TIMBER SUPPLY UNDER DEMAND UNCERTAINTY: WELFARE GAINS FROM PERFECT COMPETITION WITH RATIONAL EXPECTATIONS

ABSTRACT. This paper presents a noneconometric approach to estimating the short‐run timber supply function based on optimal harvest decisions. Determination of optimal harvest levels and estimation of supply function coefficients are integrated into one step by incorporating a parametric short‐run timber supply function into the harvest decision model. In this manner we convert the original harvest decision model into a new optimization problem with the supply function coefficients functioning as “decision variables.” Optimal solution to the new decision model gives the coefficients of the short‐run supply function and, indirectly, the optimal harvest levels. This approach enables us to develop stochastic models of the timber market that are particularly useful for forest sector analysis involving comparison of alternative institutional regimes or policy proposals and when the timber market is affected by stochastic variables. For demonstration purposes, we apply this method to compare the performances of two timber market regimes (perfect competition and monopoly) under demand uncertainty, using the Swedish data. The results show that the expected timber price is 22 percent lower and the expected annual timber supply is 43 percent higher in the competitive market than in the monopoly market. This confirms the theoretical result that monopoly reduces supply and increases price. The expected social welfare gain from perfect competition over monopoly is about 24 percent.     

AN OPTIMIZATION APPROACH TO IDENTIFYING TIMBER SUPPLY FUNCTION COEFFICIENTS

This paper examines an optimization approach to identifying short-run timber supply function coefficients when the form of the supply function is known. By definition, a short-run timber supply function is a functional relationship between the optimal harvest level in each period (e.g., each year) and the actual forest-market state in the same period. The short-run timber supply function represents the optimal harvest decision policy, and therefore, the problem of optimal harvesting can be formulated as a problem of determining this function. When the form of the supply function is known, the problem becomes one of identifying the coefficients of the supply function. If the management objective is to maximize the expected present value of net revenues from timber harvesting over an infinite time horizon, and the timber price process is, in a sense, stationary, the supply function coefficients correspond to the optimal solution to an anticipative optimization problem. In this case, the supply function coefficients can be determined by maximizing the expected present value of the net revenues from timber harvesting, where periodic harvest levels are determined using the supply function. Numerical results show that the short-run supply functions determined using this approach gives good approximations of the true supply function.     

TEMPORAL AGGREGATION AND TESTING FOR TIMBER PRICE BEHAVIOR

ABSTRACT. Different harvest timing models make different assumptions about timber price behavior. Those seeking to optimize harvest timing are thus first faced with a decision regarding which assumption of price behavior is appropriate for their market, particularly regarding the presence of a unit root in the timber price time series. Unfortunately for landowners and investors, the literature provides conflicting guidance on this subject. One source for the ambiguous results of unit root tests of timber prices may involve data problems. We used Monte Carlo simulations to show that aggregating observations below their observed rate resulted in similar power reductions and empirical size distortions across three classes of unit root tests. Moving‐average error structures can also affect power and sizes of tests on period‐averaged data. Such error structures can also be created by the kind of temporal averaging common in reported timber prices. If we take timber prices at their face value and therefore ignore these sampling error and temporal aggregation complications, we find that unit root tests on southern timber prices support a unit root in 158 out of 208 product‐deflation combinations tested, random walks in 38 of the series found to be nonsta‐tionary, and stationarity in none. However, if we recognize temporal aggregation errors, unit root tests more commonly favor stationarity, especially for pulpwood stumpage. Because price trends for sawtimber and pulpwood products may behave differently even in the same region, stochastic harvest timing models must be developed that allow their multiple products to follow different price paths.     

THE ECONOMICS OF TIMBER SUPPLY: AN ANALYTICAL SYNTHESIS OF MODELING APPROACHES

The joint supply of timber and other services from forest environments plays a central role in most forest land debates. This paper defines a general conceptual model of timber supply that provides the context for discussing both individual harvest choice and aggregate supply models. While the structure and breadth of these models has developed considerably over the last twenty years, unresolved issues remain. Supply formulations that account for the quality and vintage distribution of forest capital will be necessary for improving medium- and long-run forecasts. This will be especially important for examining the potential impacts of structural changes in forest production and timber markets. In addition, consistent aggregation of individual owners to total supply will be required to address changing forest land ownership patterns.     

VALUING A TIMBER HARVEST CONTRACT AS A HIGH‐DIMENSIONAL AMERICAN CALL OPTION VIA LEAST‐SQUARES MONTE CARLO SIMULATION

Abstract Industrial timberland ownership in the United States has shifted substantially in the last 20 years. Having sold their fee‐owned timberlands, forest products companies relied heavily on the open market for raw timber. To reduce their exposure to market risks, however, forest products companies have been using a number of supply chain instruments, such as timber harvest contracts. As these vehicles become increasingly important to the forest industry, it is necessary and important to determine their economic values. In this study, we treated a 3‐year timber harvest contract on a 30‐year‐old loblolly pine plantation as a high‐dimensional American call option and calculated its value by the least‐squares Monte Carlo simulation technique. The estimated values of such a contract ranged from $1,693/ac to $1,984/ac under two timber price assumptions. With reasonable starting timber prices and strike price in the simulation, random timber prices led to higher contract values. Results from this study can help private landowners, timber brokers, and forest products companies better manage their business risks.     

HARVESTING AN AGE‐STRUCTURED POPULATION AS BIOMASS: DOES IT WORK?

Abstract The economics of fisheries is based heavily on describing fish populations by the surplus production model. Both economists and ecologists have different opinions on whether this approach provides an adequate biological basis for economic analysis. This study takes an age‐structured population model and shows how, under equilibrium conditions, it determines the surplus production model. The surplus production model is then used to solve an optimal feedback policy for a generic optimal harvesting problem. Next, it is assumed that the fishery manager applies this feedback policy even though the fish population actually evolves according to the age‐structured model. This framework is applied to the widow rockfish, Atlantic menhaden, and Pacific halibut fisheries. Population age‐structure contains information on future harvest possibilities. The surplus production model neglects this information and may lead to major deviations between the expected and actual outcomes especially under multiple steady states and nonlinearities.     

OPTIMAL TIMING OF SALVAGE HARVEST IN RESPONSE TO A STOCHASTIC INFESTATION

Abstract Following a catastrophic disturbance, forest managers may choose to perform a salvage harvest to recoup timber losses. When the disturbance process evolves stochastically, a unique option value arises associated with the salvage harvest decision. This option value represents the value of postponing a salvage harvest to gain more information about the disturbance process. This paper uses a real options approach to determine how much of a forested area must be infested to trigger a salvage harvest when the forest provides both timber and nontimber values. Analytical results indicate slower rates of forest recovery will optimally delay a salvage harvest while forested areas with large timber values and where nontimber values are more sensitive to the presence of dead and dying trees should be harvested more immediately. The model is applied to a mountain pine beetle outbreak in Idaho's Sawtooth National Forest using readily available aerial detection survey data.     

Forestry management under uncertainty

The forest harvest and road construction planning problem consists fundamentally of managing land designated for timber production and divided into harvest cells. For each time period the planner must decide which cells to cut and what access roads to build in order to maximize expected net profit. We have previously developed deterministic mixed integer linear programming models for this problem. The main contribution of the present work is the introduction of a multistage Stochastic Integer Programming model. This enables the planner to make more robust decisions based on a range of timber price scenarios over time, maximizing the expected value instead of merely analyzing a single average scenario. We use a specialization of the Branch-and-Fix Coordination algorithmic approach. Different price and associated probability scenarios are considered, allowing us to compare expected profits when uncertainties are taken into account and when only average prices are used. The stochastic approach as formulated in this work generates solutions that were always feasible and better than the average solution, while the latter in many scenarios proved to be infeasible.     

Long-range timber supply planning for a vertically integrated paper mill

We consider a vertically integrated papermaking operation composed of an integrated pulp and paper mill with its regional supply network. Considering land procurement and harvest rotation as strategic decision variables, we construct a model to establish a long-range timber supply plan that minimizes the total discounted cost of meeting annual virgin wood fiber demand over an infinite horizon. Under appropriate assumptions on costs and storage, the land procurement and harvest rotation decisions are separable with harvest rotation being determined via a forest economics-type equation and land procurement being determined by a newsvendor-type equation.     

基于医保规制和消费者效用的双渠道医药供应链竞争策略

医药消费者在面对双渠道零售时,会明显受到实体渠道医保报销政策的影响。基于这一现象,本文构建了同时考虑医保规制政策和消费者效用的双渠道医药供应链博弈模型,研究了医保报销比例和电商佣金比例对双渠道定价、供应链绩效以及社会福利的影响规律。研究结果表明:医药双渠道定价会同时随着平台收费标准和医保报销比例的增加而降低;医保报销比例的增加会提高社会福利、降低供应链绩效,同时会弱化网络渠道低价优势,能够有效抑制渠道蚕食现象;电商平台佣金比例的增加虽然在一定程度上提高了社会福利,但是会严重瓜分渠道利润,加剧渠道竞争,导致供应链绩效降低。     

MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

ENVIRONMENTAL AND FINANCIAL SUSTAINABILITY OF FOREST MANAGEMENT PRACTICES

One of the guiding themes for forest management policy throughout much of North America is sustained yield. The basic premise behind this theme is that a constant or nondeclining flow of services from the forest is socially desirable. Unfortunately, the act of capturing the benefits of this service (timber harvesting) often has detrimental effects on the timber-productive capacity of a forest site. This paper presents a dynamic program that is used to determine the optimal harvest system choice for a timber stand described by average piece size, stand density, a measure of site quality, and stumpage value. The harvest systems are defined by logging costs, reforestation and rehabilitation costs, and the impact of the system on the productivity of the site. An application of the model is presented for lodgepole pine in Alberta. We conclude that, at high discount rates, soil conservation is not economically rational. At lower discount rates, some degree of soil conservation is desirable on the more productive sites. At lower discount rates, there also appears to be an incentive for more intensive forest management. Limitations on acceptable harvest practices can have a large impact on optimal rotation age and the volume harvested. There is a large opportunity cost resulting from a requirement for sustainable volume production because of the impact of harvesting on soil productivity.     

奖惩机制下零售商信息分享对闭环供应链的影响研究

研究奖惩机制下零售商的信息分享策略以及对闭环供应链的影响,建立了由制造商和零售商以及消费者组成的闭环供应链,其中制造商负责回收废旧产品并进行再制造。分别研究了集中式决策的情形和分散式决策下零售商信息分享和不分享的情形。研究发现,若政府在社会总福利目标中不考虑奖惩成本且回收难度较小时,零售商信息分享使社会总福利提高,反之,导致社会总福利降低;零售商信息分享总会使消费者剩余的期望值降低,但能够提高废旧产品的回收率。最后,针对零售商信息分享引起社会福利提高的情况设计了回收责任分担契约激励零售商分享信息。关键词:信息分享;奖惩机制;闭环供应链;社会福利;消费者剩余     

DIFFUSION INDUCED SHIFT OF BIFURCATION POINT IN A MANGROVE ECOSYSTEM FOOD‐CHAIN MODEL WITH HARVESTING

Abstract The present paper deals with a detritus‐based food‐chain model within a mangrove ecosystem. The top predator (mainly fish) is assumed to have a commercial value and undergoes harvesting. Stability and bifurcation behavior of the model is studied and a threshold harvest rate is obtained. Next we introduce environmental nonhomogenity into the model equation. The resulting reaction diffusion system is investigated, and the criteria for supercritical Hopf bifurcation is obtained using the method of Lyapunov first coefficient. A comparison of the critical harvest rates under the homogeneous and the nonhomogeneous context is performed both analytically and numerically.     

Asymptotically optimal dividend policy for regime-switching compound Poisson models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.     

Optimal harvest strategy for even‐aged stands with price uncertainty and risk of natural disturbances

We present a reservation price model to examine the joint impacts of natural disturbances and stumpage price uncertainty on the optimal harvesting decision for even‐aged forest stands. We consider a landowner who manages a loblolly pine stand to produce timber and amenities, under age‐dependent risk of wildfires and uncertainty in future timber prices. We show that the incorporation of risk of wildfires decreases the optimal reservation prices. The inclusion of risk of wildfires leads to lower land values and reduces the mean harvest age compared with the case of no‐risk of wildfires. Higher economic gains are obtained with the reservation price strategy compared with the deterministic rotation age model—a difference in the land value of $2,326 ha^?1 (21%) between the two approaches. Recommendations for Resource Managers

• Our adaptive harvest strategy shows that the incorporation of risk of wildfires decreases the optimal reservation prices compared with the case of no‐risk of wildfires.
• Low reservation prices—a price that makes the landowner indifferent between harvesting or waiting longer—result in lower economic benefits for landowners and potential conversions of lands to nonforest use.
• Forest management practices oriented to reduce the effects of catastrophic disturbances, for example, creating a more complex forest structure with different stand densities, become imperative to ensure the sustainability of forestlands in the US South.
• Our analysis also suggests that the valuation of forestry investments should consider not only the risk of catastrophic events but also uncertainty in future timber prices. Higher appraisals of land value are obtained when timber price uncertainty is explicitly recognized, providing financial incentives for landowners to invest in forestry.

     

REGIONAL ECONOMIC IMPACTS OF CLIMATE CHANGE: A COMPUTABLE GENERAL EQUILIBRIUM ANALYSIS FOR AN ALASKA FISHERY

We compute the effects on the Alaska economy of reduced pollock harvests from rising sea surface temperature using a regional dynamic computable general equilibrium model coupled with a stochastic stock‐yield projection model for eastern Bering Sea walleye pollock. We show that the effects of decreased pollock harvest are offset to some extent by increased pollock price, and that fuel costs and the world demand for the fish, as well as the reduced supply of the fish from rising sea surface temperature, are also important factors that determine the economic and welfare effects.     

Resale price maintenance in supply chains with general multiplicative demand

We analyze a supply chain with a Resale Price Maintenance (RPM) contract in which the manufacturer sets the retail price with a general multiplicative price–demand function and prove the existence/uniqueness of an equilibrium. We also compare the equilibrium prices and quantities, consumer surplus and total system welfare for the RPM and wholesale price contracts. We conclude that a manufacturer may capture a smaller share of the total supply chain profit despite her ability to set the retail price.     

INFERRING A BIOPOLITICAL CONSENSUS VIEW OF STOCHASTIC DYNAMICS FOR MANAGEMENT OF A TRANSBOUNDARY FISHERY

ABSTRACT. Management of trans‐boundary fisheries is a complicated problem with biological, legal, economic and political implications. We propose a simple stochastic differential‐equation model to describe a biopolitical consensus view of fish stock dynamics. Estimates of the drift and diffusion terms of three stochastic differential equations are obtained using data from the southern bluefin tuna (SBT) fishery with a method based on the Kolmogorov‐Smirnov statistic. We refer to these estimated equations as alternative biopolitical consensus views of SBT stock dynamics. Each of these is used to generate a time series of optimal harvest that achieves the objective of maximizing the present value of expected fishery returns. These time series of optimal harvests are then compared to actual harvests for the period 1981 1997.     

DOES A RENEWABLE NATURAL RESOURCE USUALLY HAVE MANY NEAR‐OPTIMAL ALLOCATION PATHS?

ABSTRACT. Utilizing a deterministic single‐species computational renewable natural resource model, it is found that there exist many dynamic allocation paths near‐optimal to the efficient path, where the latter maximizes conventionally‐defined social welfare. Some alternative paths involve substantial trading of surplus over time among market participants and hold different implications for income distribution. Universality of findings cannot be asserted, but the results are intuitively plausible and suggest that multiple near‐optimal allocation paths may exist in related models as well. Existence of many near‐optimal paths holds significant implications for theory and policy.