稀有金属商业储备决策研究

doi:10.16381/j.cnki.issn1003-207x.2023.1329

Abstract

Abstract:

Rare metals stand as a crucial cornerstone for the advancement of strategic emerging industries. In order to foster high-quality development of the rare metals sector， China enforces a system of total control management over rare metals， while steadily enhancing a reserve system that integrates physical reserves with mineral deposit reserves. Among these measures， commercial （enterprise） reserves constitute a significant approach to the physical reserves of rare metals. Taking rare earths as an example， mathematical modeling and decision analysis under stochastic demand for two types of commercial reserve models are conducted： the “policy-guided” model （where government guides firm’s reserve decisions） and the “subsidy-incentive” model （where the government incentivizes reserve decisions through subsidies）. The results show that in the “subsidy-incentive” model， the reserve quantity， the market price and the firm’s expected profit are higher， while the expected sales volume， the government's expected profit， the consumer's expected surplus and the social welfare are lower. The influences of the total quota index， the unit reserve subsidy， the market size， the unit reserve revenue/cost， and the price sensitivity coefficient of rare earth products on the decision results are also investigated. Several managerial implications are provided for rare earth firms on the joint optimization of rare earth reserve and pricing， and for governments on the enhancement of rare earth supply chain performance through total quota management and reserve subsidies.

Key words: rare metals, commercial reserve, pricing, total quota management, optimal decision

CLC Number:

F426

Jianyun Chen,Wenxing Zhu,Xianping Luo. Research on the Commercial Reserve Decisions of Rare Metals[J]. Chinese Journal of Management Science, 2025, 33(10): 138-148.

Figures/Tables 9

符号	含义
$q ¯$	稀土产品总量指标，亦为稀土生产量
$q$	稀土产品收储量（决策变量）， $q ∈ [0, q ¯]$
$p$	稀土产品单位市场价格（决策变量）
$c$	企业单位储备成本
$γ$	政府对企业的单位储备补贴， $γ < c$
$r$	储备产品单位期望收益， $r > c$
$ε$	潜在消费者规模， $ε ∼ U [0,2 μ]$
$y (p)$	价格为 $p ∈ [0, 1 t]$ 时有需求的消费者比例， $y (p) = 1 - t p$ ，其中 $t$ 为价格敏感系数
$D (p, ε)$	价格为 $p$ 时的产品需求量， $D (p, ε) = y (p) ε$
$i$	商业储备模式类型， $i ∈ I, I I$
$I$	上标，表示“政策引导型”商业储备模式
$I I$	上标，表示“补贴激励型”商业储备模式
$q S i$	稀土产品销量， $q S i = m i n {D (p, ε), q ¯ - q}$
$π G i$	政府事后利润
$π F i$	企业事后利润
$π C i$	事后消费者剩余
$π S W i$	事后社会福利， $π S W i = π F i + π G i + π C i$
$Π G i$	政府期望利润， $Π G i = E ε [π G i]$
$Π F i$	企业期望利润， $Π F i = E ε [π F i]$
$Π C i$	期望消费者剩余， $Π C i = E ε [π C i]$
$Π S W i$	期望社会福利， $Π S W i = E ε [π S W i]$
$z 1$	$= (q ¯ - q) y (p)$
$S (z)$	$= E ε [m i n {ε, z}]$
$X$	$= q ¯ μ$
$Q$	$= (q ¯ - q) μ$
$Y 1$	$= y (r - c)$
$Y 2$	$= y (r + γ - c)$

决策结果	表达式
储备量 $q I *$	$q ¯ - μ (Q I *) 2$
市场价格 $p I *$	$(2 - Q I *) (2 t)$
期望销量 $E ε [q S I *]$	$μ (Q I ) 2 (2 - Q I ) 2$
企业期望利润 $Π F I *$	$μ (1 - Y 2) [X 2 - (Q I ) 2] t$ $+ μ (2 - Q I ) 2 (Q I *) 2 (4 t)$
政府期望利润 $Π G I *$	$- μ γ [X 2 - (Q I *) 2]$
期望消费者剩余 $Π C I *$	$μ (Q I ) 3 (2 - Q I ) (8 t)$
期望社会福利 $Π S W I *$	$μ (Q I ) 2 (2 - Q I ) (4 - Q I ) (8 t)$ $+ μ (1 - Y 1) [X 2 - (Q I ) 2] t$

决策结果	表达式
储备量 $q I I *$	$q ¯ - μ (Q I I *) 2$
市场价格 $p I I *$	$(2 - Q I I *) (2 t)$
期望销量 $E ε [q S I I *]$	$μ (Q I I ) 2 (2 - Q I I ) 2$
企业期望利润 $Π F I I *$	$μ (1 - Y 2) [X 2 - (Q I I ) 2] t$ $+ μ (2 - Q I I ) 2 (Q I I *) 2 (4 t)$
政府期望利润 $Π G I I *$	$- μ γ [X 2 - (Q I I *) 2]$
消费者期望剩余 $Π C I I *$	$μ (Q I I ) 3 (2 - Q I I ) (8 t)$
期望社会福利 $Π S W I I *$	$μ (Q I I ) 2 (2 - Q I I ) (4 - Q I I ) (8 t)$ $+ μ (1 - Y 1) [X 2 - (Q I I ) 2] t$

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