The Influence of Property Rights on Cutting Decisions in
the Forestry Sector
Livia Bizikova (progbizi@savba.sk) and Birgit Friedl (birgit.friedl@uni-klu.ac.at)
December 10, 2003
Introduction
Generally, the value of a forest cannot be reduced just to its timber value, but additional values
such as providing wildlife habitat, watershed protection, or natural areas for recreation could be
recognized. However, the assessment of forest management activities is nearly exclusively
focusing on maximization of forest value, namely the timber value. One explanation for this is
that the inclusion of additional forest values is compromised by the hardship to describe them in
monetary values. Moreover, the inclusion of non-timber values can create non-convexities, which
leads to problems with maximization in the model analyses1.
For instance, in the case of transition countries of Central and Eastern Europe the property over
the forest is gradually shifted from public to private ownership. Therefore, it is of key interest
whether this change in property rights does imply changes in forest management. One trend
recognized is that the degree of both legal and illegal cutting is increasing and the coordination
between the different stakeholders becomes more complicated.
It is known from resource economics that public forest ownership can ensure also recreational
and other existence and option values to a higher extent than private ownership. Unfortunately,
the allocation of different function of forests between competing uses becomes more and more
difficult as society’s demand for all uses have increased. On the other hand, this wider
understanding of forest values requires management at a lager scale which cannot be restricted by
the boundaries of publicly owned land. Taking these into account, one solution might be the
imposition of taxes or other measures, which try to regulate private forest owners. However, these
instruments are usually hardly accepted and are often not designed to reach full internalization of
all cost of lost forest values.
In our model, we try to simulate the impact of different ownership on the timber production and
we also take account of the recreational value of the forest. More specifically, we analyze the
changes in the utility of households related to the ownership and imposed taxes on the forestry
sector. In the case of public ownership, we assume that the authority is aware of the households’
interest to avoid the cutting of the forest by means of the concept of marginal willingness to pay
(MWTP). In case of private forest, we use the value of the MWTP to determine the tax rate
necessary to internalize the loss in forest values.
1
Kant, S. 2003. Extending the boundaries of forest economics. Forest Policy and Economics 5, 39-56.
1
This short paper is organized as follows. First, the inclusion of an externality due to a diminished
forest stock into the household’s utility maximization problem is discussed. Afterwards, different
property rights regimes for the forest sector are discussed as well as their implications for the
profit maximization problem of the forest owner. Then, the equations of the model which are
identical to the 2 good – 2 factor closed economy model are briefly reviewed. Building on that the
model calibration is lined out. Thereafter, some policy and parameter simulations are undertaken.
In a final section, shortcomings and possible extensions are discussed.
The Model
As in the reference model called ‘open’, we have a 2 factor – 2 goods (=sectors) – 1 household
model with both Cobb-Douglas utility and production function with unitary elasticity of
substitution and constant returns to scale respectively. Compared to the standard model, two
major changes can be observed. First, utility is dependent on the remaining forest stock after
cutting. Second, property rights are defined by a scale parameter which can take any value
between zero and one. Let us discuss briefly each extension.
Utility is not only dependent on the consumption of the forest product (index 1) and all other
goods (index 2) but also on the value of the remaining forest stand, denoted by µF. Let FF be the
forest stand if no tree is cut. Then, the remaining forest stand is defined by F  ( FF  X 1 ) / FF ,
where X1 stands for the output in sector 1 (forestry). Thus, when assuming a Cobb-Douglas
utility function with constant returns to scale, utility is defined by:
U (C1 , C 2 , F )  C1 C 2
b
1b
e  F ,   0.
(1)
As seen from this utility function, overall utility is inversely related to the size of the remaining
forest. In other words, if the forest is not cut (and therefore the output of the forest sector is zero),
the household’s utility is equal to U (C1 , C 2 , F )  C1 C 2
b
1b
1 . On the other hand, if a positive
value is cut, the factor e  F will be smaller than one.
To assign a value to the loss in terms of utility by a reduction in the remaining forest, it is
convenient to derive the households’ marginal willingness to pay for cutting one unit less of the
forest. With respect to that, one has to rephrase the dual to the utility maximization problem
which is an expenditure minimizing problem subject to a utility constraint. Solving this problem
gives the following expenditure function:
E P1 , P2 ,U   B  P1  P2
b
1b
 U  e   F , where
B  b b (1  b) b 1 .
(2)
Accordingly, the households’ marginal willingness to pay to avoid an incremental increase in F is
E P1 , P2 ,U 
b
1b
   B  P1  P2  U  e   F .
F
(3)
As pointed out before, although the household is negatively affected by cutting the resource
stock, it does not recognize that it could reduce the negative impact by the diminished forest by
consuming less of the forest product.
2
The second major extension refers to the inclusion of property rights. We shall distinguish two
opposite property right regimes. Either the forest is owned privately or by the state. According to
that, the damage of the forest output on the representative household is either not considered at all
(in the case of private forest ownership), taken fully into account by means of the marginal
willingness to pay (MWTP) stated by the consumer in order to avoid this impact (case of public
ownership), or the forest industry is taxed at a tax rate equal to this MWTP (case of private
ownership with taxation). Both property rights and taxes are modeled by means of a dummy
variable (actually an endogenous one), denoted by m in the first case and t in the second:
t1, 2  m1, 2  0, in case of private property
t1, 2  m2  0, m1  1, in case of public property
t1  1, m1, 2  t 2  0, in case of private property w ith tax
property rights
(4)
Accordingly, the supply of firm i is determined by
Pi  t  TAX yield 
i W , R, X i 
 m  MWTP ,
X i
where MWTP 
E P1 , P2 ,U  F
 0 and TAX yield   MWTP  0 .
F
X 1
(5)
Thus, if the forest sector is in private ownership, we have as in the standard model that price
equals marginal cost. Under public ownership, however, the firm has to bear an extra cost which
is just equal to the marginal willingness to pay of the household. In the third case, a tax drives a
wedge between marginal costs and price such that the private forest industry behaves just as
under public ownership.
The remaining equations are very similar to the equilibrium conditions in the standard closed
economy model2. Disposable income is changed by the transfers on behalf of the government:
Y  W  N  R  ( K H  K G )  (t1  TAX yield  X 1  m1  MWTP  X 1 )
Due to the Cobb-Douglas utility function, both household demand and factor demand remain
unchanged:
Ci 
bi  Y
’
Pi
(6)
 ai  R
N i  A 
 1  ai .W
1
i
1 ai



 ai  R
 X i , K i  A 
 1  ai .W
1
i



 ai
 Xi .
(7)
Also market clearing in both factor and output markets look the same:
C   X
i
i
2
i
i
,
N
i
i
 N,
K
i
 K H  KG .
(8,9)
i
Derivation of the equations as well as the GAMS code can be obtained from the authors upon request.
3
Due to the change in the utility function as well as in the expenditure function, equivalent
variation is calculated according to the following:
EV  B  P1  P2
b
1b
 (U  e   F  U  e   F ), where
B  b b (1  b) b 1 .
(10)
The equivalent variation gives the change in budget necessary to keep utility of the household
before and after a change in prices just equally well off, for given initial prices. Thus, U refers to
benchmark utility and F to the benchmark remaining forest stock. Thus, a positive value implies
a decrease in utility while a negative value implies an increase.
Model Calibration
For the numerical simulation, a Social Accounting Matrix (SAM) is used as depicted in Table 1.
Note that sector 1(forestry) is labor intensive while sector 2 (all other goods) is capital intensive.
Moreover, it is worth noting that capital is an aggregate of both natural and manmade capital. For
the forestry sector, capital is interpreted as natural capital (the forest resource stock), and for the
other goods sector as manmade capital. Corresponding to this SAM, the parameters of the utility
function and the production function are given in Table 2.
Table 1: Base case SAM
Forest owned privately
X1
X2
N
K
H
G
Total
Forestry (X1)
60
60
Other products (X2)
120
120
Labor (N)
45
30
75
Capital (K)
15
90
105
Households (H)
75
180
105
0
Government (G)
Total
60
120
75
105
180
0
Starting from that, we will analyze three factor of influence: (i) the ownership structure, (ii) the
influence of the scaling factor of the cutting intensity, and (iii) the influence of the available
forest stock. Let us discuss each in turn.
4
Table 2: Parameter Values (baseline)
Parameter
Values
Utility elasticity of good 1, b
0.33
Utility elasticity of good 2, 1- b
0.67
Scaling factor in utility function, BB
2.07
Reference forest stock, FF
600
Scaling factor of cutting intensity, µ
-0.01
Output elasticity of labor (good 1), A(G1)
0.75
Output elasticity of labor (good 2), A(G2)
0.25
Scaling factor in production function, AA(G)
1.75
Benchmark utility, Ū
180
Benchmark remaining forest stock, F
0.9
MWTP dummy, m
0
Tax dummy, t
0
(i) Ownership structure
The ownership structure is grasped by the MWTP dummy. If the forest is in private property, the
forest owner is maximizing the profit from cutting the forest. This is the baseline case depicted in
column 1 of Table 3. On the other hand, if the forest is in public ownership (which means that the
government is the owner), the aim is not only to maximize profits but also to take account of the
negative impact of cutting on the utility of the representative household (column 3). Finally, in
the case that the forest is partly owned privately and partly publicly, we refer to it as ‘mixed’
ownership.
Table 3: Impact of Ownership Structure
Simulations for different type
of ownership*
Private
Mixed
Public
Private
Mixed
0
0.5
1
0
0.5
0
0
0
1
0.5
Output sector 1
(Forestry), X1
60
59
58
58
58
Output sector 2
(Other goods), X2
120
121
122
122
122
Disposable income, Y
180
181
182
182
182
Equivalent variation, EV
0.00
0.02
0.06
0.06
0.06
Price of good 1, P1
1.00
1.02
1.04
1.04
1.04
Price of good 2, P2
1.00
1.00
0.99
0.99
0.99
0
0
0
0.062
0.031
0.000
0.000
0.000
3.600
1.802
m1 (if MWTP considered = 1)
t1 (if tax imposed = 1)
Tax rate
Total tax
*µ=-0.01, FF=600
5
By comparing these three cases, it can be seen that the price of sector 1 increases the more the
forest is in public ownership. Correspondingly, the output of sector 1 is falling. The reverse
effects can be recognized in sector 2. Overall, the disposable income is increasing when one
moves from private to public ownership. What is worth noting in that case is that the equivalent
variation is increasing which implies that utility is actually decreasing. The reason for this is that
the increase in price 1 seems to reduce utility by more than the rise in the remaining forest stock
does increase utility.
Finally, in column 4 and 5, the outputs under private and mixed ownership are taxed according to
a rate equal to the marginal willingness to pay to avoid an additional unit of destruction of the
forest on behalf of the households. Not surprisingly, in either case the resulting prices and
quantities are just the same as in the public ownership case. Tables 4 and 5 give the
corresponding SAMs for column 3 (public ownership) and column 4 (private ownership plus tax).
Tables 4, 5: SAM for different ownership structures and tax rates
Forest owned publicly
X1
X2
N
K
H
Forestry (X1)
Other products (X2)
Total
G
58
58
122
122
Labor (N)
44
31
75
Capital (K)
14
91
105
Households (H)
75
Government (G)
90
15
15
15
Total
58
122
Forest owned private + tax
X1
X2
75
N
105
180
K
H
Forestry (X1)
Other products (X2)
165
0
Total
G
58
58
122
122
Labor (N)
44
31
75
Capital (K)
14
91
105
Households (H)
75
180
105
0
Government (G)
Total
58
122
75
105
180
0
6
(ii) Importance of the remaining forest stock to the household
The value the representative household attaches to the remaining forest stock F is measured by
the negative value of µ. The larger this value in absolute terms, the smaller will be both the
 F
scaling factor e
and the resulting utility level. Table 6 gives the result for different cases of µ
where its value is increasing from left to right.
The larger |µ|, the smaller is the output in forestry and the larger in all other goods. This also
translates to a decline in price 1 and an increase in price 2. Because the forest sector is assumed to
be labor intensive and its demand for labor is falling, the wage rate is declining relative to the
interest rate. The effect of all that is a decline in the remaining forest stock (see bottom row)
which implies an increasing MWTP to avoid an additional unit of the utility decreasing cutting of
the forest. In line with this is also the increase in the disposable income.
However, although the MWTP is increasing with the absolute value of µ, the equivalent variation
is negative (but increasing) for values of |µ| between 0.005 and 0.1, but then starts to turn positive
for values of |µ| larger than 0.1. Thus, compared to the base case, utility decreases if |µ| gets too
large. The reason is that in the case of a very environmentally conscious household (as depicted
by a |µ| larger than 0.1) the price of the forest product increases by up to roughly 40% which has
a very negative impact on consumption possibilities and therefore utility. Therefore, this negative
impact on utility dominates the positive effect of a reduced output in sector 1 on the remaining
forest stock F.
Table 6: The impact of the scaling factor for cutting intensity
Base case
Scaling factor of
cutting intensity, µ
Output sector 1
(Forestry), X1
-0.1
Simulations (for Public Ownership)
P = MC - MWTP, MWTP < 0.
-0.005
-0.05
-0.1
-0.15
-0.3
-0.707
60
60
59
58
57
55
49
Output sector 2
(Other goods), X2
120
120
121
122
123
127
139
Disposable income, Y
180
180
181
182
183
187
204
Equivalent variation,
EV
0.00
-14.75
-7.94
-0.10
8.07
34.58
124.9
Wage rate, W
1.00
1.00
0.99
0.97
0.96
0.94
0.91
Interest rate, R
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Price of good 1, P1
1.00
1.00
1.02
1.04
1.07
1.14
1.39
Price of good 2, P2
1.00
1.00
1.00
0.99
0.99
0.98
0.98
-0.062
-0.003
-0.031
-0.062
-0.093
-0.187
-0.453
0.900
0.900
0.902
0.903
0.905
0.909
0.918
Marginal WTP,
MWTP(G1)
Remaining forest
proportion in %, F
7
(iii) The size of the exogenous forest stock
Due to factors exogenous to the model, such as extreme weather events, the forest stock could be
destroyed. In that case, keeping the cutting rate at a high level can lead to extinction of the forest.
Therefore, the household’s utility is reduced by a larger negative externality (as measured
indirectly by the remaining forest stock) if the forest stock decreases.
The base case refers again to private ownership of the resource, the corresponding numbers under
public ownership are given in column 4 (numbers in italics). The table should be read once by
going left from that column (thereby decreasing the forest stock) and once by going right
(increasing the forest stock relative to FF = 600). If FF is decreased, the MWTP is increasing, as
well as the disposable income does because the transfers to the household increase in the case of
public ownership. Moreover, the equivalent variation is declining which implies an improvement
in terms of utility. On the other hand, if the forest stock is increasing, maybe as a consequence of
good growing conditions, the MWTP falls to virtually zero and therefore the disposable income is
not increased by transfers from the government. Moreover, the equivalent variation is decreasing
a little and approaches zero (as in the case of private ownership without tax).
Table 7: The impact of the size of the forest stock
Base
case
Simulations (for public ownership)
P = MC - MWTP, MWTP < 0.
Reference forest
stock, FF
600
100
300
600
1000
3000
6000
Output sector 1
(Forestry), X1
60
50
56
58
59
60
60
Output sector 2
(Other goods), X2
120
135
124
122
121
120
120
Disposable income, Y
180
199
184
181
181
180
180
Equivalent variation,
EV
0
-4.12
-0.39
-0.1
-0.03
0
0
Wage rate, W
1
0.91
0.95
0.97
0.98
0.99
1
Interest rate, R
1
1
1
1
1
1
1
Price of good 1, P1
1
1.313
1.09
1.04
1.03
1.01
1.00
Price of good 2, P2
1
0.99
0.99
0.99
0.99
0.99
0.99
-0.062
-0.381
-0.124
-0.062
-0.037
-0.012
-0.006
0.9
0.496
0.812
0.903
0.941
0.98
0.99
Marginal WTP,
MWTP(G1)
Remaining forest
proportion in %, F
8
Summary and outlook
The present model is an attempt to analyze the impact of different forest ownership structures on
the economic performance of the forest sector and other sectors, as well as their influence on the
utility of the households. Moreover, the sectoral changes as a consequence of the tax imposed
under different property regimes are included in the paper. To keep analysis straightforward, the
management of this natural resource was analyzed in a static two sector CGE model where one
sector uses a natural resource as input and the decrease in the resource stock affects negatively the
households. The preferences of the households for the remaining forest were grasped by means of
their willingness to pay in order to avoid the cutting of an additional unit of the forest.
The simplifications made in the model setup could influence the results and their implications for
forest management. One important basic assumption was the substitutability of natural and
manmade capital, which allows any shift from one sort of capital to another. With respect to other
factors of production, one should also take account of the value of land since a certain forest stand
can easily be converted into agricultural land. Moreover, because of just two production sectors
used in the model, the forestry industry constitutes a rather dominant sector relative to the rest of
the economy. By the inclusion of more sectors, a more realistic balance of the sectors could be
created.
The inclusion of forest resources in a static CGE model is not able to describe the dynamics of
both forest growth and its development. This is valid not only for natural increment over time, but
also the occurrence of extreme events such as floods, storms etc. An important role for the
condition of the forests plays the forest management activities implemented. The character, scale
and probably also the quality of the management activities are influenced by the profits obtained.
In our model, the imposed tax influenced the production of the forestry sector, but we cannot
estimate the change in management activities, which could have a significant impact on the
further development of a forest.
Since our model is a closed economy model, we did not take account of other determinants of
prices of the forest good, such as the exchange rate or the price of wood in the world market.
Those determinants could cause changes in the output of the sector but also in factor intensities.
Moreover, other values of the forest which could be described by option and existence values
could enrich this approach.
For the further development of our model it is necessary to include real data from SAMs to better
take account of the size of the forest sector relative to other sectors, the distribution of the factors
between sectors and the opportunity cost of land. The quality of our results can be improved also
by the diversification between households, for instance by distinguishing groups according to
differences in their dependence on the forestry sector.
9
Appendix: GAMS Code
$title A FORESTRY GAMS model
$stitle Forest Value in the Utility Function, Forest is Publicly or
Privately Owned
SET
G
GOODS
/ G1, G2 /
* good 1 = forestry product, good 2 = all other goods
H
HOUSEHOLDS
/ RICH /
PARAMETER
/ G1
A(G)
OUTPUT ELASTICITY OF LABOR
0.75, G2 0.25 /
PARAMETER AA(G) SCALE FACTOR IN PRODUCTION FUNCTION;
AA(G)=A(G)**(-A(G))*(1-A(G))**(A(G)-1);
DISPLAY AA;
PARAMETER BB(H)
SCALE FACTOR IN UTILITY FUNCTION FOR HOUSEHOLD H
/ RICH 2.067859818 /
TABLE DG(H,G)
UTILITY ELASTICITY OF GOODS FOR HOUSEHOLD H
G1
RICH
0.3333333333333333
PARAMETER TG(G)
/ G1
0, G2
0
PARAMETER LH(H)
/ RICH
PARAMETER CG
/
0.6666666666666667
TAX RATE ON GOODS
/
LABOR ENDOWMENT OF HOUSEHOLD H
75 /
PARAMETER CH(H)
/ RICH
G2
CAPITAL ENDOWMENT OF HOUSEHOLD H
90 /
CAPITAL ENDOWMENT OF GOVERNMENT
15 /
PARAMETER STRANS(H) SHARE OF TRANSFERS ACCRUING TO HOUSEHOLD H
10
/ RICH
1.00 /
PARAMETER C(G)
COST FUNCTION CONSTANT;
C(G)=(A(G)**(-A(G)))*((1-A(G))**(A(G)-1))/AA(G);
DISPLAY C;
PARAMETER MU
SCALING FACTOR OF FOREST CUTTING INTENSITY
/ -0.1 /
PARAMETER FF TOTAL FOREST STOCK
/ 600 /
PARAMETER FBENCH
BENCHMARK FOREST FRACTION
/ 0.90 /
PARAMETER UCONST(H) EXPENDITURE FUNCTION CONSTANT;
UCONST(H)=(PROD(G,DG(H,G)**(-DG(H,G))))/BB(H);
PARAMETER PGBENCH(G)
/ G1 1.000,
G2
BENCHMARK PRICES OF GOODS
1.000
/
SCALAR WBENCH BENCHMARK PRICE OF LABOR
/ 1.000 /
SCALAR RBENCH BERNCHMARK PRICE OF CAPITAL
/ 1.000 /
PARAMETER QBENCH(G)
/ G1
60, G2
BENCHMARK QUANTITIES OF GOODS
120 /
PARAMETER LGBENCH(G)
BENCHMARK ALLOCATION OF LABOR
/ G1 45, G2 90 /
PARAMETER CGBENCH(G)
BENCHMARK ALLOCATION OF CAPITAL
/ G1 15, G2 90 /
PARAMETER UBENCH(H)
/ RICH
BENCHMARK UTILITY OF HOUSEHOLD H
180 /
PARAMETER WTPCONST(G) WTP Factor
/ G1 0, G2 0 /
POSITIVE VARIABLES
W
PRICE OF LABOR
11
R
PRICE OF CAPITAL
P(G)
PRICE OF GOOD G
Q(G)
OUTPUT OF GOOD G
VARIABLES
F(G)
REMAINING FOREST
CD(H,G)
CONSUMPTION OF GOOD G BY HOUSEHOLD H
RL(G)
UNIT LABOR DEMAND IN SECTOR G
RC(G)
UNIT CAPITAL DEMAND IN SECTOR G
Y
TOTAL DISPOSABLE INCOME
YH(H)
DISPOSABLE INCOME OF HOUSEHOLD H
GNP
GROSS NATIONAL INCOME AT FACTOR COST
U(H)
UTILITY OF HOUSEHOLD H
EV(H)
EQUIVALENT VARIATION FOR HOUSEHOLD H
TAX
TOTAL TAX BILL
MWTP(G,H)
MARGINAL WILLINGNESS TO PAY
PMWTP(G)
PRICE MARK UP MWTP
TAXR(G)
PFAC(H)
TAX RATE
PRICE FACTOR
EQUATIONS
YDEF
DEFINITION OF TOTAL DISPOSABLE INCOME
* Associated free variable: Y
DISP(H)
DEFINITION OF DISPOSABLE INCOME OF HOUSEHOLD H
* Associated free variable: YH(H)
NATIO
DEFINITION OF GNP
* Associated free variable: GNP
TAXDEF
DEFINITION OF TOTAL TAX BILL
* Associated free variable: TAX
12
UTILITY(H) UTILITY FUNCTION OF HOUSEHOLD H
* Associated free variable: U(H)
EQUIVAR(H) DEFINITION OF EQUIVALENT VARIATION OF HOUSEHOLD H
* Associated free variable: EV(H)
PRICEFAC(H) PRICE PART IN EQUIVALENT VARIATION
* Associated free variable: PFAC(H)
PRICEMUP(G) PRICE MARK UP FROM MWTP
* Associated free variable: PMWTP(G)
DEMAND(H,G) DEMAND FOR GOODS BY HOUSEHOLD H
* Associated free variable: CD(H,G)
SUPPLY(G) UNIT LOSS FOR GOOD G
* Associated positive variable: Q('G1')
TAXRATE(G)
TAX RATE EQUALS MTWP
*Associated Variable: TAXR(G)
MARKET(G) MARKET CLEARING CONDITION FOR GOOD G
* Associated free variable: P(G)
LABDEM(G)
UNIT DEMAND FOR LABOR IN SECTOR G
* Associated free variable: RL(G)
CAPDEM(G)
UNIT DEMAND FOR CAPITAL IN SECTOR G
* Associated free variable: RC(G)
LABMARK
MARKET EQUILIBRIUM FOR LABOR
* Associated free variable: W
CAPMARK
MARKET EQUILIBRIUM FOR CAPITAL
* Associated free variable: R
FEQU(G)
FOREST STOCK MINUS FOREST OUTPUT
* Associated free variable: F(H)
EXTRAC(G,H)
EXTRA COST (MWTP times dF divided by dX1);
* Associated free variable: MWTP(G,H)
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YDEF..
Y=E=SUM(H,YH(H));
DISP(H)..
YH(H)=E=W*LH(H)+R*(CH(H)+CG)+STRANS(H)*
(TAX-SUM(G,PMWTP(G)*Q(G)));
* Disposable income is increased by a transfer (equal to tax income of
* the government) or by the transfer from the price wedge (caused by
the * MWTP part on the supply side)]
NATIO..
GNP=E=SUM(H,W*LH(H)+R*(CH(H)+CG))+TAXSUM(G,PMWTP(G)*Q(G));
TAXDEF..
TAX=E=SUM(G,TAXR(G)*Q(G));
UTILITY(H)..
U(H)=E=BB(H)*PROD(G,CD(H,G)**DG(H,G))*exp(MU*F('G1'));
EQUIVAR(H)..
EV(H)=E=UCONST(H)*(PROD(G,PGBENCH(G)**DG(H,G)))*
(UBENCH(H)*exp(-MU*FBENCH)-U(H)*exp(-
MU*F('G1')));
* EV gives the change in the expenditure function, given the prices at
* the initial level, necessary to make the HH just as well off as in
the
* base case
PRICEFAC(H)..
PFAC(H)=E=PROD(G,PGBENCH(G)**DG(H,G));
* the price part of the expenditure function
EXTRAC(G,H)..
FF*MWTP(G,H)=E=MU*BB(H)*UCONST(H)*U(H)*
exp(-MU*F(G))*PFAC(H);
* define the marginal willigness to pay as the derivative of the
* expenditure function with respect to the forest output
PRICEMUP(G)..
PMWTP(G)=E=WTPCONST(G)*SUM(H,MWTP(G,H));
* increase the MC of the forest product by the MWTP
DEMAND(H,G)..
P(G)*CD(H,G)=E=DG(H,G)*YH(H);
SUPPLY(G)..
C(G)*W**A(G)*R**(1-A(G))=G=P(G)+PMWTP(G)-TAXR(G);
* output price is decreased by either the MWTP (if WTPCONST=1) or the
* tax (if TG=1)
TAXRATE(G)..
TAXR(G)=E=-TG(G)*SUM(H,MWTP(G,H));
* the tax rate equals the negative of the MWTP
MARKET(G)..
Q(G)=E=SUM(H,CD(H,G));
LABDEM(G)..
RL(G)=E=C(G)*A(G)*W**(A(G)-1)*R**(1-A(G));
CAPDEM(G)..
RC(G)=E=C(G)*(1-A(G))*W**A(G)*R**(-A(G));
LABMARK..
SUM(H,LH(H))=E=SUM(G,RL(G)*Q(G));
CAPMARK..
SUM(H,CH(H))+CG=E=SUM(G,RC(G)*Q(G));
FEQU(G)..
F(G)=E=(FF-Q(G))/FF;
* how much of the forest stock remains after cutting
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MODEL OPEN SIMPLE OPEN-ECONOMY CGE MODEL
/ YDEF.Y, UTILITY.U, EQUIVAR.EV, NATIO.GNP, DISP.YH, TAXDEF.TAX,
DEMAND.CD, SUPPLY.Q, LABDEM.RL, CAPDEM.RC, LABMARK.W, CAPMARK.R,
MARKET.P, FEQU.F, EXTRAC.MWTP, PRICEFAC.PFAC, TAXRATE.TAXR,
PRICEMUP.PMWTP / ;
* NUMERAIRE
R.FX=1.000 ;
* BOUNDS ON VARIABLES
W.LO=0.01;
CD.LO(H,G)=0.01;
F.LO(G)=0.01;
* INITIAL VALUES
W.L=1.00;
Y.L=180;
YH.L(H)=180;
Q.L(G)=QBENCH(G);
SOLVE OPEN USING MCP;
DISPLAY GNP.L, Y.L, YH.L, F.L, FBENCH, U.L, UBENCH, EV.L, Q.L, CD.L,
W.L, R.L, RL.L, RC.L,TAX.L, P.L, MWTP.L;
* COMPARATIVE STATICS:
* change value of forest stock and of forest factor resp.
*FF=600;
*FBENCH=0.8;
* change value of valuation of remaining forest (the larger MU, the
more
* important to households
*MU=-0.15;
TG('G1')=0;
* change labor intensity of forestry sector
*A('G1')=0.5;
* switch on public ownership
WTPCONST('G1')=1;
SOLVE OPEN USING MCP;
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DISPLAY GNP.L, Y.L, YH.L, F.L, U.L, EV.L, Q.L, CD.L, W.L, R.L, RL.L,
RC.L,P.L, MWTP.L,PMWTP.L, TAXR.L,TAX.L;
$ONTEXT
* switch off public ownership; induce private forest owner to behave in
* best interest of all by taxing the output
WTPCONST('G1')=0;
TG('G1')=1;
SOLVE OPEN USING MCP;
DISPLAY GNP.L, Y.L, YH.L, F.L, U.L, EV.L, Q.L, CD.L, W.L, R.L, RL.L,
RC.L,P.L,
MWTP.L, PMWTP.L, TAXR.L, TAX.L;
*COMPARATIVE STATICS:
*change value of forest stock and of forest factor resp.
*FF=300;
*FBENCH=0.8;
*change value of valuation of remaining forest (the larger MU, the more
*important to households
*MU=-0.005;
$OFFTEXT
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