Understanding Firm Revenue: TR, AR, MR and Revenue Maximisation | 理解企业收益：总收益、平均收益、边际收益与收益最大化

📚 Understanding Firm Revenue: TR, AR, MR and Revenue Maximisation | 理解企业收益：总收益、平均收益、边际收益与收益最大化

Revenue is one of the most fundamental concepts in A-Level Economics. It measures the income a firm receives from selling its output, and it forms the building block for analysing profits and market behaviour. This article explains total revenue, average revenue and marginal revenue, shows how revenue curves differ across market structures, links revenue to price elasticity of demand, and clarifies the difference between revenue maximisation and profit maximisation.

收益是 A-Level 经济学中最基本的概念之一。它衡量企业销售产品所获得的收入，是分析利润和市场行为的基础。本文将解释总收益、平均收益和边际收益，说明不同市场结构中收益曲线的差异，将收益与需求价格弹性联系起来，并阐明收益最大化与利润最大化的区别。

1. Definitions: Total, Average and Marginal Revenue | 定义：总收益、平均收益与边际收益

Revenue refers to the income a firm receives from selling its output over a period of time. Total revenue (TR) is the total money received from the sale of all units: TR = Price × Quantity, or TR = P × Q. Average revenue (AR) is revenue per unit sold: AR = TR ÷ Q. Since TR = P × Q, dividing by Q gives AR = P, so average revenue is always equal to the selling price. Marginal revenue (MR) is the addition to total revenue from selling one more unit of output: MR = ΔTR ÷ ΔQ.

收益是指企业在一定时期内销售产品所获得的收入。总收益（TR）是企业销售全部产品所得到的总货币收入：TR = 价格 × 数量，即 TR = P × Q。平均收益（AR）是每单位产品带来的收益：AR = TR ÷ Q。由于 TR = P × Q，除以 Q 后可得 AR = P，因此平均收益总是等于销售价格。边际收益（MR）是每多销售一单位产品所增加的总收益：MR = ΔTR ÷ ΔQ。

TR = P × Q,    AR = TR ÷ Q = P,    MR = ΔTR ÷ ΔQ

These three measures are related but play different roles. AR tells us the price at which each unit is sold, while MR tells us how much extra revenue is generated by the last unit. Understanding the gap between AR and MR is key to analysing imperfect competition.

这三个指标相互关联但作用不同。AR 告诉我们每单位产品的销售价格，而 MR 告诉我们最后一单位产品带来了多少额外收益。理解 AR 与 MR 之间的差距是分析不完全竞争的关键。

2. Revenue Calculations and Worked Example | 收益计算与实例

Consider a firm facing the linear demand curve P = 10 − Q, where P is price in dollars and Q is quantity. The table below calculates TR, AR and MR as Q changes from 0 to 10. AR equals P at every output level. MR falls twice as steeply as the demand curve because when a firm lowers price to sell more, it gains revenue on extra units but loses revenue on units that could have been sold at the higher price.

假设某企业面临线性需求曲线 P = 10 − Q，其中 P 为价格（美元），Q 为数量。下表计算了 Q 从 0 到 10 变化时的 TR、AR 和 MR。在每个产量水平上，AR 都等于 P。MR 的下降速度是需求曲线的两倍，因为当企业降价以增加销量时，它从额外单位中获得收益，但原本可以按较高价格出售的单位却损失了收益。

The table shows that total revenue rises while MR is positive, reaches its maximum of 25 at Q = 5, and then declines as MR becomes negative. AR falls continuously from 10 to 0, while MR falls twice as fast, from 9 to −9. This example is useful for understanding why the MR curve is steeper than the demand curve.

上表显示，当 MR 为正时，总收益持续上升，在 Q = 5 时达到最大值 25，随后随着 MR 变为负值而下降。AR 从 10 持续下降到 0，而 MR 下降速度是其两倍，从 9 降至 −9。这个例子有助于理解为什么 MR 曲线比需求曲线更陡峭。

3. Revenue Curves under Perfect Competition | 完全竞争下的收益曲线

In perfect competition, each firm is a price taker: it can sell any quantity at the market price, but cannot influence that price. Therefore the demand curve facing the individual firm is perfectly elastic (horizontal) at the ruling market price. Since AR = P, the AR curve is also horizontal. Because each extra unit sells at the same price, MR equals P as well. Thus AR = MR = P, and the firm’s total revenue is a straight line through the origin with constant slope P.

在完全竞争市场中，每个企业都是价格接受者：它可以按市场价格销售任意数量，但无法影响该价格。因此单个企业面临的需求曲线是完全有弹性的（水平线），位于现行市场价格处。由于 AR = P，AR 曲线也是水平线。由于每增加一单位产品都按相同价格出售，MR 也等于 P。因此 AR = MR = P，企业的总收益是一条通过原点、斜率为 P 的直线。

AR = MR = P    and    TR = P × Q (with P constant)

Under perfect competition, the individual firm’s revenue curves are very simple. The horizontal demand curve means that the firm does not face a trade-off between price and quantity; it simply takes the market price as given and decides how much to produce based on its costs.

在完全竞争下，单个企业的收益曲线非常简单。水平的需求曲线意味着企业不需要在价格和数量之间进行权衡；它只是接受市场价格，并根据成本决定生产多少。

4. Revenue Curves under Imperfect Competition | 不完全竞争下的收益曲线

Under imperfect competition (monopoly, monopolistic competition and oligopoly with differentiated products), the firm faces a downward-sloping demand curve. To sell more output, the firm must lower its price. The demand curve is the AR curve. Because the firm lowers price on all units, the marginal revenue from an extra unit is less than the price of that unit; hence the MR curve lies below the AR curve. For a linear demand curve P = a − bQ, the marginal revenue curve is MR = a − 2bQ, so MR has the same vertical intercept but twice the slope.

在不完全竞争（垄断、垄断竞争以及产品差异化的寡头垄断）中，企业面临向下倾斜的需求曲线。为了销售更多产量，企业必须降低价格。需求曲线就是 AR 曲线。由于企业对所有单位降价，额外一单位产品的边际收益低于该单位的价格；因此 MR 曲线位于 AR 曲线下方。对于线性需求曲线 P = a − bQ，边际收益曲线为 MR = a − 2bQ，因此 MR 与需求曲线有相同的纵截距，但斜率是需求曲线的两倍。

If P = a − bQ, then MR = a − 2bQ

The downward-sloping AR curve and the steeper MR curve are essential for analysing monopoly and monopolistic competition. The vertical gap between AR and MR reflects the revenue lost on previously sold units when price is reduced to sell one more unit.

向下倾斜的 AR 曲线和更陡峭的 MR 曲线是分析垄断和垄断竞争的重要工具。AR 与 MR 之间的

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