🛒 消费者剩余与生产者剩余（线性需求与供给）Consumer & Producer Surplus Calculator (Linear Demand & Supply)
按线性需求 P = a − bQ 计算消费者剩余；填写线性供给 P = c + dQ 时求出均衡价格和数量，并给出生产者剩余与总剩余。也可以直接输入最高愿付价格、市场价格和数量。本地处理。Consumer surplus for a linear demand curve P = a − bQ; with a linear supply curve P = c + dQ it finds the equilibrium price and quantity and also gives producer and total surplus. You can also enter the maximum willingness to pay, the market price and the quantity directly. Processed locally.
使用说明与常见问题How-to & FAQ
「消费者剩余与生产者剩余（线性需求与供给）」是什么？What is the Consumer & Producer Surplus Calculator (Linear Demand & Supply) tool?
按线性需求 P = a − bQ 计算消费者剩余；填写线性供给 P = c + dQ 时求出均衡价格和数量，并给出生产者剩余与总剩余。也可以直接输入最高愿付价格、市场价格和数量。本地处理。Consumer surplus for a linear demand curve P = a − bQ; with a linear supply curve P = c + dQ it finds the equilibrium price and quantity and also gives producer and total surplus. You can also enter the maximum willingness to pay, the market price and the quantity directly. Processed locally.
如何使用「消费者剩余与生产者剩余（线性需求与供给）」？How do I use the Consumer & Producer Surplus Calculator (Linear Demand & Supply) tool?
在「消费者剩余与生产者剩余（线性需求与供给）」中，填写「模式」、「需求截距 a（最高愿付价格）」、「需求斜率 b」、「供给截距 c（可选）」、「供给斜率 d（可选）」等参数，结果会随输入实时计算并显示在下方。In the Consumer & Producer Surplus Calculator (Linear Demand & Supply): Fill in "Mode", "Demand intercept a (maximum willingness to pay)", "Demand slope b", "Supply intercept c (optional)", "Supply slope d (optional)"; results are recalculated instantly as you type.
均衡怎么算？How is the equilibrium found?
需求 P = a − bQ 与供给 P = c + dQ 相交处：Q* = (a − c) ÷ (b + d)，P* = a − bQ*。例如 a = 100、b = 2、c = 10、d = 1 时 Q* = 30、P* = 40，消费者剩余 = ½ × 30 × (100 − 40) = 900，生产者剩余 = ½ × 30 × (40 − 10) = 450。Where demand P = a − bQ meets supply P = c + dQ: Q* = (a − c) ÷ (b + d) and P* = a − bQ*. With a = 100, b = 2, c = 10 and d = 1, Q* = 30 and P* = 40, so consumer surplus = ½ × 30 × (100 − 40) = 900 and producer surplus = ½ × 30 × (40 − 10) = 450.
没有供给曲线怎么办？What if I only have a demand curve?
选“需求曲线 + 给定价格”，页面按 Q = (a − P) ÷ b 求出需求量，再算消费者剩余；或选“直接输入三角形”，填写最高愿付价格、价格和数量。数量可以是小数。Choose Demand curve at a given price: the page finds Q = (a − P) ÷ b and the consumer surplus. Or choose Enter the triangle directly with the maximum willingness to pay, the price and the quantity. Quantities can be decimals.
为什么是三角形面积？Why a triangle area?
线性需求下，消费者剩余是需求曲线以下、价格线以上的三角形面积；生产者剩余是价格线以下、供给曲线以上的三角形面积。With linear demand, consumer surplus is the triangle below the demand curve and above the price line; producer surplus is the triangle below the price line and above the supply curve.
能举个计算实例吗？Can you show a worked example?
例如在「消费者剩余与生产者剩余（线性需求与供给）」中填 模式 = 需求 P = a − bQ 与供给 P = c + dQ…，需求截距 a（最高愿付价格） = 100，需求斜率 b = 2，供给截距 c（可选） = 10，供给斜率 d（可选） = 1，市场价格 P（需求曲线 + 价格模式） = 40，结果区显示：均衡数量 Q*：30；均衡价格 P*：40.00；消费者剩余：900.00；生产者剩余：450.00；总剩余：1,350.00；ℹ Q* = (a − c) ÷ (b + d)；CS = ½Q*(a − P*)；PS = ½Q*(P* − c)For example, entering Mode = Demand P = a − bQ and supply…, Demand intercept a (maximum willingness to pay) = 100, Demand slope b = 2, Supply intercept c (optional) = 10, Supply slope d (optional) = 1, Market price P (demand curve at a price) = 40 in the Consumer & Producer Surplus Calculator (Linear Demand & Supply) gives: Equilibrium quantity Q*: 30; Equilibrium price P*: 40.00; Consumer surplus: 900.00; Producer surplus: 450.00; Total surplus: 1,350.00; ℹ Q* = (a − c) ÷ (b + d); CS = ½Q*(a − P*); PS = ½Q*(P* − c)
哪些输入会被检查？Which inputs are validated?
「消费者剩余与生产者剩余（线性需求与供给）」会检查这些输入——「需求截距 a（最高愿付价格）」、「需求斜率 b」：所选方式用到时必须填写；「供给截距 c（可选）」、「市场价格 P（需求曲线 + 价格模式）」、「数量 Q（直接输入模式）」：所选方式用到时必须填写，不能为负数；「供给斜率 d（可选）」：不能为负数；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 Consumer & Producer Surplus Calculator (Linear Demand & Supply) checks its inputs — "Demand intercept a (maximum willingness to pay)", "Demand slope b": required when the chosen option uses it; "Supply intercept c (optional)", "Market price P (demand curve at a price)", "Quantity Q (direct mode)": required when the chosen option uses it, cannot be negative; "Supply slope d (optional)": cannot be negative; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the…
有哪些选项可以调整？What options can I adjust?
「消费者剩余与生产者剩余（线性需求与供给）」的设置：「模式」可选 需求 P = a − bQ 与供给 P = c + dQ 求均衡、需求曲线 + 给定价格、直接输入三角形（默认 需求 P = a − bQ 与供给 P = c + dQ 求均衡）；「需求截距 a（最高愿付价格）」默认 100；「需求斜率 b」默认 2；「供给截距 c（可选）」默认 10；「供给斜率 d（可选）」默认 1；「市场价格 P（需求曲线 + 价格模式）」默认 40；「数量 Q（直接输入模式）」默认 10。每次生成结果都按当前设置处理。Settings in the Consumer & Producer Surplus Calculator (Linear Demand & Supply) — "Mode": Demand P = a − bQ and supply P = c + dQ (equilibrium), Demand curve at a given price, Enter the triangle directly (default Demand P = a − bQ and supply P = c + dQ (equilibrium)); "Demand intercept a (maximum willingness to pay)" default 100; "Demand slope b" default 2; "Supply intercept c (optional)" default 10; "Supply slope d (optional)" default 1; "Market price P (demand curve at a price)" default 40; "Quantity Q (direct…
计算结果可以作为最终依据吗？Can I rely on the result?
「消费者剩余与生产者剩余（线性需求与供给）」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 Consumer & Producer Surplus Calculator (Linear Demand & Supply) uses standard formulas and is for estimation only; actual figures depend on your bank, broker or tax authority's rules and rounding.
「消费者剩余与生产者剩余（线性需求与供给）」免费吗？需要注册吗？Is the Consumer & Producer Surplus Calculator (Linear Demand & Supply) free? Do I need an account?
「消费者剩余与生产者剩余（线性需求与供给）」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 Consumer & Producer Surplus Calculator (Linear Demand & Supply) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.