📈 需求交叉价格弹性计算器（简单法/中点法）Cross-Price Elasticity of Demand Calculator (Simple or Midpoint)

使用说明与常见问题How-to & FAQ

「需求交叉价格弹性计算器（简单法/中点法）」是什么？What is the Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) tool?

输入商品 B 价格变化前后的价格和商品 A 的需求量，用简单百分比法或中点（弧弹性）法计算交叉价格弹性，并判断两种商品是替代品、互补品还是基本无关。本地处理。Enter the old and new price of good B and the old and new quantity demanded of good A to get the cross-price elasticity by the simple percentage or midpoint (arc) method, and see whether the goods behave as substitutes, complements or roughly unrelated. Processed locally.

如何使用「需求交叉价格弹性计算器（简单法/中点法）」？How do I use the Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) tool?

在「需求交叉价格弹性计算器（简单法/中点法）」中，填写「方法」、「A 原需求量」、「A 新需求量」、「B 原价格」、「B 新价格」等参数，结果会随输入实时计算并显示在下方。In the Cross-Price Elasticity of Demand Calculator (Simple or Midpoint): Fill in "Method", "Old quantity of A", "New quantity of A", "Old price of B", "New price of B"; results are recalculated instantly as you type.

公式是什么？What is the formula?

交叉价格弹性 = A 需求量变化百分比 ÷ B 价格变化百分比。中点法用平均值作分母：[(Q₁ − Q₀)/((Q₁ + Q₀)/2)] ÷ [(P₁ − P₀)/((P₁ + P₀)/2)]，涨价和降价算出的结果一致。Cross-price elasticity = % change in quantity of A / % change in price of B. The midpoint method divides by the averages: [(Q₁ − Q₀)/((Q₁ + Q₀)/2)] / [(P₁ − P₀)/((P₁ + P₀)/2)], so a rise and a fall give the same answer.

正负号代表什么？What does the sign mean?

正值说明是替代品，例如咖啡涨价时茶的需求上升；负值说明是互补品，例如打印机涨价时墨盒需求下降；接近 0 说明基本无关。Positive means substitutes, such as tea demand rising when coffee costs more; negative means complements, such as ink demand falling when printers cost more; near 0 means roughly unrelated.

为什么两种方法结果不同？Why do the two methods differ?

简单法以原值为基数，换算方向不同结果就不同；中点法以平均值为基数，变化较大时更稳定。The simple method uses the old value as the base, so the direction of change matters; the midpoint method uses the average and is steadier for large changes.

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

例如在「需求交叉价格弹性计算器（简单法/中点法）」中填 方法 = 简单百分比法，A 原需求量 = 100，A 新需求量 = 110，B 原价格 = 10，B 新价格 = 12，结果区显示：交叉价格弹性：0.5；A 需求量变化：10 %；B 价格变化：20 %；判断：正值：替代品（B 的价格与 A 的需求同向变动）；强度：|E| < 1：反应较弱For example, entering Method = Simple percentage, Old quantity of A = 100, New quantity of A = 110, Old price of B = 10, New price of B = 12 in the Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) gives: Cross-price elasticity: 0.5; Change in quantity of A: 10 %; Change in price of B: 20 %; Reading: Positive: substitutes (the price of B and the demand for A move in the same direction); Strength: |E| < 1: weak response

哪些输入会被检查？Which inputs are validated?

「需求交叉价格弹性计算器（简单法/中点法）」会检查这些输入——「A 原需求量」：必须填写，须大于 0，须为整数；「A 新需求量」：所选方式用到时必须填写，不能为负数，须为整数；「B 原价格」、「B 新价格」：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 Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) checks its inputs — "Old quantity of A": required, must be greater than 0, must be a whole number; "New quantity of A": required when the chosen option uses it, cannot be negative, must be a whole number; "Old price of B", "New price of B": required, must be greater than 0; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「需求交叉价格弹性计算器（简单法/中点法）」的设置：「方法」可选 中点法（弧弹性）、简单百分比法（默认 中点法（弧弹性））；「A 原需求量」默认 100；「A 新需求量」默认 110；「B 原价格」默认 10；「B 新价格」默认 12。每次生成结果都按当前设置处理。Settings in the Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) — "Method": Midpoint (arc), Simple percentage (default Midpoint (arc)); "Old quantity of A" default 100; "New quantity of A" default 110; "Old price of B" default 10; "New price of B" default 12. 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?

「需求交叉价格弹性计算器（简单法/中点法）」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 Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) uses standard formulas and is for estimation only; actual figures depend on your bank, broker or tax authority's rules and rounding.

「需求交叉价格弹性计算器（简单法/中点法）」免费吗？需要注册吗？Is the Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) free? Do I need an account?

「需求交叉价格弹性计算器（简单法/中点法）」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 Cross-Price Elasticity of Demand Calculator (Simple or Midpoint) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.