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BALAND, J. M., PLATTEAU, J. P. Halting degradation of natural resources. Oxford: Clarendon Press, 1996.
BARTELMUS, P. Green accounting for sustainable development, In: May, P., SEROA DA MOTTA, R. (eds.). Pricing the planet. New York: Columbia University Press, 1996.
BARROS, P. C. et alii. Reservas naturais e artificiais de swietenia macrophylla king na Amazônia brasileira numa perspectiva de conservação. 1992, mimeo.
BONELLI, R., RAMOS, L. Distribuição de Renda no Brasil: Avaliação das Tendências de Longo Prazo e Mudanças na Desigualdade Desde Meados dos Anos 70.Rio de Janeiro: IPEA, 1993 (Texto para discussão 288).
CHICHILNISKY, G. North-South Trade and the Global Environment. American Economic Review, v. 84, n. 4, p. 851-874, 1994.
DASGUPTA, P. S., HEAL, G. M. Economic theory and exhaustible resources. Cambridge University Press, 1979.
DIXON, J., HAMILTON, K., KUNTE, A. Measuring the wealth of nations In: THE WORLD BANK. Expanding the measure of wealth. Washington, 1997.
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1
See Seroa da Motta (1995) for a general view of these studies and Seroa da Motta and May (1995) for the particular case of forests. It should be noted that the user cost approach was employed with sustainable output rather than net profit measures.2
See, for example, Atkinson et alii (1997) and Seroa da Motta (1993).3
See Seroa da Motta (1997) for detailed indicators on deforestation in Brazil and their respective analysis.4
The new land taxation rules will be effective only in 1997.5
See, for example, Young (1997) for a discussion on this matter and Seroa da Motta (1997) for more details on property right’s assignment in the region.6
Cleared areas are those observed in the period and include legal and illegal clearing.7
Despite the continuous efforts of the UN Statistical Office to harmonize procedures, exhaustion accounting method is still without proper guidance. See for example Bartelmus (1996).8
It also leaves aside the depreciation of human capital. UN Statistical Office efforts on environmental accounting are aimed at correcting this omission.9
These adjustments should be broader than just calculating the depreciation of timber caused by deforestation, as we are doing in the present paper. They should include other factors that can affect the value of a forest and its land. Nevertheless these adjustments were out of the scope of the present study, although very important.10
Although sustainability and sustainable development are related concepts, they are not synonyms. Sustainable development is a much more vague concept that is commonly used in many contexts without a proper definition.11
For the importance of sustainability principles in environmental accounting, see, for example, Seroa da Motta (1994).12
The elasticity of substitution is equal to one.13
Exports equal imports.14
Income defined as the dollar flow which could be consumed from wealth or capital while leaving wealth undiminished.15
This can be defined formally as
, where ρ is the discount rate.16
In this model, ρ equals the marginal product of capital (interest rate) only under steady state growth and zero population growth.17
See Atkinson et alii (1997) and Seroa da Motta (1994).18
Mathematically
19
If the resource is non-renewable and using discrete time, we can express the asset value at time t by
; where p is the price of one unit of the extracted resource (constant over time), q(s) is the quantity extracted at period t, C(q(s)) is the total cost of extraction and T is the period when the resource is exhausted. Expression 
represents the current resource rent.20
Alternatively in continuous time
.21
See, for example, Hartwick and Hageman (1993), Seroa da Motta (1994) and Atkinson et alii (1997) for criticisms on these lines.22
That is, current rent is assumed constant to estimate user cost values in a specific year, although rent can vary each year for which user cost is estimated.23
Apart from being difficult to estimate, this function may vary over time and over place. Therefore, such mathematical simplification may loose economic meaning for prediction purposes. We thank this point to Salah El Serafy.24
For a formal treatment of virgin forests as non-renewable resources, see Vincent (1997, p.30).25
We include in the open access resource definition situations where property rights over natural resources are defined by law, but there is no enforcement or monitoring over them.26
The definition of property rights is a necessary but not a sufficient condition for efficient exploitation of a natural resource. See Dasgupta and Heal (1979) for a formal treatment on necessary and sufficient conditions for efficient exploitation of natural resources.27
See the appendix for a simple model illustrating this situation.28
Refer to the first part of this paper and Schneider (1995) for an explanation of such mechanisms.29
For a model on this process, see Young (1997). He characterizes this type of property right regime as quasi-open access.30
We have pointed previously the limitations of this analysis for a sub-optimal situation. Nevertheless there is no alternative method developed for the measurement of depreciation in such cases.31
In Paragominas (Pará) in 1990, 63% of sawmills had some involvement with extraction. By 1995, 84% of small firms and 79% of large firms participated in timber extraction. On the other hand, in Tailândia (Pará), 23% of sawmills were involved with extraction in 1990, while by 1995 that number increased to 75%. See Stone (forthcoming) for more details on the process of vertical integration of sawmills in the Brazilian Amazon.32
See, for example, Funatura/Itto (1993), Prado (1995) and Seroa da Motta (1997).33
This is a really important matter. If the Brazilian Amazon was smaller we would get a higher value for the depreciation.34
With that ban the Brazilian government understood that the inclusion of mogno at the Annex 2 of the CITES was not necessary as proposed in the last general conference in 1997.35
Ideally we would have data on cost, price, stock and output for each specie of timber in the Amazon. We would then calculate the depreciation charge for each specie separately. Due to the lack of data availability, this analysis is not possible.36
We thank Michael Linddal for pointing this out.37
This is specially important if comparisons on depreciation values are going to be made among developed and developing countries. Dixon, Hamilton and Kunte (1997) suggest values in the 2%-4% range for developed countries. However, according to Seroa da Motta (1988) capital opportunity cost in Brazil has been historically around 10%.38
In many cases the timber extracted in some state is converted into processed wood in some other state. For the sawmill there is no additional transaction cost, for a given distance, to bring timber from another state for processing purposes.39
That covers states of Amazonas, Pará, Rondônia, Amapá, Roraima, Acre, Tocantins and Maranhão. Mato Grosso State, here not considered, is not relevant in terms of rain forest against the other states.40
Stone (1998) adopted a 20% rate since that was the bank rate prevailing in 1995 in Brazil after the Real stabilization plan.41
Although Verissimo et alii (1992) estimated that for every cubic meter of wood that is logged, in the region of Paragominas in Pará state, there are two cubic meters that are lost, one cannot generalizes that for the whole region. Illegal logging figures is still more controversial since, as discussed earlier, clearing licenses legalizes logging output.42
Vincent (1990), for example, uses values varying from 1.5 to 4.5 while Vincent (1997) adopts value of 3 for Malaysia. In principle, other region’s elasticity values may not keep any relevance for the Amazonian region. As we will observe later, higher elasticity values leads to results similar to those here employed.43
Remember that if β=0 the formula used is pq-c(q), although it can also be argued that net price method is the special case of zero rate of discount.44
This fact was already exposed in graphical terms by El Serafy (1989).45
That was also observed in estimations for natural capital depreciation in Brazil for 1980/90, see Seroa da Motta (1995).46
Even if lower capital costs were taken in Stone’s estimations, large firms would still face a decline profitability.47
Value added figures for timber extraction were not available for the region from national accounts, therefore, we constructed these figures using the survey data used for the depreciation estimates. It should be noted that we are measuring value added as a GDP measure, that is, gross of capital costs.48
Seroa da Motta and May (1995) had already brought about this issue since user cost measures were also very small for their estimates.49
See Chichilnisky (1994) and Ferraz (1997) for a discussion of this issue.50
See Seroa da Motta (1997) for the rationale of this initiative and its institutional and legal problems.51
For a detailed discussion on this result see Weitzman (1974).)
