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经济代写|微观经济学代写Microeconomics代考|The Single-Product Monopoly
The most studied case is the non-price-discriminating monopolist. Before discussing the circumstances under which it may be optimal to dispense with price discrimination, one should analyze how such a market functions. Assume the monopolist acts as a profit maximizer and produces with a technology that leads to a cost function $C(y)$.
A firm’s market-research department estimates a market demand function $x=$ $X(p)$ for one of the firm’s products. This function shows the amount of the good or service that can be sold at a given price $p$. In perfectly competitive markets, the perceived demand function is perfectly price elastic at the market price. This implies that the only information necessary to determine the optimal output is the existing or expected market price. However, this is no longer the case for a monopoly, where the firm needs to estimate the market demand function with as much precision as possible. The organization of the firm is hence more complex: While in perfectly competitive markets, firms only need managerial accounting to determine marginal and average costs, but a firm in a monopoly market also needs a market-research unit to estimate the demand function, because it is no longer a price taker.
At this point, one has to make a decision. One can assume that the monopolist sets a price and passively adjusts the produced quantity, $X(p)$, or one can alternatively assume that the monopolist decides on the quantity and demand determines the price at which the market clears. Both approaches lead to the same result but, since the second is somewhat simpler, it is the one that is usually applied. In order to do so, however, one has to infer the so-called inverse demand function from $X(p)$, knowing that, for any price ( $p$ ), the quantity $(x)$ that can be sold is given by $x=X(p)$. Taking the inverse function of this demand function yields $p=X^{-1}(x)$, which determines the price that clears the market for any quantity offered by the firm. The convention from the previous chapters is to denote demand by $x$ and supply by $y$. Given that one is analyzing the problem from the position of the monopolist who decides how much to supply, it makes sense, therefore, to replace $x$ by $y$ in the inverse-demand function that one denotes as $p=P(y)$.
If $\pi$ denotes the firm’s profit, then one can use this information to express it as revenues minus costs:
$$
\pi(y)=P(y) \cdot y-C(y) .
$$
The problem faced by the firm’s manager is to determine the quantity that maximizes profits. This quantity is implicitly defined by the necessary (“first-order”) condition $\pi^{\prime}(y)=0$. (Assume in the rest of the book that this condition characterizes the global profit maximum. This is guaranteed, for example, if the second derivative of the profit function is globally negative, has a positive slope at $y=0$, and has a negative slope for $y \rightarrow \infty$.) This yields
$$
P^{\prime}(y) \cdot y+P(y) \cdot 1-C^{\prime}(y)=0 .
$$
经济代写|微观经济学代写Microeconomics代考|Two- or Multi-Sided Markets
Two- or multi-sided markets are intermediation platforms that provide goods and services to two or many different groups of customers. What distinguishes them from traditional multi-product businesses is the presence of interdependencies in terms of profits from trade between the different groups (see Chap. 6). These interdependencies can be positive or negative. Facebook, for example, has two main groups of customers, users (side 2) and online advertisers placing targeted ads (side 1). Facebook collects data about its users that allows it to place ads more effectively. Thus, the willingness of online advertisers to pay for the placement of ads depends on the number of users that can be reached and the effectiveness of the targeting strategy, which creates a positive interdependency from side 2 to side 1 . At the same time, there may be a negative interdependency in the opposite direction if users do not like being exposed to too many ads.
Interdependencies between different customer groups can occur basically anywhere in the economy. They can be found in traditional industries (e.g., credit card companies connecting cardholders and merchants, shopping malls connecting customers and merchants, or organizations like alumni clubs, AIESEC, etc.). But they are particularly relevant in the digital economy, where some of the largest and most profitable companies in the world act as intermediaries or platforms. Examples include Facebook, Google, Baidu, eBay, Amazon, Microsoft, Apple, Taobao, and many others. As an example, consider Apple’s digital application platform. In this case, application developers and users form the two groups of customers. The goal of application developers is to sell their applications to iPhone, iPad, or Mac users. These users are willing to buy and install these applications. Apple has integrated this platform into its hardware and software ecosystem to bring these groups together, for which fees are charged.
Two-sided markets generally benefit from many of the factors (such as network externalities) that explain the existence and persistence of monopolies. They also have very interesting and, at first glance, potentially counterintuitive consequences for optimal pricing, which will be the focus of this section. One is that many of the services offered to one side of the market are free (have prices of zero). Facebook users do not pay a membership fee, nor do users of search engines such as Google. From the isolated perspective of this market, such a business model looks strange to say the least, although it is probably efficient since the marginal cost of an additional Facebook user or Google search is close to zero (although the fixed costs are significant). The rationality of this pricing strategy only becomes clear if you look at both sides of the market at the same time. There is the saying “If you don’t pay, you are the product,” which nicely illustrates for example Facebook’s business model. The mass of user data that Facebook collects is invaluable to online advertisers because it allows them to target users with ads and messages and is more likely to get their attention because they know their preferences well. So Facebook is free to users (side 1) because its business model is to collect data and provide advertisers (side 2) with guidance on how to identify and target their preferred customers. This service is not free, and the prices that can be charged depend on the number of users, the time they spend on the platform, and the quality of the algorithms that analyze the data and turn it into profitable information. What we can learn from this is that hecause of the interdependencies that exist in two-sided markets, optimal pricing is also interdependent. A profit-maximizing firm should not focus on each side of the market separately, but should see pricing as a task encompassing both sides of the market, the goal of which is to internalize the interdependencies as best as possible. As we will see later, such a strategy can explain prices of zero and even prices below marginal cost on one side of the market.
微观经济学代考
经济代写|微观经济学代写Microeconomics代考|The Single-Product Monopoly
研究最多的案例是非价格歧视垄断者。在讨论在什么情况下最好取消价格歧视之前，我们应该分 析这样一个市场是如何运作的。假设垄断者充当利润最大化者并使用导致成本函数的技术进行生 产 $C(y)$.
公司的市场研究部门估计市场需求函数 $x=X(p)$ 为该公司的产品之一。此函数显示可以以给定价 格出售的商品或服务的数量 $p$. 在完全竞争市场中，感知需求函数在市场价格上具有完全价格弹 性。这意味着确定最佳输出所需的唯一信息是现有或预期的市场价格。然而，这不再是垄断的情 况，企业需要尽可能精确地估计市场需求函数。公司的组织因此更加复杂：虽然在完全竞争市场 中，公司只需要管理会计来确定边际成本和平均成本，但垄断市场中的公司还需要市场研究部门 来估计需求函数，因为它不再是价格接受者。
在这一点上，一个人必须做出决定。可以假设垄断者设定价格并被动调整生产数量， $X(p)$ ，或者 也可以假设垄断者决定数量，而需求决定市场出清的价格。两种方法都会导致相同的结果，但由 于第二种方法稍微简单一些，因此通常采用这种方法。然而，为了做到这一点，必须从中推断出 所谓的逆需求函数 $X(p)$ ，知道，对于任何价格 $(p)$ ，数量 $(x)$ 可以出售的是由 $x=X(p)$. 取这 个需求函数的反函数得到 $p=X^{-1}(x)$ ，它决定了公司提供的任何数量的市场清算价格。前几章的 惯例是用 $x$ 并由 $y$. 鉴于从决定供应量的垄断者的立场分析问题，因此，替换为 $x$ 经过 $y$ 在反需求函数 中，一个表示为 $p=P(y)$.
如果 $\pi$ 表示公司的利润，然后可以使用此信息将其表示为收入减去成本:
$$
\pi(y)=P(y) \cdot y-C(y) .
$$
公司经理面临的问题是确定使利润最大化的数量。该数量由必要的（”一阶”) 条件隐式定义 $\pi^{\prime}(y)=0$ ．(假设在本书的其余部分，这种情况表征了全局利润最大值。这是有保证的，例如， 如果利润函数的二阶导数全局为负，则斜率为正 $y=0$ ，并且具有负斜率 $y \rightarrow \infty$.) 这产生
$$
P^{\prime}(y) \cdot y+P(y) \cdot 1-C^{\prime}(y)=0 \text {. }
$$
经济代写|微观经济学代写Microeconomics代考|Two- or Multi-Sided Markets
双边或多边市场是向两个或多个不同客户群提供商品和服务的中介平台。它们与传统的多产品企业的区别在于，在不同集团之间的贸易利润方面存在相互依赖性（见第 6 章）。这些相互依存关系可以是积极的，也可以是消极的。例如，Facebook 有两个主要客户群，即用户（第 2 方）和投放定向广告的在线广告商（第 1 方）。Facebook 收集有关其用户的数据，使其能够更有效地投放广告。因此，在线广告商是否愿意为广告投放付费取决于可触达的用户数量和目标定位策略的有效性，这会产生从第 2 方到第 1 方的正相关关系。同时，
不同客户群之间的相互依赖基本上可以发生在经济的任何地方。它们可以在传统行业中找到（例如，连接持卡人和商户的信用卡公司，连接客户和商户的购物中心，或像校友会、AIESEC 等组织）。但它们在数字经济中尤其重要，在数字经济中，世界上一些最大和最赚钱的公司充当中介或平台。示例包括 Facebook、谷歌、百度、eBay、亚马逊、微软、苹果、淘宝等。例如，考虑一下 Apple 的数字应用程序平台。在这种情况下，应用开发者和用户形成了两组客户。应用程序开发人员的目标是将他们的应用程序出售给 iPhone、iPad 或 Mac 用户。这些用户愿意购买并安装这些应用程序。Apple 已将该平台整合到其硬件和软件生态系统中，以将这些群体聚集在一起，为此收取费用。
双边市场通常受益于许多解释垄断存在和持续存在的因素（例如网络外部性）。它们对最优定价也有非常有趣且乍一看可能违反直觉的后果，这将是本节的重点。一是向市场的一方提供的许多服务都是免费的（价格为零）。Facebook 用户不需要支付会员费，谷歌等搜索引擎的用户也不需要。从这个市场的孤立角度来看，这样的商业模式至少可以说是奇怪的，尽管它可能是有效的，因为额外的 Facebook 用户或谷歌搜索的边际成本接近于零（尽管固定成本很高）。只有同时观察市场的两面，这种定价策略的合理性才会变得清晰。有句话说“如果你不付钱，你就是产品”，这很好地说明了 Facebook 的商业模式。Facebook 收集的大量用户数据对在线广告商来说是无价的，因为它允许他们向用户投放广告和消息，并且更容易引起他们的注意，因为他们非常了解他们的偏好。所以 Facebook 对用户（第 1 方）是免费的，因为它的商业模式是收集数据并为广告商（第 2 方）提供有关如何识别和定位其首选客户的指导。这项服务不是免费的，可以收取的价格取决于用户数量、他们在平台上花费的时间、以及分析数据并将其转化为有利可图信息的算法的质量。我们可以从中了解到，由于双边市场中存在的相互依赖性，最优定价也是相互依赖的。追求利润最大化的公司不应分别关注市场的每一侧，而应将定价视为一项涵盖市场两侧的任务，其目标是尽可能将相互依赖性内部化。正如我们稍后将看到的，这样的策略可以解释市场一侧的零价格甚至低于边际成本的价格。但应该将定价视为一项涵盖市场双方的任务，其目标是尽可能将相互依赖关系内部化。正如我们稍后将看到的，这样的策略可以解释市场一侧的零价格甚至低于边际成本的价格。但应该将定价视为一项涵盖市场双方的任务，其目标是尽可能将相互依赖关系内部化。正如我们稍后将看到的，这样的策略可以解释市场一侧的零价格甚至低于边际成本的价格。
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