基于广义Faustmann模型的营林管理决策方法学研究前沿及展望

doi:10.11707/j.1001-7488.LYKX20220833

Abstract

Abstract:

Sustainable forest management and related optimal rotation decision are important ways to mitigate global climate change. Due to the basic assumption of the classical Faustmann model that all parameters are consistent in different rotation cycles cannot be satisfied, it is necessary to explore the optimal rotation decision-making problem under the influence of multiple factors based on the generalized Faustmann model. This study focuses on the generalized Faustmann model, summarizes its theoretical expansion and frontier application, and analyses the research frontier of the generalized Faustmann model in sustainable forest management decision-making methodology. The research finds that: 1) The generalized Faustmann model has been expanded in four directions, carbon sequestration benefits, uneven-aged forest management, natural risk and tax policy, among them, the land expectation value and the corresponding first-order conditions for profit maximization can help forest owners to formulate a reasonable forest management plan. 2) By using the generalized Faustmann model, the quantity growth rate, quality growth rate and price growth rate in the Pressler indicator rate can be specified, it allows forest owners to make decision in advance in conjunction with their own risk preferences to decide whether to cut the stand in the current year. 3) The land value and timber value of the forest can be clearly distinguished under the generalized Faustmann model, so that when transferring an immature forest, the accurate valuation of forest land and timber can be achieved, and their respective tax rates can be determined under different tax policies. The extension direction of the generalized Faustmann model in the future optimal rotation decision-making research also includes the following aspects: 1) Expanding carbon sequestration benefits from aboveground biomass carbon pool to complete forestry carbon pools. 2) Expanding tax policies from foreign policies to the forestry tax and fee system with Chinese characteristics. 3) Extending model assumptions from deterministic environments to stochastic environments. 4) Expanding the research scale from stand-level to forest-level. 5) Expanding ecological benefits from carbon sequestration benefits to forest ecosystem services.

Key words: generalized Faustmann model, optimal rotation period, carbon sequestration benefits, risk management, forestry taxation and valuation, Pressler indicator rate

CLC Number:

S7-9
F307.2

Zhihan Yu,Hongqiang Yang. Research Frontier and Prospect of Forest Management Decision-Making Methodology Based on Generalized Faustmann Model[J]. Scientia Silvae Sinicae, 2024, 60(9): 170-182.

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References 0

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参数发生变化的时间 Time of parameters change	发生“一次性增长”的参数名称 Parameter name where “one-time increase” occurs	最优轮伐期 Optimal rotation period
参数发生变化的时间 Time of parameters change		经典Faustmann模型	广义Faustmann模型
当前轮伐期 During the current rotation period	重置成本 Replacement cost（$ {C}_{k} $）	延长 Increase	不变 No change
	木材价格 Timber price（$ {P}_{k}） $	缩短 Decrease	延长 Increase
	折现率 Discount rate $ {（r}_{i}） $	缩短 Decrease	缩短 Decrease
	碳价格 Carbon price $ （P\mathrm{_c}） $	延长 Increase	延长 Increase
	碳转换系数 Carbon conversion factor $ （{\alpha }_{i}） $	延长 Increase	延长 Increase
	木材的长期储存比例 Long-term storage ratio of wood（$ {\beta }_{i} $）	缩短 Decrease	不确定 Uncertain
未来轮伐期 During the future rotation period	重置成本 Replacement cost（$ {C}_{k} $）	延长 Increase	延长 Increase
	木材价格 Timber price（$ {P}_{k} $）	缩短 Decrease	缩短 Decrease
	折现率 Discount rate（$ {r}_{i} $）	缩短 Decrease	延长 Increase
	碳价格 Carbon price（$ P\mathrm{_c} $）	延长 Increase	缩短 Decrease
	碳转换系数 Carbon conversion factor（$ {\alpha }_{i} $）	延长 Increase	缩短 Decrease
	木材的长期储存比例 Long-term storage ratio of wood（$ {\beta }_{i} $）	缩短 Decrease	延长 Increase

税收政策 Tax policy	公式类别 Formula category	公式 Formula
UPT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\left[\dfrac{{r}_{1}+{y}_{1}}{\left({r}_{1}+{x}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}-{x}_{1}+{y}_{1}}\right]\times \left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{({r}_{1}+{y}_{1})({t}_{1}-{s}_{1})}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\right]\end{array} $
UPT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1}+{x}_{1} $
SVT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\left[\dfrac{{r}_{1}}{\left({r}_{1}+{x}_{1}\right){\mathrm{e}}^{{r}_{1}{t}_{1}-{x}_{1}}-{x}_{1}}\right]\times \left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}({t}_{1}-{s}_{1})}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\right]\end{array} $
SVT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{x}_{1}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $
GFRPT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\dfrac{\left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}-{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\right]}{{e}^{{r}_{1}{t}_{1}}-1}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}}{\bar{r}}}{{r}_{1}}\end{array} $
GFRPT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}}{\bar{r}}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $
NFRPT	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\dfrac{\left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}-{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\right]}{{\mathrm{e}}^{{r}_{1}{t}_{1}}-1}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}-\mathrm{A}\mathrm{M}\mathrm{C}}{\bar{r}}}{{r}_{1}}\end{array} $
NFRPT	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}-\mathrm{A}\mathrm{M}\mathrm{C}}{\bar{r}}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $
FTP	土地期望值 Land expectation value	$ \begin{array}{c}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}=\left[{V}_{1}\left({t}_{1}\right)+{\displaystyle\int }_{0}^{{t}_{1}}{A}_{1}\left({s}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}\mathrm{d}{s}_{1}-{C}_{1}{\mathrm{e}}^{{r}_{1}{t}_{1}}\right]{\mathrm{e}}^{-{r}_{1}{t}_{1}}-{Y}_{1}\left(1-\dfrac{{\mathrm{e}}^{-{r}_{1}{t}_{1}}}{{r}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}{\mathrm{e}}^{-{r}_{1}{t}_{1}}\end{array} $
FTP	一阶条件 First-order condition	$ \dfrac{\dfrac{\mathrm{d}{V}_{1}\left({t}_{1}\right)}{\mathrm{d}{t}_{1}}+{A}_{1}\left({t}_{1}\right)-{Y}_{1}}{{V}_{1}\left({t}_{1}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}}={r}_{1} $

税收政策 Tax policy	价值类别 Value category	公式 Formula
UPT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{s}_{1}\right)}}+\left(\dfrac{{y}_{1}-{x}_{1}}{{r}_{1}+{y}_{1}}\right){\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left[1-{\mathrm{e}}^{-\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
UPT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}-{\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){s}_{1}}-1\right)}{\left({\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right){t}_{1}}-1\right)} $
SVT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{{r}_{1}\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{x}_{1}}{{r}_{1}}{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
SVT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $
GFRPT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}}{\bar{r}}}{{r}_{1}}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
GFRPT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $
NFRPT	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{x}_{1}\dfrac{\bar{p}\mathrm{F}\mathrm{P}-\mathrm{A}\mathrm{M}\mathrm{C}}{\bar{r}}}{{r}_{1}}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
NFRPT	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $
FTP	林分价值 Forest value	$ \begin{array}{c}{\mathrm{F}\mathrm{V}}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}+\displaystyle\sum _{{z}_{1}={s}_{1}+1}^{{t}_{1}}{A}_{1}\left({z}_{1}\right){\mathrm{e}}^{\left({r}_{1}+{y}_{1}\right)\left({t}_{1}-{z}_{1}\right)}+{V}_{1}\left({t}_{1}\right)}{{\mathrm{e}}^{{r}_{1}\left({t}_{1}-{s}_{1}\right)}}-\dfrac{{Y}_{1}}{{r}_{1}}\left[1-{\mathrm{e}}^{-{r}_{1}\left({t}_{1}-{s}_{1}\right)}\right]\end{array} $
FTP	土地价值 Land value	$ {L}_{1}\left({s}_{1}\right)=\dfrac{{\mathrm{L}\mathrm{E}\mathrm{V}}_{1}\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-{\mathrm{e}}^{{r}_{1}{s}_{1}}\right)+{\mathrm{L}\mathrm{E}\mathrm{V}}_{2}\left({\mathrm{e}}^{{r}_{1}{s}_{1}}-1\right)}{\left({\mathrm{e}}^{{r}_{1}{t}_{1}}-1\right)} $

Research Frontier and Prospect of Forest Management Decision-Making Methodology Based on Generalized Faustmann Model

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