Executive Summary

Old Adages

As the once famous adage goes, “The most famous law in economics, and the one economists are most sure of, is the law of demand—一条定律，说明给定商品的购买量与其价格成反比关系.e., higher prices lead to lower quantities demanded, and that lower prices lead to higher quantities demanded. 整个微观经济学学科就是在这个前提下建立起来的.

需求量(Q)的变化对任何给定的单价(P)变化的相对响应性称为 price elasticity of demand, also referred to as PED or price elasticity. 本文将以讲座的形式介绍价格弹性理论的基本原理，然后迫使我们走出课堂，探索实际应用, including pricing and promotion strategy design, 行为学和消费者心理学的因素是如何使诺贝尔获奖理论的原始性复杂化的, 以及将优步的高峰期定价模式作为需求价格弹性的完美应用的实际案例.

But first, let’s begin with the basics. To deeply understand what price elasticity of demand measures, 我必须带你回到最开始——经济学的基本原理——并帮助你理解的核心概念 demand.

Economics 101: Understanding Demand

At its most elemental, demand 消费者在每一个价格上都愿意并且能够购买的给定商品的数量是连续的吗. 理论经济学家和商业人士都使用 demand curve, 哪一种形式被正式定义为任意时间点价格与需求量关系的图形表示.

在一个典型的表示中(如上面图1中所示), 需求曲线的纵轴(y)为价格，横轴(x)为数量, 与绘制的函数(曲线)通常反映负关联- i.e., a downward slope—that migrates from left to right.

Analyzing a typical representation further, 需求曲线与y轴相交的点表示价格，在此价格下，消费者将购买零单位的给定产品，因为该产品太贵了. This indicates the outer bound of a customer’s willingness to pay. Conversely, 需求曲线与x轴相交的点表示顾客在任何价格下愿意购买的最大数量. Or framed differently, 假设给定公司将其产品定价为零，它所能销售的最大单位数.

需求曲线的最基本形式是线性的，其斜率表示在不同价格下的可能购买量, calculable using the following formula:

With the abstract concept of demand introduced, 接下来，我们必须了解支配它的主要规律和相关因素.

The Law of Demand

The law of demand states that, ceteris paribus, 换句话说，某种商品的需求量与其价格成反比关系, that higher prices lead to lower quantities demanded, and lower prices lead to higher quantities demanded. Excluding price, there are five other factors that conventionally govern demand elasticity. They are as follows:

1. Price of related goods. Related goods come in the form of either complements; i.e., goods with a positive cross-elasticity of demand, and thus typically consumed together (think, cars and petrol), or substitutes; i.e., goods with a negative cross-elasticity of demand, which are thus easily substitutable for one another (e.g., bottled vs. tap water). Specifically to the point, 一种补品价格的上涨通常会导致这一捆商品的总成本上升, and thus a fall in the quantities demanded of both. Whereas with substitutes, the opposite effect takes place.
2. Income of buyers. When the income of an individual or the aggregate rises, individual and aggregate demand rises in line with the product’s marginal utility function. Marginal utility, in this case, is defined as the additional unit of satisfaction a consumer gains from consuming one more unit of a given good; utility which typically diminishes over time and/or with each additional unit consumed.
3. Tastes or preferences of consumers. 口味或偏好的积极变化有利于一种好产品(或一个好品类中的品牌), naturally increases demand, and vice versa. 正是由于这个原因，每年在品牌上花费数十亿美元, advertising, and marketing in an effort to shift or manipulate tastes, preferences, and the stickiness of customers in favor of a given firm’s product/brand.
4. Consumer Expectations. 这个变量的内在是另外两个基本的经济原则. The first is the concept of future value, and the second, the concept of discounting to present value. Explained simply, 当消费者预期某一特定产品的价值在未来会上涨时, there will be a higher willingness to pay for it in the present, thereby inducing greater demand. 这一概念存在于连基本的非必需消费品都可以开始仅仅根据感知被视为投资的连接点, consumer psychology, and fashions/trends.
5. Number of buyers in the marketplace. Simply put, holding income per capita constant, a rise in the aggregate number of addressable consumers, either due to demographic shifts or improvements in product relevance, will induce greater demand. The more people exist to consume a product that is relevant, affordable, and accessible, the higher overall demand, and vice versa.

The Demand Curve Revisited: A Shift in… vs. A Movement along…

在这个关键时刻，值得强调的是，在经济学中，有两种不同的表达 change in demand exist. 第一种是需求曲线的移动，第二种是沿着需求曲线移动. A shift in the curve can only be induced by changes in one of the five non-price determinants of demand, as detailed above and illustrated below in Figure 2.

A movement along the demand curve, on the other hand, only takes place in response to price changes, 引起需求数量的变化，但在需求函数/曲线的范围内. Again, 需求量变化对选定价格变化的敏感性被称为 price elasticity of demand and what we will delve into next.

Price Elasticity of Demand

The price elasticity of demand (PED)衡量的是由于价格的百分比变化而引起的消费者需求量的百分比变化. 需求的价格弹性是用需求量变化的百分比除以价格变化的百分比来计算的, represented in the PED ratio.

The elasticity coefficient—i.e., 由于需求量和价格之间的反比关系(需求定律)，价格弹性公式的产出几乎总是负的。. It is worth noting, however, that the negative sign is traditionally ignored, 因为数字的大小通常是分析的唯一焦点.

Interpreting Elasticities

Demand is considered elastic 当一个相对较小的价格变化伴随着一个不成比例的较大的需求量变化时, and demand is inelastic 相对较大的价格变化伴随着不成比例的较小的需求量变化. Outside of these extremities, unit elasticity 指价格变化伴随着需求量精确/成比例变化的任何情形.

Mathematically, 当一个给定产品的弹性系数大于1时，它被认为是相对有弹性的，当它的系数小于1时，它被认为是相对无弹性的. 最后，当PED系数恰好为1时，需求被称为单位弹性.

The Full Range of Elasticities

According to Thomas Steenburgh and Jill Avery, 达顿商学院和哈佛商学院的高级讲师, there are five primary zones of elasticity:

How Do Companies Use Price Elasticity of Demand?

Switching gears somewhat, 我现在想探讨公司如何利用需求的价格弹性的问题. To answer this effectively, 我们必须重新回到起点，重新定义/澄清公司的功能.

At its most fundamental, the function of a firm is twofold: (1) to create value for its customers, and (2) to capture value for its stakeholders. Businesses create value, or at least the perception of value, in their choice of what goods/services to produce and distribute; and capture value 以利润的形式，以他们对如何定价和采用何种成本结构的选择. 因此，更粗略地说，可以推测企业的核心目标是利润最大化.

解决了这个问题后，我们的下一个任务是了解营销人员的角色. We can probably all agree that their role, alongside other managers within a firm, is to further the goal of their firm, which we’ve defined as maximizing profit. And given that costs do not fall under the marketer’s purview, they must accomplish this by maximizing revenue. Adding a bit more structure to the conversation, 营销人员通过优化经典商业理论家所说的方法来做到这一点 The Four P’s: Product, Price, Place, and Promotion, where product describes the nature and relative differentiation of a good/service; price, what a good is sold for; place, where and how easily a good is accessed; and promotion是一种营销方法，用来告知或说服目标受众一种商品的优点.

Most specifically, it is the marketer’s job to estimate demand, 预测各种可能的价格组合的影响(价格弹性), and use that data to inform management on the most suitable pricing and promotion strategies 对于公司及其产品，假设产品和地点都已优化.

The problem with price elasticity theory in the real world is that ceteris paribus can never hold; said differently, variables in competitive marketplaces can never be held constant. In reality, firms operate in dynamic, complex, and multivariate environments, 充满了无形的竞争力量，以无法预测/量化的方式相互作用. 根据定义，现实世界是不完美的、不稳定的、不精确的，没有考虑到消费者.

A Brief Interlude: Price Elasticity and Behavioral Psychology

It is worth noting that the theory of price elasticity is a classical one and thus also ignores all the psychological, social, cognitive, 以及构成人的情感因素(通常在 behavioral economics). 具体来说，经典理论的核心是假设市场参与者是 rational 因此，总是做出最规范、最合理/最优的决定. The reality is, and leaning on a recent and thoroughly insightful piece by Toptal Expert Melissa Lin, 80% of economic agents deviate from the objectively rational choice due to cognitive and emotional biases that influence how they process and act on information. This is a timely subtopic, given that Richard Thaler, Professor at the University of Chicago, 因其在行为经济学方面的工作而获得2017年诺贝尔经济学奖.

A Real Life Case Study: Uber and the Phenomenon of Surge Pricing

优步(Uber)是一个极好的现实案例，研究了实际价格弹性以及行为因素通常如何影响预期结果. Specifically, its once contentious surge pricing Feature是利用大量关于供给(司机)和需求(乘客)的数据来实时调节价格，并时刻保持平衡.

注意:这个厚脸皮的评论没有说出来，但却巧妙地传达了这样的信息:“需求已经突破了记录! Fares have increased to get more consumers off the app.”

Uber, given the sheer volume of real-time data it has available to it, 是否能够持续三角测量其价格弹性商，并利用该信息来调节需求, moment-to-moment, 它是通过定价排除其价格敏感范围内的不同客户群来实现的. Paraphrasing Keith Chen, 加州大学洛杉矶分校行为经济学家、优步经济研究主管:正如传统经济学所预测的那样, surging the price dampens demand. 具体来说，在增兵的早期，你会从0到1.2x surge, you would see a consistently precise 27% drop in demand. 将数字应用于理论，这意味着价格弹性商为1.35, 假设在病例的地理范围内有合理一致的基线票价, and a conclusion that Uber’s customers are relatively price elastic.

当行为心理学开始发挥作用时，事情就变得更有趣了. In Uber’s case, Chen goes on to explain that a strong round number effect, where pricing is concerned, seems to be at play with Uber’s consumers. Specifically, when Uber would go from 1.9x to 2.当需求量从1倍上升到0倍时，需求量的下降幅度将是从1倍上升到0倍时的6倍.8x to 1.9x surge. Further analysis revealed that the 2.0x number just felt viscerally larger and thus “capricious and unfair.”

更有趣的是，当浪涌乘数从2.0x to 2.1x, people actually took more rides. But it wasn’t that that customers preferred to pay 2.1倍于2倍，但是因为他们假设如果旅行的价格是2.1x, there must be a smart algorithm in the background at work and thus, it didn’t seem quite as unfair. Classic cognitive dissonance at play.

优步作为一个案例研究完美地概括了将理论价格弹性理论应用于现实世界多元环境的挑战. 事实证明，即使是科学，也更像是艺术而不是科学，至少在现实世界中是这样.

潜意识信息:需求价格弹性的其他应用

除了用作主动/预测工具外，价格弹性还有其他应用. Specifically, it is often used as a lag indicator该指标用于了解企业在一系列参数方面的表现. These parameters include product performance, branding/marketing performance, competitor and complement performance, and even overall macroeconomic health.

Product. Paraphrasing Jill Avery, Senior Lecturer at Harvard Business School, 所有的公司都在寻求创造能够为客户提供独特和可持续价值的产品和服务, especially relative to marketplace substitutes. Referring briefly to Figure 5, the more unique/differentiated a given product, 在相同的总成本基础上，客户的支付意愿越高, and the more inelastic its demand will be. Price elasticity of demand is thus an effective indicator of both true or perceived product differentiation within a market.

Branding/Marketing. Related to this is the distinction between true and perceived product differentiation. True product differentiation aside for the moment, the perception alone of uniqueness, captured through the power of effective branding, 成功的强大心理决定因素是否必须由营销人员加以利用. 因此，价格弹性是衡量公司/产品在市场上相对于竞争对手的品牌资产的有效滞后指标. 当一种产品的需求相对有弹性时，它被认为是一种商品.e., 品牌弱或没有区别，因此很容易被消费者取代为下一个最好的(最低价格的替代品).

Competition and Complements. 一个公司的需求价格弹性也是一个很好的指标，以竞争强度(i.e.(可行的替代品的发生率)和市场上的补充. 相对有弹性的价格弹性表明，在该价格点上，商品的竞争非常激烈，或者补品的成本/价格正在上升.

Product/Business Lifecycle. According to Joel Deal, author of an HBR piece on new product pricing policies, price elasticity is also an accurate gauge of where your company is in its maturity; a concept he breaks down further into three distinct elements.

1. Technical Maturity: This is indicated by a declining rate of product development, 品牌之间的特征和性能日益标准化或商品化, 当一个给定的产品在市场上花费更多的时间时，顾客的期望就会稳定.
2. Market Maturity: 这种形式的成熟度是通过消费者对某一产品的接受程度来表示的, its service idea, value proposition, 以及对它会令人满意的信念的稳定.
3. Competitive Maturity: 现有玩家和品牌的稳定和巩固表明了这一点, their market share, pricing, and positioning as a product continues to exist in the market.

State of Overall Economy. 需求价格弹性间接反映的最后一个参数是产品销售所在经济体的整体健康状况. Specifically, this parameter relates to both demographics (i.e., (目标人口的规模)和构成该消费市场的成分的收入水平. Related to this is also the overall cost of the product being offered. Low income, 高成本的产品环境自然会产生相对弹性的需求曲线, while high income, low-cost products will yield relatively inelastic demand curves.

Looking forward…

Setting the right price 对于一个给定的产品是很难的，更糟糕的是，一直都不是一门精确的科学. 尽管价格弹性理论已经存在了一个多世纪, 它通常被用作一个理论框架，用来不精确地理解市场对价格变化的反应, 这些数据将被用来笨拙地预测未来的行为. 这是一个伟大的开始——我们尽了最大的努力，它当然达到了它的目的.

But times are changing. The combination of big data’s proliferation and the rapid A/B testing 数字经济提供的可能性正在改变PED的精确性和历史适用性. Be it from Uber whose dynamic (surge) pricing feature helps it maintain supply-demand equilibrium in real time using price; to startups such as 100% Pure who have lifted operating profits by 13.5% 在三个多月的时间里，公司现在能够以惊人的准确度进行预测，而不仅仅是通过 how much demand will change with every unit change in price, but also why—i.e., the psychology behind the swings.