MR 边际收入计算器（两点、价格表、线性需求）Marginal Revenue Calculator (Two Points, Price Table, Linear Demand)
三种算法：由两个销量和对应总收入求边际收入 ΔTR/ΔQ；由一组价格和销量逐段计算总收入和边际收入；或由线性需求 P = a − bQ 求 MR = a − 2bQ、收入最大的销量和价格，以及该点的需求价格弹性。本地处理。Three ways: marginal revenue ΔTR/ΔQ from two sales levels and their total revenue; total and marginal revenue step by step from a list of prices and quantities; or, for linear demand P = a − bQ, MR = a − 2bQ, the revenue-maximising quantity and price, and the price elasticity there. Processed locally.
使用说明与常见问题How-to & FAQ
「边际收入计算器（两点、价格表、线性需求）」是什么？What is the Marginal Revenue Calculator (Two Points, Price Table, Linear Demand) tool?
三种算法：由两个销量和对应总收入求边际收入 ΔTR/ΔQ；由一组价格和销量逐段计算总收入和边际收入；或由线性需求 P = a − bQ 求 MR = a − 2bQ、收入最大的销量和价格，以及该点的需求价格弹性。本地处理。Three ways: marginal revenue ΔTR/ΔQ from two sales levels and their total revenue; total and marginal revenue step by step from a list of prices and quantities; or, for linear demand P = a − bQ, MR = a − 2bQ, the revenue-maximising quantity and price, and the price elasticity there. Processed locally.
如何使用「边际收入计算器（两点、价格表、线性需求）」？How do I use the Marginal Revenue Calculator (Two Points, Price Table, Linear Demand) tool?
在「边际收入计算器（两点、价格表、线性需求）」中，填写「算法」、「原总收入」、「新总收入」、「原销量」、「新销量」等参数，结果会随输入实时计算并显示在下方。In the Marginal Revenue Calculator (Two Points, Price Table, Linear Demand): Fill in "Method", "Old total revenue", "New total revenue", "Old quantity", "New quantity"; results are recalculated instantly as you type.
边际收入是什么？What is marginal revenue?
多卖一单位产品带来的总收入增加，MR = ΔTR ÷ ΔQ。需要降价才能多卖时，MR 小于价格。The extra total revenue from selling one more unit, MR = ΔTR / ΔQ. When you must cut the price to sell more, MR is below the price.
线性需求下 MR 为什么是 a − 2bQ？Why is MR = a − 2bQ for linear demand?
总收入 TR = P × Q = aQ − bQ²，对 Q 求导得 MR = a − 2bQ。所以 MR 曲线的斜率是需求曲线的两倍，MR = 0 时总收入最大。Total revenue TR = P × Q = aQ − bQ², and differentiating gives MR = a − 2bQ. The MR line is twice as steep as demand, and revenue peaks where MR = 0.
MR 和弹性有什么关系？How does MR relate to elasticity?
MR = P × (1 + 1/E)。需求富有弹性 (|E| > 1) 时 MR 为正，降价能增加收入；缺乏弹性时 MR 为负。MR = P × (1 + 1/E). With elastic demand (|E| > 1) MR is positive and a price cut raises revenue; with inelastic demand MR is negative.
能举个计算实例吗？Can you show a worked example?
例如在「边际收入计算器（两点、价格表、线性需求）」中填 算法 = 两点，原总收入 = 500，新总收入 = 540，原销量 = 50，新销量 = 54，结果区显示：边际收入：10；总收入变化：40For example, entering Method = Two points, Old total revenue = 500, New total revenue = 540, Old quantity = 50, New quantity = 54 in the Marginal Revenue Calculator (Two Points, Price Table, Linear Demand) gives: Marginal revenue: 10; Change in total revenue: 40
哪些输入会被检查？Which inputs are validated?
「边际收入计算器（两点、价格表、线性需求）」会检查这些输入——「原总收入」：所选方式用到时必须填写，不能为负数；「新总收入」：不能为负数；「原销量」、「销量 Q」：所选方式用到时必须填写，不能为负数，须为整数；「新销量」：不能为负数，须为整数；「需求截距 a」、「需求斜率 b」：所选方式用到时必须填写，须大于 0；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 Marginal Revenue Calculator (Two Points, Price Table, Linear Demand) checks its inputs — "Old total revenue": required when the chosen option uses it, cannot be negative; "New total revenue": cannot be negative; "Old quantity", "Quantity Q": required when the chosen option uses it, cannot be negative, must be a whole number; "New quantity": cannot be negative, must be a whole number; "Demand intercept a", "Demand slope b": required when the chosen option uses it, must be greater than 0; numbers above 10¹⁵ in…
有哪些选项可以调整？What options can I adjust?
「边际收入计算器（两点、价格表、线性需求）」的设置：「算法」可选 两点、价格表、线性需求（默认 两点）；「原总收入」默认 500；「新总收入」默认 540；「原销量」默认 50；「新销量」默认 54；「价格列表」默认 10 9 8 7 6；「销量列表」默认 1 2 3 4 5；「需求截距 a」默认 100；「需求斜率 b」默认 2；「销量 Q」默认 10。每次生成结果都按当前设置处理。Settings in the Marginal Revenue Calculator (Two Points, Price Table, Linear Demand) — "Method": Two points, Price table, Linear demand (default Two points); "Old total revenue" default 500; "New total revenue" default 540; "Old quantity" default 50; "New quantity" default 54; "Prices" default 10 9 8 7 6; "Quantities" default 1 2 3 4 5; "Demand intercept a" default 100; "Demand slope b" default 2; "Quantity Q" 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?
「边际收入计算器（两点、价格表、线性需求）」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 Marginal Revenue Calculator (Two Points, Price Table, Linear Demand) uses standard formulas and is for estimation only; actual figures depend on your bank, broker or tax authority's rules and rounding.
「边际收入计算器（两点、价格表、线性需求）」免费吗？需要注册吗？Is the Marginal Revenue Calculator (Two Points, Price Table, Linear Demand) free? Do I need an account?
「边际收入计算器（两点、价格表、线性需求）」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 Marginal Revenue Calculator (Two Points, Price Table, Linear 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.