# 经济代写|微观经济学代写Microeconomics代考|BEA470

## 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

$$\pi(y)=P(y) \cdot y-C(y) .$$

$$P^{\prime}(y) \cdot y+P(y) \cdot 1-C^{\prime}(y)=0 \text {. }$$

## 经济代写|微观经济学代写Microeconomics代考|Two- or Multi-Sided Markets

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