AN AGE-CLASS FOREST MODEL WITH SILVICULTURAL INPUTS AND CARBON PAYMENTS

Transcription

1 AN AGE-CLASS FOREST MODEL WITH SILVICULTURAL INPUTS AND CARBON PAYMENTS Jussi Uusivuori, Metla Jani Laturi, Metla Forest ecosystem carbon and its economic implications seminar

2 The aims of the study The aim is to study the impacts of policies aimed at encouraging private landowners to increase sequestered carbon in their forests Examples of practicable policies It has been presented that forest owners could receive compensation for the sequestered carbon in their forests Alternatively, subsidies could be targeted at silvicultural activities that increase forest growth

3 Main questions How will the private forest owner react under a certain policy? How do policies affect the optimal rotation length? How do policies affect the use of silvicultural inputs? => What will be the effects on the amount of sequestered carbon in the forest in the short and long run? What would be the prices of sequestered carbon (CO 2 )? How will policies affect the timber supply? In the short run In the long run

4 Basics of the study Forest owner can use silvicultural inputs to increase the growth of forest Carbon compensation is paid to forest owner for parcels which he will save uncut at that period Selected policies in the study 1. Carbon compensation to the landowner 2. Subsidy to silvicultural investment

5 Literature Englin, J. & Callaway, J.M. (1993). Global Climate Change and Optimal Forest Management. Natural Resource Modeling. 7 (3), G.C. van Kooten, C.S. Binkley and G. Delcourt [1995], Effect of Carbon Taxes and Subsidies on Optimal Forest Rotation Age and Supply of Carbon Services. American J. of Agric. Econ. 77, B. Sohngen and R. Mendelsohn [2003], An Optimal Control Model of Forest Carbon Sequestration. American J. of Agric. Econ 85,

6 The model in the study The landowner's infinite horizon utility maximizing problem t = 0 β Consumption restriction Max i i { a j, m j, h} 1 t t u ( c ) t t= 0 1+ r i= 0 t n i c w+ LV( x) 1 β = 1 + ρ is the discount term with ρ (>0) as the subjective time preference rate uc ( t ) is the landowner's utility function a s are periodical harvesting decision variables for each age-class m s are periodical silvicultural investment variables for each age-class Consumption restriction define life-time budget constraint stating that the present value of the consumption flow cannot exceed the initial value of the assets. The total assets are the sum of the nonforestry assets w plus the total land n value i LV ( x ) i= 0

7 Carbon compensation in the model T 1 1 PV = PC r q 0 1+ r ( α ) T 1 1 PV = PCα r q 0 1+ r t ( ) t Carbon compensation is paid to forest owner for parcels which he will save uncut at that period PV is the present value of carbon uptake over one rotation P C is the price of carbon dioxide α is the tons of carbon dioxide per m 3 of timber biomass

8 Silvicultural investments in the model The effect of silvicultural inputs is increasing but the marginal effect is negative In the study the effect of subsidy on silvicultural inputs is done by comparing optimal use of inputs and rotation length with different price levels of silvicultural inputs l Growing forest example: Forest owner wants to know the optimal input level of a 60 year-old forest which will be cut after 20 years. The optimal using level of inputs m 60+20,60 in current year is found when the discounted marginal benefits from the growth of forest + the discounted marginal benefit of carbon compensation over next 19 years equals to marginal price of silvicultural inputs l 1 l = 1+ r q p m 0 80, , k = r k 60 q PC αr m 0 80, k 0 80,60

9 Optimal rotation length for bareland The benefits over one rotation consist of timber supply and carbon compensation Timber supply benefits r j ( pq k) 0 j, j Carbon compensation over rotation lengt j The optimal rotation cycle for bareland forest can be found as: j 1 h j j (1 + r) ( pqjj, k) + ( Pcα r qjh, m jh, l) j 1+ r h= r (1 + r) 1 >< () j+ 1 j h j (1 + r) ( pqj+ 1, j+ 1 k) + ( Pcα r qj + 1, h m j+ 1, hl ) j r h= r (1 + r) 1 j 1 h= r h 0 0 ( Pcα r qj, h mj, hl)

10 Optimal rotation length for growing forest The optimal rotation cycle for growing forest can be found using bareland value LV * as: j * j 1 h 1 i LV ( x0 ) 1 i i + j, j + 1+ r x0 h= 1 1+ r > ( < ) ( cα j, h j, h ) pq P r pq m l j+ 1 * j h 1 i LV ( x0 ) 1 i i + j+ 1, j r x0 h= 1 1+ r ( cα j+ 1, h j+ 1, h ) pq P r q m l

11 The parametrized growth function i 2, 1 (1 β i β i i jh+ = α ) jh, + α 1 + γ jh, ( γ jh, ) q h q h G m m α where and β are parameters controlling the concavity of the growth function G is a parameter defining the maximum carrying capacity per unit of hectare of timber biomass without the silvicultural inputs γ is a parameter for the impact of the silvicultural inputs

12 Numerical analysis One period is 10 years Periodical interest rate 0.5 ( 0.04 / year ) The silvicultural input price is 30 Landowner has 11 ha forest land 10 ha is evenly allocated between 1-10 period old forest 1 ha is older than 10 periods (100 years) Price of timber is constant 40 /m 3 In the calculation we have used sequestered carbon dioxide ratio 0,8 t CO2 per m 3 of timber wood

13 Growth function Years Annual growth rate 7,18% 5,54% 4,03% 2,75% 1,68% 0,85% 0,31% 0,06% 0,00%

14 Carbon compensation P C =15 Forest owner uses more silvicultural investments and the growth of the forest increases Both bareland and growing forest optimal rotation length increases Bareland optimal rotation lenght increases from 6 periods (60 years) to 7 periods (70 years) Long run average timber volume / rotation increases from 897 m 3 to 1201 m3 (82 m 3 /ha to 109 m 3 /ha) Long run periodical compensation is 4594

15 Sequestered carbon dioxide / ha with different level of P C While the carbon compensation increases the forest owner prefers longer rotations and uses more silvicultural investments As a consequence the amount of sequestered carbon (dioxide) increases At carbon dioxide price of 36,5 / t CO2 forest owner is willing to stop harvesting and conserve his forest assets permanently

16 40 % subsidy to silvicultural Price of silvicultural investment l = 18 Forest owner uses more silvicultural investments and the growth of the forest increases Optimal rotation for both bareland and growing forest doesn t change Long run average timber volume / rotation increase from 897 m 3 to 913 m 3 (82 m 3 /ha to 84 m 3 /ha) Long run periodical subsidy is 203 / period The price CO 2 = 30,4 / t CO2 investments

17 87 % subsidy to silvicultural investments Price of silvicultural investment l =4 Forest owner uses more silvicultural investments and the growth of the forest increases Optimal rotation for both bareland and growing forest shortens The optimal rotation leng for bareland shortens from 6 periods (60 years) to 5 periods (50 years) Long run average timber volume / rotation decreases from 897 m 3 to 682 m 3 (82 m 3 /ha to 62 m 3 /ha) The price CO 2 is then infinite

18 Cost of silvicultural subsidy The cost of subsidy is first increasing (price of CO 2 increasing) Between percentage subsidy reaches its lowest cost point At the 87 percentage subsidy, the average carbon storage starts to decrease and the cost of sequestered carbon becomes infinite.

19 Conclusions Policy instruments aimed at increasing carbon sequestration in private forests may offer an effective way to control climate change. Adverse effects are possible. A policy based on carbon payments should be carried out cautiously to avoid timber market disruptions in the short run. More research is needed on this!