Consumer Surplus Calculator
From the maximum willingness-to-pay, market price and quantity, estimate consumer surplus under a linear-demand approximation.
輸入資料
計算結果
重點速覽：Consumer surplus is the sum of the gap between what consumers are willing to pay and what they actually pay — the net benefit from trade. Under a linear-demand approximation: CS = ½ x (max willingness-to-pay - market price) x quantity. Example: intercept 100, price 60, qty 500 → CS = ½ x 40 x 500 = HK$10,000. WARNING: Linear triangle approximation; max WTP is the demand intercept, not an individual bid; real demand may be non-linear (use integration); if price ≥ intercept, CS = 0. Education, not advice.
計算公式
消費者剩餘 = ½ × (最高願付價 − 市場價) × 成交量。
$$CS = \tfrac{1}{2} \times (P_{max} - P_{market}) \times Q$$使用說明
- Enter the demand curve's maximum willingness-to-pay (intercept).
- Enter the actual market price and quantity.
- View the approximate consumer surplus.
消費者剩餘計算範例
| 情境 | 最高願付價 | 市場價 | 成交量 | 消費者剩餘 |
|---|---|---|---|---|
| 基準 | 100 | 60 | 500 | 10,000 |
| 價差擴大 | 120 | 80 | 300 | 6,000 |
| 大量交易 | 50 | 30 | 1,000 | 10,000 |
消費者剩餘 = ½ × (最高願付價 − 市場價) × 成交量。市場價越低、願付價越高、成交量越大，消費者剩餘越大。
理財情境案例
案例一：計算市場的消費者剩餘
假設某商品的需求呈線性，最高願付價 (需求曲線與縱軸交點) 為 100 元，實際市場成交價為 60 元，成交量為 500 單位。
套用公式：消費者剩餘 = ½ × (最高願付價 − 市場價) × 成交量 = ½ × (100 − 60) × 500 = ½ × 40 × 500 = 10,000 元。
這 10,000 元代表：消費者整體『願意付、但實際不必付』的金額總和 — 也就是購買這批商品為消費者帶來的淨效益 (物超所值的部分)。它在需求曲線與市場價格線之間，形成一個三角形的面積。
案例二：降價如何增加消費者剩餘
延續上例 (最高願付價 100)，若市場價從 60 元降到 40 元，且成交量因降價從 500 升至 700 單位。
新消費者剩餘 = ½ × (100 − 40) × 700 = ½ × 60 × 700 = 21,000 元，比原本的 10,000 元大幅增加。
降價帶來兩重效果：一是原有買家每單位省更多錢 (價差從 40 擴大到 60)，二是吸引更多買家入場 (成交量增加)，兩者共同推升消費者剩餘。這解釋了為何競爭與效率提升帶來的降價能提升消費者福利;而生產者剩餘與消費者剩餘之和 (社會總剩餘) 的變化，則是評估市場效率與政策 (如稅、補貼) 得失的基礎，若市場被扭曲則會產生『無謂損失』。
常見問題
What does consumer surplus represent?
It is the sum of the gap between what consumers are willing to pay and what they actually pay — the extra value they get from trade. If you would pay HK$100 but only pay HK$60, you 'gain' HK$40 of satisfaction; summing all such gaps is consumer surplus, a key measure of consumer welfare and market efficiency.
Why is there a ½ in the formula?
Under a linear demand curve, consumer surplus is the triangle between the demand curve and the price line. Triangle area = ½ x base x height, where base = quantity and height = (max WTP - price). For non-linear demand, integrate the area under the curve.
How does a price rise affect consumer surplus?
A higher price shrinks (max WTP - price) and usually also quantity, so consumer surplus falls — which is why taxes and price controls are analysed for their welfare impact. Lower prices enlarge it. Policy analysis compares the change in consumer (and producer) surplus.
How is it related to producer surplus and total surplus?
Consumer surplus (below price, above demand) plus producer surplus (above supply, below price) equals total surplus (social welfare). In an undistorted competitive market, total surplus is maximised; taxes, price caps, monopolies or subsidies cause a deadweight loss — the surplus that disappears. See the deadweight-loss calculator.
Why the ½ again?
The ½ comes from the geometry: linear demand makes the surplus a right triangle (area = ½ x base x height). Here base = quantity Q and height = (P_max - P_market), giving CS = ½ x (P_max - P_market) x Q. This is a linear simplification; real demand curves may be curved, in which case the area is an integral, not exactly a triangle. Still, the ½ formula conveys the concept and magnitude well for teaching and estimates.
相關工具
參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。