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# Environmental Economics ENVECON C101

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This 20 page Class Notes was uploaded by Josefa Conn on Thursday October 22, 2015. The Class Notes belongs to ENVECON C101 at University of California - Berkeley taught by D. Zilberman in Fall. Since its upload, it has received 51 views. For similar materials see /class/226617/envecon-c101-university-of-california-berkeley in Environmental Science & Policy at University of California - Berkeley.

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Date Created: 10/22/15

Chapter 15 Forestry Economics Contents General Overview Differences Between Issues of Forestry and Fisheries The Economic Decision to Harvest a Stand The Case of an In nite Forest Rotation Management of Forest Resources Factors Affecting Forest Resources Dynamics General Overview The economics of forest resources are very similar to the dynamic management of a fishery Both forests and fisheries are renewable resource systems The economic principles that determine optimal management are very much the same The major difference between the economics of a forest and a fishery resource are related to biological principles The central question of commercial or social forest economics is When should we cut a stand of trees We will assume that the land has no available alternative use If we had an alternative use it would 1 introduce opportunity cost in the model Differences Between Issues of Forestry and Fisheries The forest problem is a problem of divestment which means the solution calculates the optimal time to consolidate and sell the entire stock and begin the next rotation The analogy of a forest rotation is that of a conventional crop which does not get harvested every season However the growth cycle of a forest resource a period of centuries instead of months is so long that resource owners get really impatient and discounting dynamic analysis is important How Is the Forestry Problem Different From a Fishery 1 Forestry solutions determine when rather than how much Growth occurs over long time periods and can be measured The forestry problem solves for the optimal time to harvest the entire stock and the solution gives the optimal length of each rotation of stock 4 Property rights are secure no openaccess problems LAN VV In the forestry problem the critical element is that the growth function is a function of time not a function of stock Figure 151 The Forestry Growth Function Q t Volume of Timber ie Board Feet 0r Cubic Feet T Ray Q my T msy Qt QT1 T1 Time T2 Tmsy TmaX T1 The growth function of a typical stand of trees looks like this At first the volume increases at an increasing rate for very young trees Then growth of volume slows and increases at a decreasing rate Finally when the trees are very old they begin to have negative growth as they rot decay and become subject to disease and pests The volume of a stand of trees is maximized at time Tm with a volume Qme Yet this is not the volume associated with the Maximum Sustainable Yield MSY occurs where the growth rate equals the Average Growth per rotation Recall that our goal is to replant new trees The average growth rate of a stand at any time t is t A G which can be shown by a ray through the origin Ray 1 shows that the average growth can be achieved by either cutting at time T1 or at time T2 but neither time gives the Maximum Average Growth What we want is the highest average growth over all harvests Finding T msy The MSY occurs at a rotation length that maximizes the average annual growth of the stands through time Max Qtt implies the FOC t Q39tt Qt dt t2 0 where we have used the quotient rule of calculus Rearranging terms we get w39a Thus in order to harvest the MSY we should cut the stand of trees when marginal growth equals average growth of the stand Ray 2 shows where this condition is met where the average growth is tangent to the growth function In biology this concept is known as Maximizing the Mean Annual Increment Figure 152 Harvest Pattern Over Time Q0 Tmsy 2Tmsy 3Tmsy Time Graphically the harvest pattern over time is shown above As in the case of the fishery when moving from two time periods to T periods the optimal dynamic solution is to replicate a single optimal decision many times The Economic Decision to Harvest a Stand Since the value of the stand grows over time like a conventional asset such as a stock or money in an interest bearing bank account the optimal solution will occur where the value of the forest asset is in equilibrium with other assets in the economy That is we want to incorporate into the analysis the rate of time preference of the forester ie the discount rate The F orestty Optimization Problem Because the growth rate is a function of time it is necessary to formulate the optimization problem in continuous time 1 t J The continuous time analog to this is found as 0 gt 0 In discrete time we find that P I 1 t as t gt 0 gt e lr In the economic optimization problem we want to maximize the present value of the forest stand with respect to the time period of harvest That is we want to find the point in time where the NPV is maximized The Optimal Single Rotation We will first look at the problem as a single rotation In the single rotation there is no opportunity cost incurred by failing to plant the next stand of trees at the optimal time Thus the problem is really that of determining the optimal time to harvest a crop Suppose a crop is planted at time t 0 and grows in value to PQt at time t The goal is to find the harvest time that will maximize the NPV of a single rotation Let P constant price per pound of the crop There are no harvesting costs so that PQt Total Revenue The Objective Function is Mflx7r e39 PQt with the FOC PQ te PQte quot r 0 which can be written as PQ I rPQI or MB of waiting value of new growth MC of waiting lost interest on Total Revenue If the forest manager delays the harvest she will not earn interest on revenues PQt If the forest manager delays the harvest she will gain the value of new growth Q t This is the trade off to consider in forestry economics We can rearrange the optimality condition to get Q0 r which states that the percent rate of growth in volume should equal the discount rate Profit maximization therefore dictates that the stand should be harvested when the percentage rate of growth of crop value equals the value of alternative investments Q39 I If Q0 gt r then the crop is increasing in value quicker than market investments and the farmer should delay the harvest decision If lt r then market investments are increasing in value quicker than the growth in value of the crop harvesting should have already occurred The Case of an In nite Forest Rotation The relevant case for most foresters is that of continuous stand rotation over time When the forester plans to replant a new forest stand immediately after cutting the old one there is now an opportunity cost that must be considered the opportunity cost of future rotations Before we begin we need to review a calculus identity that we will The sum of an infinite series is For IX lt 1 0 l X 1XX2X3 l H In our problem of infinite rotation we will use this as follows 7 7 7 7 1 Zoe le397emem1 e7 1 where T is the length of each rotation The infinite rotation problem is commonly called the Faustmann Rotation after the German forester from the early 1900s Assume a constant net price or profit per cubic foot of timber That is if harvesting or replanting costs eXist then what we hold constant is net price price per unit harvesting and replanting costs Let P the constant price per cubic foot of timber Q the volume of timber in cubic feet We can now write forester pro t as 7239 PQTe T PQTe m PQTe 3 T PQTe T e e 3 7 PQTe T1 e e PQT7 PQT e Tl 647 PQT e T l PQT e39 l 61 PQ39TPQT1Ve 7 The optimization problem is Max7r T with the FOC dT e l 8 7 12 which can be rearranged to yield P T 7 P T We can now crossmultiply and write the optimality condition as PQ39T rPQT PQ39T87 T lVlR of delaying MC of waiting MC of delaying future income stream The first two terms are identical to those in the single stand or cropping decision The last term represents an additional opportunity cost of delaying the harvest As delaying the current harvest also delays income received from future harvests Therefore the optimal rotation time T requires the forester to equate the marginal value of waiting to the marginal cost of delaying the harvest of current and future stands In general 7 lt T single rotation lt Tmsy It is also important to analyze the effect of different parameters of the harvesting decision An Increase in the Price of Timber An increase in P will tend to shorten the rotation length because higher timber prices increase the profitability of each harvest Cutting trees earlier moves the profit of future harvests closer to the present An Increase in the Interest Rate An increase in r will tend to shorten the optimal rotation length because the forest owner is now relatively more impatient The owner is now more eager to move profit up into the present An Increase in Harvesting Costs Recall how we absorbed harvesting costs into the net price Thus an increase in c is analogous to a decrease in price An increase in c will tend to increase the rotation length because cutting trees has now become less profitable the owner wishes to delay paying future harvesting costs Management of Forest Resources Forest management is more than efficient harvesting of trees It actually may be more efficient to grow desirable tree species in forest farms Forests are rich ecosystems that include several varieties of trees with other species of ora and fauna Forest resources thus provide multiple benefits that need to be re ected in management plans The benefits from forest resources include 1 Timber and other forest products 2 Support of wildlife 3 Presentation of biodiversity 4 Carbon sequestration 5 Prevention of soil erosion 6 Flood and water quality control 7 Recreational services The volume and manner of forest harvesting affects the other environmental amenities provided by forests Clear cutting of parcels of forests is a lowcost harvesting of wood in many situations but it entails significant cost of l Destruction of nontargeted species of wood 2 Damage to dependent plants and wildlife 3 Increased likelihood of soil erosion 4 Endogenous populations of forest communities Forest modeling is used to illustrate some of the choices associated with forest management Suppose a parcel of land contains two types of trees Let X1 quantity of tree 1 harvested in period t X 2 quantity of tree 2 harvested in period t Sit denotes stock of tree 139 at period t The equation of motion of stock 1 and 2 respectively are Slt1 S11 g1SnSzr hlHtX21 X1 32m 2 g2SnSzr hz HtaX21 X2 where g1 and g2 are growth functions of stock 1 and 2 respectively Growth depends on both species population sizes The function h ihXZI is the loss of stock trees 1 because of harvesting of tree 2 with harvesting technology H I Higher H I re ects more precision in harvesting The loss of tree 2 stock because of harvesting of tree 1 is given by h2HIX1 The objective of policymakers is to maximize eXpected benefits from wood and benefits of environmental amenities BS11S2 minus environmental damages hdx2x2H and cost of harvesting and mining technology Thus the social optimization problem is w I f 1 N d Xltfgngtgkm PSlzaszz XlrP2X2z h XiszpHr ClXlISlIHI C2 091321110 where C10 and C2 are cost of harvesting of the two trees We don t solve this problem formally but its structure suggests that for each species optimal harvesting is determined where Price marginal harvesting cost marginal externality cost user cost Marginal externality cost re ects the impact of harvesting on other species and user cost the cost of reducing stock at the present Furthermore in this system in addition to the choice of harvesting X2PX1 I there is a choice of harvesting technology H I The optimal level of H I index of harvesting equipment is determined so that marginal gain from less externalities marginal gain from growth marginal cost of harvesting Without government regulation when there is open access to forest there is overharvesting as firms do not consider marginal externality cost and user cost There will also be underinvestment in precision H equipment as firms will consider the cost of extra equipment but undervalue the benefits When private parties own forests they may consider the user costs but not the externality costs They thus may underinvest in precision and overharvest Addressing market failure may entail a combination of policies depending on ability of government to monitor behavior or enforce choices They may include Timber taxes Externality penalties Technology subsidies Quotas and transferable rights to harvest etc In the United States forests are owned by the government The U S Forest Service however decides on the harvesting quota and companies bids on it In the past externalities were ignored Currently new timber allocations attempt to take into account environmental costs as well as forest dynamics and new forest policies attempt to recognize multiple services that forests provide Factors Affecting Forest Resources Dynamics Deforestation is a major environmental problem Forests are removed 1 Provide wood for fire construction etc 2 Obtain land for settlement The demand for wood is affected by other economic factors Wood has been and is a major source of energy The replacement of wood by fossil fuels reduces the demand and harvesting in many developed countries Now the main use of wood in the developed world is to make paper Recycling and productive food farming will reduce this demand In developing countries there is a growing demand for wood as a source of energy driven by population growth etc Again the transition is toward alternative fuels solar or fossil fuels and to adoption of biofuel technology converting wood to energy while increasing energy use efficiency may reduce this demand for wood The issue of conversion of land is more difficult Increased productivity of existing land resources and incentive to preserve forest resources will reduce this source of desertification Chapter 15 Forestry Economics Contents General Overview Differences Between Issues of Forestry and Fisheries The Economic Decision to Harvest a Stand The Case of an In nite Forest Rotation General Overview The economics of forest resources are very similar to the dynamic management of a fishery Both forests and fisheries are renewable resource systems The economic principles that determine optimal management are very much the same The major difference between the economics of a forest and a fishery resource are related to biological principles The central question of commercial or social forest economics is When should we cut a stand of trees We will assume that the land has no available alternative use If we had an alternative use it would 1 introduce opportunity cost in the model Differences Between Issues of Forestry and Fisheries The forest problem is a problem of divestment which means the solution calculates the optimal time to consolidate and sell the entire stock and begin the next rotation The analogy of a forest rotation is that of a conventional crop which does not get harvested every season However the growth cycle of a forest resource a period of centuries instead of months is so long that resource owners get really impatient and discounting dynamic analysis is important How Is The Forestry Problem Different From a Fishery 1 Forestry solutions determine when rather than how much 2 Growth occurs over long time periods and can be measured 3 The forestry problem solves for the optimal time to harvest entire stock and the solution gives the optimal length of each rotation of stock 4 Property rights are secure no open access problems In the forestry problem the critical element is that the growth function is a function of time not a function of stock Figure 151 The Forestry Growth Function Qt Volume of Timber ie Board Feet 0r Cubic Feet QTmsy R 2 ay Tmsy Qt 7 QTl Rayli T1 Time T2 Tmsy TmaX T1 The growth function of a typical stand of trees looks like this At first the volume increases at an increasing rate for very young trees Then growth of volume slows and increases at a decreasing rate Finally when the trees are very old they begin to have negative growth as they rot decay and become subject to disease and pests The volume of a stand of trees is maximized at time Tmax with a volume QTmax Yet this is not the volume associated with the Maximum Sustainable Yield MSY occurs where the growth rate equals the Average Growth per rotation Recall that our goal is to replant new trees The average growth rate of a stand at any time t is AG which can be shown by a ray through the origin Ray 1 shows that the average growth can be achieved by either cutting at time T1 or at time T2 but neither time gives the Maximum Average Growth What we want is the highest average growth over all harvests Finding T msy The MSY occurs at a rotation length that maximizes the average annual growth of the stands through time Max Qtt implies the FOC 4 t Q39U QU 0 dt t2 where we have used the quotient rule of calculus Rearranging terms we get Q Q t Thus in order to harvest the MSY we should cut the stand of trees when marginal growth equals average growth of the stand Ray 2 shows where this condition is met where the average growth is tangent to the growth function In biology this concept is known as Maximizing the Mean Annual Increment Figure 152 Harvest Pattern Over Time Q0 Tmsy 2Tmsy 3Tmsy Time Graphically the harvest pattern over time is shown above As in the case of the fishery when moving from two time periods to T periods the optimal dynamic solution is to replicate a single optimal decision many times The Economic Decision to Harvest a Stand Since the value of the stand grows over time like a conventional asset such as a stock or money in an interest bearing bank account the optimal solution will occur where the value of the forest asset is in equilibrium with other assets in the economy That is we want to incorporate into the analysis the rate of time preference of the forester ie the discount rate The Forestry Optimization Problem Because the growth rate is a function of time it is necessary to formulate the optimization problem in continuous time 1 2 39 In discrete tlme we nd that P 1 r The continuous time analog to this is found as B t gt 0 1 t asat gt0 1 quot l r In the economic optimization problem we want to maximize the present value of the forest stand with respect to the time period of harvest That is we want to find the point in time where the NPV is maximized The Optimal Single Rotation We will first look at the problem as a single rotation In the single rotation there is no opportunity cost incurred by failing to plant the next stand of trees at the optimal time Thus the problem is really that of determining the optimal time to harvest a crop Suppose a crop is planted at time t0 and grows in value to PQt at time t The goal is to find the harvest time that will maximize the NPV of a single rotation Let P constant price per pound of the crop There are no harvesting costs so that PQt Total Revenue The Objective Function is Maxi equot PQt with the FOC 2 PQtquot PQte quot r 0 which can be written as PQ I rPQt or NIB of waiting value of new growth MC of waiting lost interest on Total Revenue If the forest manager delays the harvest she will not earn interest on revenues PQt If the forest manager delays the harvest she will gain the value of new growth Q t This is the trade off to consider in forestry economics We can rearrange the optimality condition to get Q I r Q0 which states that the percent rate of growth in volume should equal the discount rate Profit maximization therefore dictates that the stand should be harvested when the percentage rate of growth of crop value equals the value of alternative investments Q t If Q0 gt r then the crop is increasing in value quicker than market investments and the farmer should delay the harvest decision Q I Q0 If lt r then market investments are increasing in value quicker than the growth in value of the crop harvesting should have already occurred The Case of An Infinite Forest Rotation The relevant case for most foresters is that of continuous stand rotation over time When the forester plans to replant a new forest stand immediately after cutting the old one there is now an opportunity cost that must be considered the opportunity cost of future rotations Before we begin we need to review a calculus identity that we will The sum of an infinite series is For X lt 1 l ZX 1XX2 X3 10 l X In our problem of infinite rotation we will use this as follows 1 Eer le T 672 873 T W where T is the length of each rotation The infinite rotation problem is commonly called the Faustmann Rotation after the German Forester from the early 1900 s Assume a constant net price or profit per cubic foot of timber That is if harvesting or replanting costs eXist then what we hold constant is Net Price Price per unit harvesting and replanting costs Let P the constant price per cubic foot of timber Q the volume of timber in cubic feet We can now write forester profit as n PQTequotT PQTe39 PQTe393 T PQTequotT e39Z T e39S T PQTe T1 e T e 847 PQT1 e PQT T 7 er il e err l The Optimization Problem is ng1c Pan with the FOC d1 PQ U PQT1re 7 0 dT e T l gulf which can be rearranged to yield P T 7 P PQ39ltTgtfi 3 f 19 We can now crossmultiply and write the optimality condition as PQ39T rPQT PQ39TequotT lVTR of delaying MC of waiting MC of delaying future income stream The first two terms are identical to those in the single stand or cropping decision The last term represents an additional opportunity cost of delaying the harvest As delaying the current harvest also delays income received from future harvests Therefore the optimal rotation time T requires the forester to equate the marginal value of waiting to the marginal cost of delaying the harvest of current and future stands In general T lt T single rotation lt Tmsy It is also important to analyze the effect of different parameters of the harvesting decision An Increase in the Price of Timber An increase in P will tend to shorten the rotation length because higher timber prices increase the profitability of each harvest Cutting trees earlier moves the profit of future harvests closer to the present An Increase in the Interest Rate An increase in r will tend to shorten the optimal rotation length because the forest owner is now relatively more impatient The owner is now more eager to move profit up into the present An Increase in Harvesting Costs Recall how we absorbed harvesting costs into the Net Price Thus an increase in c is analogous to a decrease in Price An increase in c will tend to increase the rotation length because cutting trees has now become less profitable the owner wishes to delay paying future harvesting costs

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