMs by specifying an explicit resource amenity, following Krautkraemer 1985. In terms
of the model, the biogeochemical system produces emission units e
t
, and environmental services b
t
. It is a renewable resource that, however, deteriorates
because of emissions, and this is the core of the problem Clark, 1997. This is in accordance with
the environmental concerns underlying the issue of climate change.
We will now describe how this resource amenity relates to greenhouse gas emissions. As the emis-
sions of CO
2
account for the main anthropogenic contribution to the greenhouse effect, we focus on
the carbon cycle and its relation to climate change. ALICE 2.0 follows CETA Peck and
Teisberg, 1992, linking emissions to concentra- tions, concentrations to temperatures, and tem-
peratures to damages. We use the ‘linear box’ model in which one distinguishes between five
separate spheres, each having different properties with respect to carbon dioxide absorption Maier-
Reimer and Hasselmann, 1987. It is assumed that the CO
2
emitted is distributed over the five boxes in amounts corresponding to shares a
i
i = 1,…,5 of total emissions. Within each box, the CO
2
concentration exponentially adjusts to its natural level at an annual adjustment rate 1t
i
. Let s
t i
denote the accumulated anthropogenic emissions in box i at the beginning of period t. We then
have:
s
t = 1 i
= e
− Nt
i
s
t i
+ a
i
e
t
, 16
where S
i
a
i
= 1 and N is the period length in the
discrete time model.The accumulation of GHGs causes an increase of the equilibrium global mean
temperature. For CO
2
, the temperature increase is expected to be of approximate logarithmic nature,
T
t eq
= T
2
log 1 +
i
s
t i
s¯ ,
17 where T
t eq
is the long-term equilibrium tempera- ture for given concentrations S
i
s
t i
, and T is the
benchmark equilibrium temperature associated with a doubling of total accumulated anthropo-
genic GHGs in the atmosphere compared with the ‘natural’ level s¯ see IPCC, 1992.
The earth surface and atmosphere have a cer- tain warmth capacity. Therefore, the temperature,
denoted by T
t
, slowly adjusts to the long-term equilibrium level:
T
t + 1
= e
− No
T
t
+ 1 − e
− No
T
t + 1 eq
, 18
where o is the annual adjustment rate. However, when calculating impacts of climate
change, the scientific understanding is grossly in- sufficient to warrant even something like a ‘best
guess’ IPCC, 1996a, Section 6.2.13. In general, it is assumed that damages caused by climate
change will outweigh its benefits. The lack of knowledge is unmistakably revealed by the sensi-
tivity analyses carried out with a variety of differ-
10
This value is an average of the numbers found in the literature, ranging from 1 to 6 UStC Cline 1992, Ch. 4.
This implies that a 100 percent decrease in CO
2
emissions corresponds to a price of 400 UStC.
ent damage functions cf. Tol, 1995. These damage functions are supposed to provide a re-
duced form of the many complex damages asso- ciated with climate change, such as the loss of
coastal zones due to sea level rise, the loss of biodiversity, the spread of vector-borne diseases,
and the occurrence of extreme climate events. Most IAMs subtract damages from production
or consumption, or directly from utility. ALICE 2.0 differs from these models and defines a non-
rival
good labelled
‘environmental services’,
which level is given by: b
t + 1
= e
− Nd
b
t
+ 1 − e
− Nd
1 − fT
t + 1
, 19
where T
t
is the global mean surface temperature relative to the pre-industrial level, d is the an-
nual adjustment rate, and f· is the reduced form function that describes long-term losses of
environmental services which we take to be in- creasing on its positive domain, and for which
f0 = 0; see Tol, 1995 for various functions.
11
For ALICE 2.0, f· is taken to be quadratic, and fT
t + 1
= 1 for T
t + 1
a 6°C temperature in- crease. Hence, for a 3°C temperature increase
the usual benchmark case for 2100, the long- term resource amenity decreases by 25 percent.
By taking the value share of the resource amenity as 10 percent n = 0.1 in Eq. 2, this
amounts to a welfare loss equivalent of a 3 per- cent decrease of GDP.
These assumptions on climate change damages imply that, over the next century, welfare in-
crease through economic growth will more than compensate any level of climate change dam-
ages. Concerns for decreasing welfare levels are thus unwarranted. We accept these benchmark
values, not because we adhere to this optimistic view, but because we want two areas of debate
well separated. On the one hand, a debate on the correct estimation of present costs and fu-
ture benefits of climate change regulations to which we do not pretend to contribute, and on
the other hand the question as to the effect on actual resource use of including demography
and using various distributional rules. We will abstain from presenting welfare levels which we
do not think to be reliable, but only show graphs that are directly related to the resource
use, and refer to an early stabilisation of climate change as resource conservation.
3
.
3
. Markets We have the commodity balance for labour,
l
t
= l
t t − 2
+ l
t t − 1
+ l
t t
, 20
and for the consumer good, c
t t − 2
+ c
t t − 1
+ c
t t
= y
t
. 21
The regulatory mechanism for controlling re- source extraction and distributing income from
the natural resource, as well as the correspond- ing regulations, are specified in Section 3. The
Lindahl equilibrium represents an economy gov- erned by a mixture of competitive markets and
policies to achieve collective action. Since the summation of budgets of all generations has to
balance, the sum of the resource income shares should equal the total value of the resource,
that is:
i = 0,…,
b
1 t
H
t
=
t = 1,…,
b
1 t
p
t e
e
t
+ p
t b
b
t
. 22
where b
1 t
is the price deflator for period t rela- tive to period 1, where the income claim is dif-
ferentiated by date of accrual using the super- and subscripts as H
t
= H
t t
+ H
t + 1 t
+ H
t + 2 t
, and this allows defining the period-specific claim as
H
t
= H
t t
+ + H
t t − 1
+ H
t t − 2
. Notice that genera- tion t = 0 only has a claim H
1
to the resource.
3
.
4
. Sa6ings balances For the coming analysis, it is convenient to
distinguish between the value of the environ- mental resource at any point in time,
V
t
=
t = t,…,
b
t t
p
t e
e
t
+ p
t b
b
t
, 23
and the value of total assets to be reserved in any period t for meeting future claims,
11
If a decrease in the amenity b
t
persists, this could be incorporated e.g. in a possible next version of our model by
taking b
t + 1
to constitute the minimum of b
t
and the RHS of the equation.
F
t
=
t = t,…,
b
t t
H
t
=
t = t,…,
b
t t
H
t t −
2
+ H
t t −
1
+ H
t t
. 24
These relations can be written recursively as V
t
= p
t e
e
t
+ p
t b
b
t
+ b
t
V
t + 1,
25 respectively as
F
t
= H
t t − 2
+ H
t t − 1
+ H
t t
+ b
t
F
t + 1
. 26
To implement the intergenerational distribution of claims H
t i
, we introduce a trust fund that reserves the value of total assets. In particular,
income from emission taxes is not directly dis- tributed among the generations alive the pol-
luters, but is attributed to the trust fund for meeting future claims F
t
, so that every generation in every period is paid its share H
t i
, according to Eq. 26. Initially, the trust fund assets equal total
resource income shares, which should sum to the total value of the resource, that is:
F
1
= V
1
. 27
We are now in a position to specify the savings- capital balance, which has a central role in the
scenario analysis. Let S
t + 1 t
and S
t + 2 t
be the sav- ings of generation t at the beginning of period
t + 1 and t + 2, respectively. These are defined by the expenditure budgets when young,
b
t
S
t + 1 t
= w
t
l
t t
+ H
t t
− c
t t
− 8
t t
b
t
, 28
and when middle-aged, b
t + 1
S
t + 2 t
= S
t + 1 t
+ w
t + 1
l
t + 1 t
+ H
t + 1 t
− c
t + 1 t
− 8
t + 1 t
b
t + 1
. 29
The life-cycle budget constraint Eq. 5 ensures that savings are exhausted when old:
0 = S
t + 2 t
+ w
t + 2
l
t + 2 t
+ H
t + 2 t
− c
t + 2 t
− 8
t + 2 t
b
t + 2
. 30
The capital-savings balance equals total sav- ings, which consists of private savings plus the
assets held by the trust fund, with the value of capital, which consists of man-made capital and
the resource value:
S
t t − 1
+ S
t t − 2
+ F
t
= c
t
k
t
+ V
t
. 31
The equation explicitly shows the trust fund’s wealth transfer to future generations through sav-
ings F
t
that are additional to private savings S
t i
. A more extensive description of the set up and
working of a trust fund is given in Gerlagh and Keyzer forthcoming. Validity of the savings-cap-
ital equation for t = 2 is ensured by summation of Eqs. 4, 27 and 28, subtracting Eqs. 12 and
20 multiplied by wages w
1
, Eq. 21, Eq. 7 multiplied by the amenity level b
1
, and Eq. 26. After using Eq. 13 for substitution, we have:
b
1
S
2 1
+ F
2
= b
1
c
2
k
2
+ V
2
, 32
which is the second period savings-capital balance multiplied by the price factor b
1
.
12
For t = 3, …, , validity follows from forward induction.
To complete the model specification, we define equilibrium:
Definition 1. A competitive equilibrium of model Eqs. 1 – 31 is an intertemporal allocation sup-
ported by prices w
t
, p
t e
, p
t b
, 8
t t − 2
, 8
t t − 1
, 8
t t
, c
t
, b
t
, for t = 1, …, , that satisfies the production iden-
tities Eqs. 9 and 10, the environmental identi- ties Eqs. 16 – 19, the first order conditions Eqs.
6 – 8, 11, 13 – 15, the commodity balances Eqs. 20 and 21, the savings identities Eqs. 28
and 29, and the savings-capital balance Eq. 31, for a given environmental regulatory policy that
satisfies Eqs. 25 – 27.
3
.
5
. Scenario specification ALICE 2.0 is calibrated to replicate the so-
called Business as Usual IS92a-scenario IPCC, 1992 for the case that climate change is not
internalised in the economy. This benchmark sce- nario is not displayed in this paper. Four scenar-
ios are specified to show how the demographic change and the intergenerational distribution of
property rights over the environmental resource affect efficient climate change policies vis-a`-vis
emission reductions. The scenarios are sum- marised in Table 2. The first scenario, labelled I,
12
As an exception, generation t = 0 does not reach old age, and thus we have S
2
= 0.
Table 2 Scenario specification
No ageing Ageing included
‘Victims pay’ Environmental resource Scenario I
endowed to first generation: Grandfathering — No ageing
Scenario II Grandfathering — Ageing Grandfathering
‘Polluters pay’ Environmental resource Scenario III
Scenario IV shared with future generations:
Trust fund Trust fund — No ageing
Trust fund — Ageing
assumes that the environmental resource is given, or ‘grandfathered’, to the first generation. This
scenario abstracts from any increase in life expec- tancy. The second scenario, labelled II, includes
the above-described demographic change, in addi- tion to the grandfathering of the environmental
resource to the first generation. Since grandfather- ing implies that future generations will have to
pay if they want to enjoy a clean environment, scenarios I and II may collectively be denomi-
nated ‘Victims Pay’. The third scenario, labelled III, assumes that the property rights over the
environmental resource are equally distributed over all generations by the use of a trust fund
Gerlagh, 1998a, Section 4.3.3, while abstracting from the demographic change of an ageing popu-
lation. The fourth scenario, labelled IV, includes the demographic change of ageing, in addition to
the equal distribution of the environmental re- source over all generations via a trust fund.
Sharing the property rights over the resource im- plies that the polluters will have to buy the per-
mits to emit; the scenarios III and IV are therefore also labelled ‘Polluters Pay’.
Using the formal framework of the previous section, we can now describe the scenarios in
formulas. Scenarios I and III abstract from age- ing, and thus have n
t + 2 t
= 0 for all t. Scenarios II
and IV include ageing as specified in Section 2. Scenarios I and II grandfather the resource to the
first generation, t = 0, which receives all present and future revenues as income:
H =
V
1
, 33
H
t
= for t = 1, 2, …
34 Scenarios III and IV set up a the trust fund so
that all generations receive a claim that is equal to the value of the maximum environmental services
level being unity:
H
t i
= 8
t i
. 35
However, if all generations together receive the value of the potential output as in this equation, it
is not clear whether this distributes the entire actual value of the environmental resource.
Sharing the value of the environmental resource should also satisfy Eq. 27. Now, let us treat the
environment similar to a profit-maximising firm.
13
The value of the actual output may exceed the value of the potential outputs, which is equal to
the value of the claims received by all generations Eq. 35. In this paper, we employ an ad-hoc
rule, and give the surplus between potential and actual output to the first generation,
H
1
= 8
1
+ V
1
−
t = 1,…,
p
t b
, 36
so that Eq. 27 is satisfied. Before giving numerical results, we analyse the
scenarios by means of studying the savings-capital balance Eq. 31. Fig. 1 illustrates the equi-
librium E by plotting the impact of a change on the interest rate for the level of life-cycle savings
and the demand for capital by firms. At equi- librium, cumulative savings S curves match cu-
mulative capital investments K curves. As
13
Profit maximising is only feasible if the resource produc- tion set is convex. This, in general, need not be the case.
Nonetheless, a numerical analysis Gerlagh, 1998a, Section 5.2.4 shows that the overall production set is locally convex,
so that optimisation under restrictions can be applied.
depicted in this figure, capital investment is as- sumed to decrease with an increase in the interest
rate. The rationale behind this relation is that there is little incentive to invest capital when the
interest rates are high. On the other hand, savings are supposed to increase with higher levels of the
interest rate. Such savings behaviour can be ex- plained by the relatively high incentive for post-
poning expenses, allowing profits from saving, when these interest rates are high. From the graph
one can see that if either the savings or capital curve changes, a corresponding change in the
equilibrium interest rate will occur.
14
A potential cause for a major change in future interest rates is the global demographic transfor-
mation, described in Section 2. The answer to the question whether such an alteration in demogra-
phy will increase or decrease the long-run interest rate is ambivalent. In case of a pay-as-you-go
system, the ageing will increase transfers from the young to the old generation. This could induce a
diminishing savings behaviour, which, as can be deduced from Fig. 1, leads to an increase in the
interest rate see Auerbach et al., 1989. If, how- ever, retirement is mainly paid for through private
savings, ageing will increase the need for life-cycle savings in order to allow paying for a longer
retirement period. This is also the case in ALICE 2.0, where we have not modelled a social security
system, and every generation pays for its own retirement. In Fig. 1, ageing shifts the savings
curve upwards, which shifts the equilibrium E to smaller values of the interest rate. The effects can
be substantial, as will be demonstrated in Section 4 by comparison of scenarios I and III, with II
and IV, respectively.
A substantial change in interest rates in an OLG framework can also originate from a vary-
ing public savings behaviour. In the simple two- generation one-good pure exchange model by
Gale 1973, it is shown that a forward transfer of income to future generations can substantially
decrease the interest rate. In a three-period OLG natural resource economy, Howarth and Nor-
gaard 1992 show that the intergenerational dis- tribution of property rights over the resource
affects the interest rate. Gerlagh 1998a, Theorem 4.6 and Gerlagh and Keyzer forthcoming go
further and extend the result of Howarth and Norgaard to an infinite horizon OLG economy
with an environmental resource that has amenity value. They analyse a policy which sets aside part
of the value of the environmental resource for future generations — which can be interpreted as
a transfer of income to those future generations — and show that it reduces the interest rate
similar to Gale’s result. More importantly, how- ever, is that Gerlagh and Keyzer show that the
decreasing interest rate ensures that the welfare of future generations exceeds a reference level set by
a conservation policy that protects the environ- ment by the use of strict environmental measures.
Thereby, the intergenerational distribution of property rights over the environmental resource,
via the use of a trust fund, is effectively used to let the interest rate endogenously decrease to a level
that supports resource conservation.
To see how ‘climate endowments’ affect the interest rate in our model, we interpret the S-
curves and K-curves in Fig. 1 in the following way. Life-cycle savings to pay for retirement S
t t − 1
+ S
t t − 2
are indicated by the curve S1. Demand for capital by private firms, c
t
k
t
, is indicated by the curve K1. Under business as usual, equi-
librium is depicted by E1. Internalising the envi- ronmental capital in the economy raises the
Fig. 1. The equilibria E intersections between savings S curves and capital investment K curves.
14
Note that, though the figure applies to ALICE 2.0 for chosen parameters, in general, the relation between savings
and the interest rate is ambiguous. See Blanchard and Fischer 1989, Section 3.5 for a further discussion on the relation
between interest rates and savings.
capital curve, by V
t
, to K2. If the resource is grandfathered so that F
t
= 0, this results in an
equilibrium with higher interest rates, depicted by E2. If there are publicly held assets F
t
, these increase the saving curve S1 to curve S2 or S3. If
future generations receive claims for an unspoiled environment, so that environmental damages are
compensated, this implies that the publicly held assets exceed the value of the partly spoiled
resource, F
t
\
V
t
, and thus, the equilibrium moves to E3. We will thus expect that grandfathering
raises the interest rate, whereas a trust fund re- duces the interest rate. This will become clear
from a comparison of scenarios I and II with III and IV, respectively.
4. Numerical illustration
