Baseline scenario calculations (i.e. a carbon price of 0 US$/tC is assumed) show that close to 200 mil ha or around 5% of todays forest area will be lost between 2006 and 2025, resulting in a release of additional 17.5 GtC to the atmospheric carbon pool. The baseline deforestation speed is decreasing over time, which is caused by a decreasing forest area in regions with hight deforestation pressure. In the year 2025 the annual deforested area decreases to 8.2 million hectares, compared to 12.9 million hectares in 2005. By the year 2100 deforestation rates decline to some 1.1 million hectares. According to the base line scenario, today's forest cover will shrink by around 500 million hectares or by more than 1/8 within the next 100 years (figure 1).

Carbon emissions from deforestation in 2005 is 1.1 GtC/year and decreases to 0.68 GtC/year in 2025 and further to 0.09 GtC/year in 2100. The accumulated carbon release during the next 100 years amounts to 45 GtC which is 15% of the total carbon stored in forests today. To bring deforestation down by 50%, incentives of 6 US$/tC/5 year or a land clearance tax of between 9 US$/tC and 25 US$/tC would be necessary, depending whether the harvested wood is burned on the spot (e. g. slash-and-burn agriculture) or sold. In the latter case, a higher carbon tax of up to 25 US$/tC is necessary to effectively reduce incentives to deforest, to a degree that cuts overall global deforestation by 50%. If the wood is further used and converted into products, only 18% of the biomass could be saved by a carbon price of 9 US$/tC, caused by the compensating effect of an income by selling wood and a longer time-period for releasing carbon. On the other hand, if the carbon price is 25$/tC and the wood is assumed to be slash burned, the reduction of deforestation calculated to be 91% (figure 1 and 2). On a first sight it seems, that incentive payments might be more effective, than taxation. However, incentives payment contracts have to be renewed every 5 year for the actual standing biomass and the change of biomass has to be known to detect a breach of the contract, while a deforestation tax will be payed once for the harvested biomass once detected by targeted earth observation systems (see figure 3 and 4). In the latter, transactions costs for implementing avoided deforestation are small.

The assumption, that either only slash burn or all wood will be sold is unrealistic. Thus, a scenario where Latin America has 90% slash burn and 10% selling, Africa 50% slash burned and 50% selling and in the remaining area 10% slash burned and 90% selling, was examined. Under such scenario assumptions a carbon tax of 12 $/tC will cut deforestation in half. Also the assumption, that a carbon price will stay constant over time may not be close to reality but it can be used to see the long-term influence of a given carbon price.

We differentiate between the following cases:

Baseline: Introducing no carbon price.

Incentives: Introducing a carbon price which will be payed periodic for the carbon stored in the standing forest biomass.

All: Payments are done, without considering the effectiveness of the payment, in all regions.

Region: Payments are done in regions where the payments protect forest against deforestation.

Affected: Payments are done for forests where the payments protect them against deforestation.

Tax: Introducing a carbon price which has to be paid for releasing the stored carbon to the atmosphere.

Burn: All wood will be burned immediately.

Sell: All harvested wood will be sold.

Burn/Sell: A share of the wood will be burned and the other part sold.

The effectiveness of introducing a carbon price to influence deforestation decisions depends largely on the levels set for carbon prices, apart from considerations of political feasibility and implementability. Low prices have little impact on deforestation rates. During the 21^st century carbon tax schemes of 9 US$/tC for slash burn and 25 US$/tC for situations when removed wood enters a harvested wood products pool (HWP) would generate some 2 to 5.7 billion US$/year respectively when emissions from deforestation are to be cut in half. For the variant of 12 US$/tC, with regionally differentiated slash burn and HWP assumptions, the average annual income for the next 100 years are calculated to be around 2.7 billion US$. These tax revenues decrease dramatically over time mainly due to the declining baseline deforestation rate. Tax revenues are computed to be 6 billion US$ in 2005, 4.3 billion US$ in 2025 and 0.7 billion US$ in 2100. This indicates the magnitudes and their temporal change of funds generated from a deforestation tax scheme aiming at a 50% emission reduction (figure 5 and 7).

In the alternative incentive scheme, the amount of funds necessary, is depending on the strategy of payments, either increasing, staying constant or decreasing over time. If incentives are paid only for those forest areas that are about to be deforested, and with a global target of cutting deforestation by 50%, a minimum payment of 6 US$/tC/5 year or 0.24 billion US$ in 2006 would be required. This amount rises to some 1.2 billion US$ in 2010, 4.1 billion US$ in 2025 and 10 billion US$ in 2100 caused by the increasing area of saved forest area. As precise information of forests about to be deforested is absent, incentive payment schemes would have to focus on regions under deforestation pressure. Given that incentives are only spent on regions of 0.5° × 0.5° where they can effectively reduce deforestation in an amount that they will balance out the income difference between forests and alternative land use up the 6 US$/tC/5 year, this would come at a cost of 34 billion US$/year (figure 6 and 8). It should be noted that the tax applies only on places currently deforested while the subsidy applies to larger areas depending on how far it is in practice possible to restrict the subsidy to vulnerable areas. All figures above are intentionally free of transaction costs. Transaction costs would inter alia include expenditure for protecting the forests against illegal logging by force and expenditures monitoring small scale forest degregation. Governance issues such as corruption and risk adjustment, depending on the country are, however, considered in the analysis to the extent possible.

Sources of deforestation in the model are expansion of agriculture and buildup areas as well as from unsustainable timber harvesting operations impairing sufficient reforestation. Deforestation results from many pressures, both local and international. While the more direct causes are rather well established as being agricultural expansion, infrastructure extension and wood extraction, indirect drivers of deforestation are made up of a complex web of interlinked and place-specific factors. There is large spatially differentiated heterogeneity of deforestation pressures. Within a forest-agriculture mosaic, forests are under high deforestation pressure unless they are on sites which are less suitable for agriculture (swamp, slope, altitude). Closed forests at the frontier to agriculture land are also under a high deforestation pressure while forest beyond this frontier are under low pressure as long as they are badly attainable. The model was build to capture such heterogeneity in deforestation pressures.

Figure 9 shows that the model predicts deforestation to continue at the frontier to agricultural land and in areas which are easly accessible. Trans-frontier forests are also predicted to be deforested due to their relative accessibility and agricultural suitablility. Forests in mosaic lands continue to be under strong pressure. Figure 10 illustrates the geography of carbon saved at a carbon tax of 12 US$/tC compared to biomass lost through deforestation. Under this scenario deforestation is maily occurring in clusters, which are sometimes surrounded by forests (e.g. Central Africa) or are concentrated along a line (Amazon). The geography of the remaining deforestation pattern indicates that large areas are prevented from deforestation at the frontier by the 12 US$/tC tax. The remaining emissions from deforestation are explained mainly by their accessibility and favourable agricultural suitability.

The net present value of forestry is determined by the planting costs, the harvestable wood volume, the wood-price and benefits from carbon sequestration.

For existing forests which are assumed to be under active managment the net present value of forestry given multiple rotations (F_i) over the simulation horizon is calculated from the net present value for one rotation (f_i) (equation 1). This is calculated by taking into account the planting costs (cp_i) at the begin of the rotation period and the income from selling the harvested wood (pw_i·V_i) at the end of the rotation period. Also the benefits from carbon sequestration are included denoted as (B_i).

The planting costs (eq. 3) are calculated by multiplying the planting costs of the reference country (cp_ref) with a price index (px_i) and a factor which describes the share of natural regeneration (pr_i). The ratio of plantation to natural regeneration is assumed to increase with increasing yield for the respective forests (eq. 4). The price index (eq. 5) is calculated using the purchasing power parity of the respective countries. The stumpage wood price (eq. 6) is calculated from the harvest cost free income range of wood in the reference country. This price is at the lower bound when the population density is low and the forest share is high and at the higher bound when the population density is high and the forest share is low. The price is also multiplied with a price index converting the price range from the reference country to the examined country. The population-density and forest-share was standardized between 1 and 10 by using equation (7) and equation (8) respectively.

The harvested volume (V_i) is calculated by multiplying the mean annual increment (MAI_i) with the rotation period length (R_i) accounting for harvesting losses (eq. 9).

The rotation period length (eq. 10) depends on the yield. Fast growing stands have a short and slow growing sites a long rotation length. In this study the rotation length is in the range between 5 and 140 years.

The mean annual increment (eq. 11) is calculated by multiplying the estimated carbon uptake (ω_i) and a transformation factor which brings the carbon weight to a wood volume (C2W_i). The carbon uptake (ω_i) is calculated by multiplying the net primary production (NPP_i) with a factor describing the share of carbon uptake from the net primary production (eq. 12).

The benefits of carbon sequestration (eq. 13) are calculated by discounting the annual income from additional carbon sequestration and subtracting the expenses incurred from harvesting operations and silvicultural production. At the end of a rotation period the harvested carbon is still stored in harvested wood products and will come back to atmosphere with a delay. This is considered in the factor (θ_i) which shares the harvested wood volume to short and long living products(eq. 14).

The effective carbon price represents the benefit which will directly go to the forest owner. In equation (16) a factor describing the percentage of the transaction cost free carbon price is used. A factor leak_i is calculated as the average of the percentile rank from "political stability", "government effectiveness" and "control of corruption" 5.

F i = f i ⋅ [ 1 − ( 1 + r ) − R i ] − 1       ( 1 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGgbGrdaWgaaWcbaGaemyAaKgabeaakiabg2da9iabdAgaMnaaBaaaleaacqWGPbqAaeqaaOGaeyyXICTaei4waSLaeGymaeJaeyOeI0IaeiikaGIaeGymaeJaey4kaSIaemOCaiNaeiykaKYaaWbaaSqabeaacqGHsislcqWGsbGudaWgaaadbaGaemyAaKgabeaaaaGccqGGDbqxdaahaaWcbeqaaiabgkHiTiabigdaXaaakiaaxMaacaWLjaWaaeWaaeaacqaIXaqmaiaawIcacaGLPaaaaaa@4880@

f_i = -cp_i + pw_i·V_i + B_i     (2)

cp_i = cp_ref·pr_i·px_i     (3)

p r i = { 0 M A I i < 3 ( M A I i − 3 ) / 6 3 ≤ M A I i ≤ 9 1 M A I i > 9       ( 4 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@5B20@

p x i = P P P i P P P r e f       ( 5 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCcqWG4baEdaWgaaWcbaGaemyAaKgabeaakiabg2da9maalaaabaGaemiuaaLaemiuaaLaemiuaa1aaSbaaSqaaiabdMgaPbqabaaakeaacqWGqbaucqWGqbaucqWGqbaudaWgaaWcbaGaemOCaiNaemyzauMaemOzaygabeaaaaGccaWLjaGaaCzcamaabmaabaGaeGynaudacaGLOaGaayzkaaaaaa@42CC@

p w i = p w m i n − p w m a x − p w m i n 99 + p w m a x − p w m i n 99 ⋅ S P d ⋅ S N F s ⋅ p x i       ( 6 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCcqWG3bWDdaWgaaWcbaGaemyAaKgabeaakiabg2da9iabdchaWjabdEha3naaBaaaleaaieGacqWFTbqBcqWFPbqAcqWFUbGBaeqaaOGaeyOeI0YaaSaaaeaacqWGWbaCcqWG3bWDdaWgaaWcbaGae8xBa0Mae8xyaeMae8hEaGhabeaakiabgkHiTiabdchaWjabdEha3naaBaaaleaacqWFTbqBcqWFPbqAcqWFUbGBaeqaaaGcbaGaeGyoaKJaeGyoaKdaaiabgUcaRmaalaaabaGaemiCaaNaem4DaC3aaSbaaSqaaiab=1gaTjab=fgaHjab=Hha4bqabaGccqGHsislcqWGWbaCcqWG3bWDdaWgaaWcbaGae8xBa0Mae8xAaKMae8NBa4gabeaaaOqaaiabiMda5iabiMda5aaacqGHflY1cqWGtbWucqWGqbaucqWGKbazcqGHflY1cqWGtbWucqWGobGtcqWGgbGrcqWGZbWCcqGHflY1cqWGWbaCcqWG4baEdaWgaaWcbaGaemyAaKgabeaakiaaxMaacaWLjaWaaeWaaeaacqaI2aGnaiaawIcacaGLPaaaaaa@7579@

S P d = { 1 + P d ⋅ 9 100 P d ≤ 100 10 P d > 100       ( 7 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGtbWucqWGqbaucqWGKbazcqGH9aqpdaGabeqaauaabmqaciaaaeaacqaIXaqmcqGHRaWkdaWcaaqaaiabdcfaqjabdsgaKjabgwSixlabiMda5aqaaiabigdaXiabicdaWiabicdaWaaaaeaacqWGqbaucqWGKbazcqGHKjYOcqaIXaqmcqaIWaamcqaIWaamaeaacqaIXaqmcqaIWaamaeaacqWGqbaucqWGKbazcqGH+aGpcqaIXaqmcqaIWaamcqaIWaamaaaacaGL7baacaWLjaGaaCzcamaabmaabaGaeG4naCdacaGLOaGaayzkaaaaaa@4FEA@

SNFs = 1 + (1 - Fs) * 9     (8)

V_i = MAI_i·R_i·(1 - HL_i)     (9)

R i = { 5 M A I i > 180 / 10 600 − | M A I i − 6 | ⋅ 50 M A I i 10 3 ≤ M A I i ≤ 180 10 140 M A I i < 10 / 3       ( 10 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@75BA@

MAI_i = ω_i·C2W     (11)

ω_i = NPP_i·CU     (12)

B i = e p c i ⋅ ω i ⋅ ( 1 − b i ) ⋅ { r − 1 ⋅ [ 1 − ( 1 + r ) − R i ] − R i ⋅ ( 1 − θ i ) ⋅ ( 1 + r ) − R i }       ( 13 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGcbGqdaWgaaWcbaGaemyAaKgabeaakiabg2da9iabdwgaLjabdchaWjabdogaJnaaBaaaleaacqWGPbqAaeqaaOGaeyyXICncciGae8xYdC3aaSbaaSqaaiabdMgaPbqabaGccqGHflY1cqGGOaakcqaIXaqmcqGHsislcqWGIbGydaWgaaWcbaGaemyAaKgabeaakiabcMcaPiabgwSixlabcUha7jabdkhaYnaaCaaaleqabaGaeyOeI0IaeGymaedaaOGaeyyXICTaei4waSLaeGymaeJaeyOeI0IaeiikaGIaeGymaeJaey4kaSIaemOCaiNaeiykaKYaaWbaaSqabeaacqGHsislcqWGsbGudaWgaaadbaGaemyAaKgabeaaaaGccqGGDbqxcqGHsislcqWGsbGudaWgaaWcbaGaemyAaKgabeaakiabgwSixlabcIcaOiabigdaXiabgkHiTiab=H7aXnaaBaaaleaacqWGPbqAaeqaaOGaeiykaKIaeyyXICTaeiikaGIaeGymaeJaey4kaSIaemOCaiNaeiykaKYaaWbaaSqabeaacqGHsislcqWGsbGudaWgaaadbaGaemyAaKgabeaaaaGccqGG9bqFcaWLjaGaaCzcamaabmaabaGaeGymaeJaeG4mamdacaGLOaGaayzkaaaaaa@7919@

θ i = ( 1 − d e c l l p ⋅ f r a c l l p d e c l l p + r − d e c s l p ⋅ f r a c s l p d e c s l p + r ) ⋅ ( 1 − f r a c s b ) + ( 1 − f r a c s b ) ∗ f r a c s b       ( 14 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@9C98@

frac_slp = 1 - frac_llp     (15)

epc_i = pc_i·leak_i     (16)

The net present value of agriculture (A_i) is calculated with a two-factor Cobb-Douglas production function (equation 17). It depends on the agriculture suitability and the population density. A high agriculture suitability and a high population density causes high agricultural values. The value ranges between a given minimum and a maximum land price. The parameters a_i and γ_i determine the relative importance of the agriculture suitability and the population density and ν_i determines the price level for land. The agriculture suitability and the population density are normalized between 1 and 10.

A i = ν i ⋅ S A g S i α i ⋅ S P d i γ i       ( 17 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGbbqqdaWgaaWcbaGaemyAaKgabeaakiabg2da9GGaciab=17aUnaaBaaaleaacqWGPbqAaeqaaOGaeyyXICTaem4uamLaemyqaeKaem4zaCMaem4uam1aa0baaSqaaiabdMgaPbqaaiab=f7aHnaaBaaameaacqWGPbqAaeqaaaaakiabgwSixlabdofatjabdcfaqjabdsgaKnaaDaaaleaacqWGPbqAaeaacqWFZoWzdaWgaaadbaGaemyAaKgabeaaaaGccaWLjaGaaCzcamaabmaabaGaeGymaeJaeG4naCdacaGLOaGaayzkaaaaaa@4EC4@

S A g S i = { 10 A g S i ≥ 0.5 1 + 9 ⋅ A g S / 0.5 A g S i < 0.5       ( 18 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGtbWucqWGbbqqcqWGNbWzcqWGtbWudaWgaaWcbaGaemyAaKgabeaakiabg2da9maaceqabaqbaeaabiGaaaqaaiabigdaXiabicdaWaqaaiabdgeabjabdEgaNjabdofatnaaBaaaleaacqWGPbqAaeqaaOGaeyyzImRaeGimaaJaeiOla4IaeGynaudabaGaeGymaeJaey4kaSIaeGyoaKJaeyyXICTaemyqaeKaem4zaCMaem4uamLaei4la8IaeGimaaJaeiOla4IaeGynaudabaGaemyqaeKaem4zaCMaem4uam1aaSbaaSqaaiabdMgaPbqabaGccqGH8aapcqaIWaamcqGGUaGlcqaI1aqnaaaacaGL7baacaWLjaGaaCzcamaabmaabaGaeGymaeJaeGioaGdacaGLOaGaayzkaaaaaa@5AC5@

α i = ln ⁡ ( P L m a x ) − ln ⁡ ( P L m i n ) 2 ⋅ ln ⁡ ( 10 )       ( 19 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFXoqydaWgaaWcbaGaemyAaKgabeaakiabg2da9maalaaabaGagiiBaWMaeiOBa4MaeiikaGIaemiuaaLaemitaW0aaSbaaSqaaGqaciab+1gaTjab+fgaHjab+Hha4bqabaGccqGGPaqkcqGHsislcyGGSbaBcqGGUbGBcqGGOaakcqWGqbaucqWGmbatdaWgaaWcbaGae4xBa0Mae4xAaKMae4NBa4gabeaakiabcMcaPaqaaiabikdaYiabgwSixlGbcYgaSjabc6gaUjabcIcaOiabigdaXiabicdaWiabcMcaPaaacaWLjaGaaCzcamaabmaabaGaeGymaeJaeGyoaKdacaGLOaGaayzkaaaaaa@565C@

γ_i = α_i     (20)

The deforestation decision is expressed by equation (21). It compares the agricultural and forestry net present values corrected by values for deforestation and carbon sequestration. For the deforestation decision the amount of removed biomass from the forest is an important variable. The agricultural value needed for deforestation increases with the amount of timber sales and its concomitant flow to the HWP pool. On the other hand the agriculture value will be decreased by the amount of released carbon to the atmosphere. This mechanism is expressed by a deforestation value (DV_i, eq. 22). The model also allows for compensation of ancillary benefits from forests. This additional income is modeled either as a periodical income or a one time payment and will increase the forestry value by (IP_i). If it is a periodic payment it has to be discounted, which has been done in equation (23).

Defor = { Yes A i + D V i > F i ⋅ H i + I P i ∧ not Protected No A i + D V i ≤ F i ⋅ H i + I P i ∨ Protected       ( 21 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@8B31@

D V i = B M i ⋅ { p w i ⋅ C 2 W ⋅ ( 1 − H L i ) − e p c i ⋅ [ ( 1 + r ) ⋅ ( f r a c l l p ⋅ d e c l l p d e c l l p + r + f r a c s l p ⋅ d e c s l p d e c s l p + r ) ⋅ ( 1 − f r a c s b ) + f r a c s b ] }       ( 22 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@BC16@

I P i = ( B M i + B M P i ) ⋅ p c a i ⋅ ( r + 1 ) f r i ( r + 1 ) f r i − 1       ( 23 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@6072@

There exist several ways of how financial transfers can be handled. Two mechanisms are realized in equation (21). One is to pay the forest owner to avert from the deforestation, the other is to introduce a carbon price that the forest owner gets money by storing carbon and paying for releasing it. The introduction of a carbon price focuses the money transfer to the regions where a change in biomass takes place. Payments to avoid emissions from deforestation can be transfered to cover all of the globe's forests, target to large "deforestation regions" or individual grids.

Once the principle deforestation decision has been made for a particular grid cell (i.e. the indicator variable Defor_i = 1) the actual area to be deforested within the respective grid is to be determined. This is done by the auxiliary equation (24 – 25) computing the decrease in forest share. We model the deforestation rate within a particular grid as a function of its share of forest cover, agricultural suitability, population density and gross domestic product. The coefficients c₁ to c₆ were estimated with a generalized linear model of the quasibinomial family with a logit link. Values significant at a level of 5% were taken and are shown in table 1. The parameters of the regression model were estimated using R 6. The value of c₀ was determined upon conjecture and directly influences the maximum possible deforestation rate. For our scenarios the maximum possible deforestation is set to 5% of the total land area per year. That means, a 0.5° × 0.5° grid covered totally with forests can not be deforested in a shorter time period than 20 years.

F d e c i = { 0 Defor = No F s i F t d e c i > F s i ∧ Defor = Yes F t d e c i F t d e c i ≤ F s i ∧ Defor = Yes       ( 24 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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@86A2@

F t d e c i = { 0 F s i = 0 ∨ A g S i = 0 x i F