📉 无谓损失计算器（税收、价格上限/下限，线性供需）Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand)

使用说明与常见问题How-to & FAQ

「无谓损失计算器（税收、价格上限/下限，线性供需）」是什么？What is the Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) tool?

用线性需求 P = a − bQ 和供给 P = c + dQ 求均衡价格和数量，再加入单位税、价格上限或价格下限，算出新的成交量、消费者剩余、生产者剩余、税收收入和无谓损失（三角形面积）。也可以直接用价格差和数量差计算。本地处理。Use linear demand P = a − bQ and supply P = c + dQ to find the equilibrium, then add a per-unit tax, a price ceiling or a price floor to get the new quantity, consumer and producer surplus, tax revenue and deadweight loss (the triangle area). You can also work straight from a price gap and quantity gap. Processed locally.

如何使用「无谓损失计算器（税收、价格上限/下限，线性供需）」？How do I use the Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) tool?

在「无谓损失计算器（税收、价格上限/下限，线性供需）」中，填写「情形」、「需求截距 a」、「需求斜率 b」、「供给截距 c」、「供给斜率 d」等参数，结果会随输入实时计算并显示在下方。In the Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand): Fill in "Case", "Demand intercept a", "Demand slope b", "Supply intercept c", "Supply slope d"; results are recalculated instantly as you type.

无谓损失是什么？What is deadweight loss?

因税收或价格管制使成交量低于均衡量，原本对买卖双方都有利的交易没有发生，损失的总剩余就是无谓损失，在图上是均衡点附近的三角形。When a tax or price control pushes trade below the equilibrium quantity, deals that would have benefited both sides do not happen. The lost total surplus is the deadweight loss, the triangle next to the equilibrium on the graph.

税收的无谓损失怎么算？How is the deadweight loss of a tax worked out?

线性供需下，加税 t 后成交量 Q₁ = (a − c − t)/(b + d)，无谓损失 = ½ × t × (Q* − Q₁)。税收收入 = t × Q₁。With linear curves, a tax t gives Q₁ = (a − c − t)/(b + d), deadweight loss = ½ × t × (Q* − Q₁) and revenue = t × Q₁.

价格上限什么时候才起作用？When does a price ceiling bind?

上限低于均衡价格才有约束力，会造成短缺；价格下限高于均衡价格才有约束力，会造成过剩。本页的剩余计算假设配给是有效率的。A ceiling only binds below the equilibrium price and causes a shortage; a floor only binds above it and causes a surplus. The surplus figures here assume efficient rationing.

能举个计算实例吗？Can you show a worked example?

例如在「无谓损失计算器（税收、价格上限/下限，线性供需）」中填 情形 = 单位税，需求截距 a = 100，需求斜率 b = 2，供给截距 c = 10，供给斜率 d = 1，税额或管制价格 = 15，结果区显示：均衡价格 / 数量：40 / 30；新的成交量：25；买方价格 / 卖方所得：50 / 35；税收收入：375；消费者剩余：625；生产者剩余：312.5；无谓损失：37.5For example, entering Case = Per-unit tax, Demand intercept a = 100, Demand slope b = 2, Supply intercept c = 10, Supply slope d = 1, Tax or controlled price = 15 in the Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) gives: Equilibrium price / quantity: 40 / 30; New quantity: 25; Buyer price / seller price: 50 / 35; Tax revenue: 375; Consumer surplus: 625; Producer surplus: 312.5; Deadweight loss: 37.5

哪些输入会被检查？Which inputs are validated?

「无谓损失计算器（税收、价格上限/下限，线性供需）」会检查这些输入——「需求截距 a」：所选方式用到时必须填写；「需求斜率 b」、「供给斜率 d」：所选方式用到时必须填写，须大于 0；「供给截距 c」：不能为负数；「税额或管制价格」、「价格差」：所选方式用到时必须填写，不能为负数；「数量差」：不能为负数，须为整数；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) checks its inputs — "Demand intercept a": required when the chosen option uses it; "Demand slope b", "Supply slope d": required when the chosen option uses it, must be greater than 0; "Supply intercept c": cannot be negative; "Tax or controlled price", "Price gap": required when the chosen option uses it, cannot be negative; "Quantity gap": cannot be negative, must be a whole number; numbers above 10¹⁵ in absolute value are…

有哪些选项可以调整？What options can I adjust?

「无谓损失计算器（税收、价格上限/下限，线性供需）」的设置：「情形」可选 单位税、价格上限、价格下限、已知价格差和数量差（默认 单位税）；「需求截距 a」默认 100；「需求斜率 b」默认 2；「供给截距 c」默认 10；「供给斜率 d」默认 1；「税额或管制价格」默认 15；「价格差」默认 2；「数量差」默认 10。每次生成结果都按当前设置处理。Settings in the Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) — "Case": Per-unit tax, Price ceiling, Price floor, Known gaps (default Per-unit tax); "Demand intercept a" default 100; "Demand slope b" default 2; "Supply intercept c" default 10; "Supply slope d" default 1; "Tax or controlled price" default 15; "Price gap" default 2; "Quantity gap" default 10. The result always uses the current settings.

计算结果可以作为最终依据吗？Can I rely on the result?

「无谓损失计算器（税收、价格上限/下限，线性供需）」按标准公式计算，结果仅供参考；实际金额以银行、券商或税务机关的规则和四舍五入方式为准。The Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) uses standard formulas and is for estimation only; actual figures depend on your bank, broker or tax authority's rules and rounding.

「无谓损失计算器（税收、价格上限/下限，线性供需）」免费吗？需要注册吗？Is the Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) free? Do I need an account?

「无谓损失计算器（税收、价格上限/下限，线性供需）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Deadweight Loss Calculator (Tax, Price Ceiling or Floor, Linear Supply and Demand) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.