User:TDang/Econ452/rough lecture notes

This class is to cover “Information Economics and the Internet”.


 * Looking at information goods
 * books, software, music, lectures?, movies, databases, drugs?


 * Looking at networked goods:
 * email, Facebook, online games

We’ll be looking a lot at business strategy for those kinds of goods, with an underpinning in the economics.

“Information economics” can mean a number of things. To an economist, it generally brings up the idea of markets where people have idfferent information. This is a vital part of the health insurance market, for instance. We’re not (mostly) going to concentrate on that. kind of infoormation economics, though it will come up.

As I said, we’ll be spending a fair amount of time on information goods. A text which will help there is a custom selection from Carlton and Perloff’s book. Some of this will probably overlap with other classes such as ECON 407 or ECON 460. Hopefully if you’re doing more than one of these courses, the different perspectives will help.

There is some textbook-like material online, but we’ll need to manage without a particular textbook for material on networks, (which will be a significant part of the course). One optional book which could be useful is by Carl Shapiro and Hal Varian, but that isn’t necessary, it could just be a complement to online readings and lecture.

We’ll look some at how a flow of information affects the market. And near the end we’ll look at how institutions “aggregate and disseminate” information (aggregate meaning collect it, disseminate meaning tell people about it). This is an area that economists think about, including at least two Nobel prize winners, Friedrich Hayek and Leonid Hurwicz.

The text which will orient us partly through that section is by Cass Sunstein. Sunstein is a law professor, not an economist. He’s currently head of the White House Office of Information and Regulatory Affairs.

Guided by that book, we’ll look at how groups of people can decide things using different ways of getting the “Wisdom of the Crowd”, which will naturally include internet-based institutions.

Anything I assign you to read you need to read, but this isn’t a course where the material is all available in a book. It’s very lecture-oriented.

= What is information? =

Several approaches:


 * Information theory
 * telecommunications
 * encryption
 * data compression
 * Can be (but rarely is) used in analysis of information aggregation and dissemination, so it’s possible I’ll talk about it then. Otherwise, we’ll mostly ignore this.


 * Game theory
 * Asymmetric information
 * Mechanism design


 * Information economics (largely applications of the game theory)
 * Adverse selection
 * Moral hazard


 * Contrasting (Ackoff, R. L., &quot;From Data to Wisdom&quot;, Journal of Applies Systems Analysis, Volume 16, 1989 p 3-9 http://www.systems-thinking.org/dikw/dikw.htm)
 * Data: symbols
 * Information: data that are processed to be useful; provides answers to “who”, “what”, “where”, and “when” questions
 * Knowledge: application of data and information; answers “how” questions
 * Understanding: appreciation of “why”
 * Wisdom: evaluated understanding

For the purposes of this course, I’ll mostly be talking about information goods and that will mean essentially, “anything that can be digitized”.

(What might this include? Discussion)

= Features of information goods (demand side) =

What are features of information goods? Several, which we’ll get to a little at a time, including


 * non-rival
 * maybe excludable, maybe not
 * experience
 * durable
 * discrete choice

Starting with the first two, non-rival, maybe excludable&quot;


 * Rival good
 * If Karl gets more, Rose gets less. There’s a limited amount to be consumed.


 * Excludable good
 * If Rose has it, she can keep Karl from getting/using it.

Jefferson: “He who receives an idea from me, receives instruction himself without lessening mine; as he who lites his taper at mine, receives light without darkening me.”

Augustine: “The words I am uttering penetrate your senses, so that every hearer holds them, yet withholds them from no other. …I have no worry that, by giving all to one, the others are deprived.”

(http://lessig.org/blog/2009/05/jeffersons_remix_of_augustines.html)




 * “typical” good
 * rival and excludable. My phone, a pancake, etc. (Note that I’m using the word “typical” in a non-technical way since the expressions “normal” and “ordinary” already have technical definitions in economics.)


 * commons
 * …as in the “Tragedy of the Commons”. Fisheries, old growth forest, etc. The trouble with the commons is that it may be over-used / abused / depleted. (also called “common pool resources”)


 * public good
 * broadcast media, public libraries. The trouble with public goods is that it can be hard to convince people to invest in them.


 * club good
 * sorta like a public good, but you can restrict access. (swimming pool for a particular apartment complex)

Q: Which of these 4 best captures information goods? Discuss.

Information goods are most naturally a public good. They are pretty clearly non-rival. If another student came in the classroom while I was giving this lecture, that wouldn’t mean you get less lecture. Information goods are not completely non-excludable, but that is their most natural state. This is evidenced by software, music, and movie piracy, for instance. It’s very hard to keep information from spreading. A famous line about information is “Information wants to be free”. (Others have joked “Information wants to be anthropomorphized”.)

This non-exludability can potentially raise serious problems because excludability is how we most often make markets work. It’s “I exclude you from eating this sandwich unless you pay me $5.” Excludability is usually what allows sales. SO, without excludability, it’s hard to sell something (the person who wants it can just acquire it) which means there’s no profit in creating it in the first place, which could mean it never gets created.

A lot of the action in information goods is therefore moving them from being public goods to being club goods by adding excludability. This excludability primarily comesi n the form of intellectual property (IP) laws. Those laws don’t change the physics of excludability, but they can impose penalities for people who treat information goods as public goods.

Q: Are information goods ever rivalrous?

Not really, but practically they could be:


 * attention?
 * bandwidth?
 * hot stock tip?

It’s best to assume they are non-rivalrous unless you can think of a good reason they could be rivalrous.

Other properties of information goods. Often (not always) one or several of these


 * Durable good
 * Once a consumer has purchased the item, they may never have to purchase it again (ever, or for a long time).


 * Books can last a very long time. I’m reading my kids picture books my mother had when she was a kid. I have an old copy of the (which recommends grey squirrels as tastier than red squirrels and shows you how to skin them), and I have a few books from pre-1900.
 * This is potentially even more true with digital media.
 * This has implications we’ll get to later. Essentially the seller might be competing with themselves over time (Coase).


 * Experience good
 * It may be that the good has to be consumed first for the consumer to have a good idea of how they value it.


 * This has implications for marketing and can be especially tricky when combined with non-excludability and durability.


 * Discrete choice
 * Frequently, a consumer’s decision for an information good is “Yes” or “No” instead of “How much”.


 * So we’ll often talk about information goods in that sense, of each individual deciding whether or not to purchase rather than how much to purchase …
 * …but this can also depend on how the product is marketed. It can be possible to make a “naturally” discrete good into a more typical good where each consumer decides (for instance) how much time they want to spend reading a book.

= Supply-side nature of information goods =

Those are typical characteristics of an information good from the consumer’s point of view. There’s also a vey important feature on the supply side which will drive how we start looking at them. It relates to non-excludability.

Information goods usually have relatively high sunk cost and near-zero marginal cost. (Of course “relatively high” compared to “near-zero” leaves a lot of room. Some fairly valuable information goods take someone an afternoon to create—maybe a new piece of music or a magazine article. Many take huge investments of time and reseources, like a major movie.) Fixed costs can vary.


 * Fixed cost
 * a cost the firm has to pay regardless of how much of the product they sell


 * For instance, even if a firm is selling things via internet download, they probably have to maintain some level of staffing, some physical space, computers and utilities, etc. That’s all costs that need to be paid for even if they don’t actually sell anything …


 * Quasi-fixed cost
 * a cost the firm has to pay if they sell more than zero of a product


 * Sometimes costs are really, truly fixed. But often they are “quasi-fixed” in that the firm could fire everyone, stop paying rent and turn off the lights if they don’t want to sell anything.
 * For now, we’ll ignore this distinction and just talk about fixed costs, but it’s possible the distinction could be useful.


 * Sunk cost
 * a cost which is unrecoverable even if the firm shut down


 * This can be tricky, but time is the critical element here. A sunk cost has been paid, and that’s the end of it.
 * It’s different than a fixed cost. For instance, a fixed cost of running a restaurant is paying the rent on the location. That’s paid for each month the restaurant is in business, but once the firm goes out of business they can stop paying the rent. A sunk cost might be developing the initial menu. It doesn’t need to be repeated every month, but once that’s done there’s no way to go back and undo it to recover the cost.


 * Variable cost
 * the cost of producing which depends on how much is produced.


 * Marginal cost
 * the cost of producing one more unit of a good.


 * Average cost
 * the average cost per unit produced (more with pictures shortly)

I’m going to start with the comparisons of fixed cost, marginal cost and average cost. For most information goods, the marginal cost is very low, and constant. It doesn’t particularly get cheaper or more expensive (on the margin) to make and sell an information good as more is sold.

We broke up goods this way:



Information goods are most “naturally” public goods, but intellectual property laws add a bit of excludability, making them potentially club goods

Q: Are information goods ever rivalrous?

Not really, but sometimes the value of the goods may be rivalrous:


 * attention? (not really an information good)
 * bandwidth? (not really an information good)
 * hot stock tip? (The information in the tip isn’t rivalrous, but the profitable use of the information might be.)

It’s best to assume they are non-rivalrous unless you can think of a good reason they could be rivalrous.

Other properties of information goods. Often (not always) one or several of these


 * Durable good
 * Once a consumer has purchased the item, they may never have to purchase it again (ever, or for a long time).


 * Books can last a very long time. I’m reading my kids picture books my mother had when she was a kid. I have an old copy of the Joy of Cooking (which recommends grey squirrels as tastier than red squirrels and shows you how to skin them), and I have a few books from pre-1900.
 * This is potentially even more true with digital information products.
 * This has implications we’ll get to later. Essentially the seller might be competing with themselves over time (“Coase Conjecture”).


 * Experience good
 * It may be that the good has to be consumed first for the consumer to have a good idea of how they value it.


 * This has implications for marketing and can be especially tricky when combined with non-excludability and durability.


 * Discrete choice
 * Frequently, a consumer’s decision for an information good is “Yes” or “No” instead of “How much”.


 * So we’ll often talk about information goods in that sense, of each individual deciding whether or not to purchase rather than how much to purchase …
 * …but this can also depend on how the product is marketed. It can be possible to make a “naturally” discrete good into a more typical good where each consumer decides (for instance) how much time they want to spend reading a book.
 * …and there many things (whether strictly information goods or not) which are “naturally” continuous, but are sold as if discrete.

= Supply-side nature of information goods =

Those are typical characteristics of an information good from the consumer’s point of view. There’s also a very important feature on the supply side which will drive how we start looking at them. It relates to non-excludability.

Information goods usually have relatively high sunk cost and near-zero marginal cost. (Of course “relatively high” compared to “near-zero” leaves a lot of room. Some fairly valuable information goods take someone an afternoon to create—maybe a new piece of music or a magazine article. Many take huge investments of time and resources, like a major movie.) Fixed costs can vary.


 * Fixed cost
 * a cost the firm has to pay regardless of how much of the product they sell


 * For instance, even if a firm is selling things via internet download, they probably have to maintain some level of staffing, some physical space, computers and utilities, etc. That’s all costs that need to be paid for even if they don’t actually sell anything …


 * Sunk cost
 * a cost which is unrecoverable even if the firm shut down


 * This can be tricky, but time is the critical element here. A sunk cost has been paid, and that’s the end of it.
 * It’s different than a fixed cost. For instance, a fixed cost of running a restaurant is paying the rent on the location. That’s paid for each month the restaurant is in business, but once the firm goes out of business they can stop paying the rent. A sunk cost might be developing the initial menu. It doesn’t need to be repeated every month, but once that’s done there’s no way to go back and undo it to recover the cost.


 * Variable cost
 * the cost of producing which depends on how much is produced.


 * Marginal cost
 * the cost of producing one more unit of a good.


 * Average cost
 * the average cost per unit produced (more with pictures shortly)

I’m going to start with the comparisons of fixed cost, marginal cost and average cost. For most information goods, the marginal cost is very low, and constant. It doesn’t particularly get cheaper or more expensive (on the margin) to make and sell an information good as more is sold.

$$\begin{aligned*} TC(Q) &= FC + VC(Q)\end{aligned*}$$

In the above, $$FC$$ is the fixed cost, so it doesn’t depend on how much is produced (no $$Q$$ in there). $$VC(Q)$$ is the variable cost, so it does depend on quantity. Notice how variable cost is different than marginal or average cost. It’s the total variable cost for producing all that stuff.

$$\begin{aligned*} MC(Q) &= \frac{d TC}{d Q}(Q)\\ &= \frac{d VC}{d Q}(Q)\end{aligned*}$$

The marginal cost in calculus terms is the derivative of total cost with respect to output, so the cost of selling just one more unit. (Or, sometimes we’ll want to think about it as the amount which can be saved by reducing output by one unit.)

$$\begin{aligned*} AC(Q) &= \frac{TC(Q)}{Q}\end{aligned*}$$

The average cost is simply that—the average, so the total cost is divided by the amount sold.

So, for a lot of non-information markets, we think that marginal cost increases (or increases after some point). That can lead to things like in this graph.




 * When $$MC < AC$$, $$AC$$ is going down
 * When $$MC > AC$$, $$AC$$ is going up
 * When $$MC = AC$$, $$AC$$ is at its minimum (this will be important for us)

Economies of scale (supply-side)
(The “supply-side” is a qualifier which isn’t usually used. When someone talks about economies of scale, they almost always mean supply-side. However, in this class we’ll spend a good bit of time (later) on demand-side economies of scale.)

A technology has economies of scale when increasing output decreases the average cost. (There is another definition for economies of scale which relates the amount of inputs used to the amount of output created. They usually amount to the same thing, and in this class we’ll concentrate on the cost part.)




 * Minimum efficient scale (MES)
 * The smallest level of output at which economies of scale are exhausted.



Economies of scale come largely from …


 * …spreading of fixed costs
 * …efficiencies from specialization (of labor and capital) within the firm

Diseconomies of scale come largely from …


 * …bureaucracy
 * …incentives to work
 * …possibly limited resources

(In fact it’s not clear how important diseconomies of scale are. There’s some reasoning that there should be at worst constant returns to scale. By duplicating the current setup exactly, costs and output are both doubled. That’s constant returns to scale, if it can work.)

If marginal cost is low and constant, then the plot might instead look like this:



Technically, in this case, there is no MES.

Back to MES and all that in a little bit. First, let’s think about competitive markets and information goods. Let’s assume there’s excludability in the sense that your customers can’t just copy what you sell them and then re-sell it for cheaper. But there’s market competition. Someone is selling a product which the consumers think is just as good as yours.

What happens with a competitive market? Price equals marginal cost; you get just as much on the last unit you sell as it costs you to produce that last unit.

Q: Why is that? If price was more than marginal cost, another firm would undersell you to steal the market and make more money. If price was less than marginal cost, you’d want to sell less (as long as marginal cost was increasing).

How would that look? Let’s put demand on the same graph.



If price equals marginal cost, then it’s less than average cost. The business will be losing money.



(The red area is $$AC(Q) \cdot Q$$, so is the firm’s total cost. The striped area is $$P \cdot Q$$, so is the firm’s total revenue, which is less than their cost).

So, competitive markets are lousy for information goods. We’ll largely be ignoring them, which is why we’re starting with monopolies.

= Odd markets =

Perfect competition is a problem—reason #1
If price equals marginal cost, then it’s less than average cost. The business will be losing money.



(The red area is $$AC(Q) \cdot Q$$, so is the firm’s total cost. The striped area is $$P \cdot Q$$, so is the firm’s total revenue, which is less than their cost)

Natural monopoly
As long as we’re looking at that decreasing average cost curve, let’s talk about natural monopoly. Informally, a natural monopoly is an industry where it makes sense to have a monopoly.

Somewhat more formally, we’ll use this definition of a natural monopoly, based on the cost structure:


 * Natural monopoly
 * An industry is a natural monopoly when the production technology is sub-additive over the range of quantity which might be demanded.


 * i.e. $$TC(q_1 + q_2 + \ldots + q_3) < TC(q_1) + TC(q_2) + \ldots + TC(q_3)$$ for any $$Q = q_1 + q_2 + \ldots + q_3$$ which might be demanded.

We’ll leave the “range of quantity which might be demanded” informal.

What this means is that the industry is a natural monopoly if it’s cheaper for one firm to satisfy all the demand than for multiple firms to satisfy the same demand.

The cost structure we’re looking at—constant marginal cost—fits this. (It’s not the only kind of cost structure which does so; it’s sufficient, but not necessary for natural monopoly.) Let’s look at the simple example by dividing the quantity into two equal-sized firms.

Aside: relationship between non-rivalry and zero marginal cost.



If we suppose the monopolist provides quantity $$Q^m$$ (and we don’t really have to worry for this part why the monopolist decides to do that), they face a total cost of $$TC(Q^m) = AC(Q^m) \cdot Q^m$$.

If we break that quantity in half, then firm 1 sells half the quantity (we don’t need to worry about the price), and their total cost is $$TC(q_1) = TC(\frac{Q^m}{2}) = AC(\frac{Q^m}{2}) \cdot \frac{Q^m}{2}$$, but since average cost is falling as the quantity rises, this is more than half of the total cost of the monopolist. With firm 2 doing the same thing, we can graphically see that the combined cost for the two smaller firms is more than the cost for the monopolist.

So—there’s an argument to be made here that a monopoly makes sense. With some cost structures, it’s cheaper for a monopoly to provide the good than multiple firms. This does, however, ignore the firms’ decisions about what prices to set.

There may be limits to this, in theory and in practice.

In theory, if average cost doesn’t keep declining but levels out, and demand is great enough, then the total $$Q$$ for the market might be great enough that more than one smaller firm can reach the leveling-out point of the MES, and it won’t be a natural monopoly.

In practice, what counts as “levelling out” could happen even if it won’t happen when we look at mathematically-perfect asymptotic convergence.

Perfect competition is a problem—reason #2
And let’s now remember sunk costs. Whatever this information good was, the sunk costs are likely to be relatively large:


 * R&amp;D for new drug
 * Development cost for new movie
 * Time spent writing a book

Even if the business is only losing a tiny bit of money when looking at average cost, how will they ever earn enough to cover their sunk costs?

We’ll look at this a little more formally very soon.

Fixed versus sunk costs
Frequently, particularly with texts on information goods, fixed and sunk costs will be clumped together carelessly. There may be a good reason to clump them together, but not carelessly.

Remember that fixed costs are the costs of being in operation over some period of time. That’s different than sunk costs which are paid just once—or it might be. It depends on the nature of the analysis.


 * If you want to study the market over a relatively short period—say, a year—then you’ll want to keep the fixed and sunk costs separate.
 * For instance, if you’re thinking about the market for a new cookbook this year, you’ll want to keep the fixed costs (marketing, administration, etc.) separate from the sunk costs (writing and editing).


 * If you want to study the market over the life of the product, then you can clump the sunk costs into the fixed costs.
 * For instance, if you want to study overall demand for a computer game over an expected useful commercial life of 10 years, you could put the ongoing marketing costs and the one-time development costs all together as fixed costs


 * If in doubt, separating the sunk costs is safer.

Whichever you do, remember to think about the demand for the product in the same way—is it demand per week, or demand over a 20 year product lifespan?

So, market power
So, competitive markets for information goods are kinda broken. It’s just too hard to be profitable (or even make “zero economic profit”). Therefore, we’ll mostly be ignoring perfect competition. We’ll assume instead that any business involved in selling an information good has some market power.

A firm has market power if it is not a price-taker. A price taker is someone who has to take price as a given. In a competitive market, a business can’t really raise its price because even a small increase in price will decrease the quantity demanded from that firm to zero. It could lower its price, in which case it would increase the quantity demanded by taking the demand from all the other firms, but it would be losing money at that lower price.

From a single firm’s point of view, if it is a price-taker the demand curve is flat (even though the market demand curve slopes downward as usual). If it is not a price-taker, the demand curve for that individual firm slopes downward (whether or not the firm’s demand curve is the same as the market demand curve.)

There are several ways a firm might have market power. For most of this class, we won’t worry too much about which is occuring, so long as we can assume a firm faces a downward-sloping demand curve.


 * Monopoly
 * only one firm selling the product, with no close substitutes


 * Differentiated product
 * various substitutes, but the product is different enough from its substitutes that the firm has some amount of market power.


 * There’s a euphemistic use of the word “differentiate” sometimes used in business which means “make our product better than the competition’s”.
 * That’s not really differentiating. It’s certainly a good thing, but not differentiating.
 * Differentiation is about trading a large market with little market power for a smaller market with more market power.
 * In the computer business, Apple has differentiated. Whether you think their computers are “better” or not, they have chosen to make their product different enough that they have some market power, even if it cuts them out of a lot of the personal computer market.
 * Many information goods are mostly about differentiation—music, movies, books, games, etc. (to some degree also with productivity software, but less of a clear case there).


 * Dominant product (market leader)
 * one firm has the clearly-leading product in the market, but there are many smaller firms following behind.


 * The firm could be dominant because of some kind of “first-mover advantage”.
 * It could be dominant because it has a cost advantage.
 * It could be dominant because of differentiation.
 * It could be dominant because of network externalities.


 * Oligopoly
 * firms are offering pretty close substitutes, but there are few enough that each has some market power.


 * This kind of model often overlaps with differentiated products.

What all of those have in common, which we’ll use, is a downward-sloping demand curve.

Monopoly pricing
Very particular case: Suppose the firm has a demand curve (the demand curve being for that one firm whether because it’s a monopoly or one of the other reasons above) of $$Q_D(p) = 100 - p$$. (I’m keeping this model very simple for now.) Marginal cost equals $20 (most likely we’re more interested in $$MC = 0$$, but I’ll use $$MC = \$20$$ because it might show things better) …and for the time being we’ll just leave fixed costs as an unknown, $$FC$$.

Two kinds of ways of going about this. For both approaches, I’m going to switch from demand to inverse demand.

$$\begin{aligned*} Q_D(p) &= 100 - p\\ p &= 100 - Q_D(p)\\ p(Q) &= 100 - Q\end{aligned*}$$

First approach—maximize profit function
The first is to set things up to maximize profit (which we’ll label as $$\pi$$).

$$\begin{aligned*} \pi(Q) &= p(Q) Q - TC(Q)\\ &= p(Q) Q - FC - VC(Q)\\ &= p(Q) Q - FC - MC \cdot Q\\\end{aligned*}$$

(Note that we can only break $$TC(Q)$$ up into $$FC$$ and $$MC \cdot Q$$ like that if there are constant marginal costs.)

$$\begin{aligned*} \pi(Q) &= p(Q) Q - FC - MC \cdot Q\\ &= (100 - Q) Q - FC - 20 Q\\ &= 100 Q - Q^2 - FC - 20 Q\\\end{aligned*}$$

(Talk about maximizing functions and zero derivatives.)

$$\begin{aligned*} \frac{d \pi}{d Q} &= 100 - 2 Q - 20\\ &= 80 - 2 Q\\\end{aligned*}$$

Solving for $$\frac{d \pi}{d Q} = 0$$:

$$\begin{aligned*} \frac{d \pi}{d Q} &= 0\\ 80 - 2 Q              &= 0\\ 2 Q                     &= 80\\ Q                        &= 40\\ p(Q)                   &= 100 - 40 = 60\end{aligned*}$$

Second approach—marginal revenue equal marginal cost
The second way to figure out what the monopoly will do is to think in terms of $$MR = MC$$.


 * if $$MR < MC$$, then the firm is losing money on each extra unit it sells …
 * …so it will sell less …
 * …which will usually push the marginal revenue ($$MR$$) up, so closer to equaling $$MC$$.


 * if $$MR > MC$$, then the firm is profiting on each additional unit it sells …
 * …so it will sell more …
 * …which will usually push the marginal revenue ($$MR$$) down, so closer to equaling $$MC$$.


 * if $$MR = MC$$, then the firm is OK with the quantity that it’s selling.

We find marginal revenue by using the inverse demand function to find the revenue function:

$$\begin{aligned*} Revenue &= p(Q) Q\\ &= (100 - Q) Q\\ &= 100 Q - Q^2\\\end{aligned*}$$

Then, the marginal revenue is the derivative of revenue with respect to quantity:

$$\begin{aligned*} MR &= \frac{d}{d Q}\left[100 Q - Q^2\right]\\ &= 100 - 2 Q\end{aligned*}$$

Now we solve for $$MR = MC$$:

$$\begin{aligned*} MR          &= MC\\ 100 - 2 Q &= 20\\ 80           &= 2 Q\\ Q            &= 40\end{aligned*}$$

…and that’s the same as we found with the first approach. The profit-maximizing price will also be the same as using the first approach.

= Monopoly pricing =

Could revisit the case we started before, but might as well do a different one (which was on the homework). We know how to solve it, but we should also know how to draw it.

I’ll use the $$MR = MC$$ approach, because that’s what’s clearest on the picture:

$$\begin{aligned*} Q_D(p) &= 200 - p\\ p(Q)    &= 200 - Q\\ R(Q)    &= (200 - Q) Q\\ &= 200 Q - Q^2\\ MR(Q) &= 200 - 2 Q\end{aligned*}$$

Solving for $$MR = MC$$:

$$\begin{aligned*} MR          &= MC\\ 200 - 2 Q &= 20\\ 2 Q         &= 180\\ Q            &= 90\\ P(Q)       &= 200 - 90 = 110\\\end{aligned*}$$



One thing we can see on that graph is consumer surplus.

''Consumer surplus is pretty easy to compute with known, linear demand. In practice it can be much harder, but we’ll mostly be computing consumer surplus not because we plan to really compute consumer surplus a lot in the future, but because we’d like to have a rough idea, particularly about comparing consumer surplus in one circumstance to another.''


 * Consumer surplus
 * is the amount of value consumers receive from purchasing something over-and-above what they have to pay to get it.

To figure out consumer surplus, we need to think of the demand curve in a different way than usual. We most often think of demand $$Q(p)$$ as telling us how much quantity will be demanded if the price is set to $$p$$. The inverse demand function inverts that.

The inverse demand function also tells us something else, though. The inverse demand function $$p(Q)$$ also tells us the marginal willingness-to-pay for the $$Q^{th}$$ unit sold. It says that if we want to see $$Q$$ units, then the last unit purchased will be just worth $$p(Q)$$ to the person purchasing it. Another way to think about it is that they’re indifferent between purchasing and not purchasing at that price.

Because we can interpret the inverse demand curve that way, we can use the area under the demand curve to figure out how well off consumers are …use picture and storytelling integration here.

= Monopoly and consumer surplus =

= Monopoly and elasticity =

= Price discrimination =

Perfect price discrimination (“first-degree”)
Perfect price discrimination is when the firm can charge exactly the wiilingness-to-pay for each unit sold.


 * That can mean charging each person the price they’re willing to pay (if selling one unit per customer) …
 * …or it could mean charging one person exactly what they’re willing to pay for each unit (possible paying different amounts for the different units) …
 * …or likely some combination of the two.

(Draw pictures)

Perfect price discrimination is primarily a thought-experiment to think about price discrimination generally. It’s hard to imagine when it could occur:


 * Maybe a vendor who is really good at haggling could get close.
 * There is an argument to be made that higher education can get close.
 * Possibly some “sliding scale” services, if the service provider knows enough about their clients

Price discrimination is (statically) efficient.

Aside: See if we can better define static and dynamic efficiency

 Static efficiency  A market is statically efficient if it maximizes the total value (to consumers and sellers) given:   the market already exists   the particular cost structure 

  Essentially, this means it maximizes total value given that sunk and fixed costs are already allocated.   Dynamic efficiency</dt> <dd> A market is dynamically efficient if it maximizes the total value (to consumers and sellers): <ol> <li> over different possible states of the market (existent, non-existent, various cost structures, various product offerings) </li> <li> taking into account fixed and sunk costs which are not yet allocated </li></ol> </dd></dl>

So, perfect price discrimination is (statically) efficient because it maximizes the total value in the market. It does that by selling just as much as would be sold in a competitive market, but giving all the surplus to the seller.

Q: What might this imply about dynamic efficiency?

Q: What does the marginal revenue curve look like for perfect price discrimination?

Group pricing (“third-degree”)
Group pricing is charging different prices to different groups. To be really strict about classification, this would require that the firm can identify who belongs to which group and charge them different prices. In practice, this often blurs with self-selection.

I’m not going to concentrate on this too much, because the practice of it can be interesting (how does the firm identify who is in what group, get an idea about demand for each group, and prevent arbitrage?) in theory it’s just two separate monopolies.

Versioning (self-selection)
Versioning is offering different versions of the product which will encourage buyers to sort themselves into different groups in a way which is profitable. There are many ways to do this. Often it means finding a feature of the product which is under the firm’s control and correlated with demand elasticity.

Note that when the features are changed in order to allow versioning, costs might change as well. This can muddy the notion that price discrimination isn’t about costs. If different versions are offered, there will probably be additional fixed costs for each version, and the different versions (such as a paperback and hardcover book) might have different marginal costs. But the costs could go either way: the version which costs more to produce might be sold at a higher (hardcover book) or lower (486SX33) price.

There are two major points of interest with versioning:


 * First, versioning means the various versions are competing with each other—they are almost certainly at least weak substitutes.
 * Some versioning strategies make things different in ways which weaken the substitutability—such as air travel on different days, but there is still some substitutability.
 * But some versioning strategies make one version better than the other, in which clase they will remain close substitutes.
 * In any case, since the versions are competing with each other, the overall characteristics of each version need to be selected so that the cheaper versions don’t draw the low-elasticity customers away from the more expensive versions.
 * That is largely a matter of selecting the product features—if the second-tier version is “too good” then it can draw people away from the top-tier.
 * But it is also a matter of price—selecting the price for each version needs to be done not just recognizing the effect on its own demand, but also on the demand for the other versions (i.e. don’t make the cheap version too cheap.)


 * Second, there is a behavioral-economics aspect to versioning …

Independence of irrelevant alternatives (violations)
The independence of irrelevant alternatives (IIA) is a property of decision-making which is a big part of what economists mean when they say people act “rationally”.

One way to describe (Sen, 1970, page 17) the rule is that if ldots


 * 1) an alternative $$x$$ is chosen from the set $$T$$,
 * 2) and the set $$S$$ is a subset of $$T$$
 * 3) and $$x$$ is an element of $$S$$,
 * 4) then $$x$$ must be chosen from the set $$S$$.

This is best seen by looking at violations. I’ll start by going back to intermediate micro and budget sets:

(Draw pictures)

Another example, suppose you’re at a restaurant, looking at the menu and there’s a nice pasta entrée and a chicken entrée.

So the choice set is $$\left\{Pasta, Chicken\right\}$$.

When the server comes, you tell them you’d like to order the chicken. The server then says they have a special fish dinner tonight, and you respond, “O, in that case I’ll take the pasta!”

So the choice set is $$\left\{Pasta, Chicken, Fish\right\}$$.

And it seems irrational to switch to the pasta—switching to the fish might make sense, but why switch to something which was already available?

But here’s another example: you’re thinking about ordering the wine and there are two choices both of which sound pretty good, one bottle for $18, and one bottle for $30. You figure the $18 bottle is probably good enough, and are ready to order it. Then you notice a third offering of a premium wine for $50 a bottle.

Frequently, in such circumstances, people will switch and order the $30 bottle of wine. Although that violates IIA, it is a standard marketing gimic, where people will often purchase either the second-cheapest or second-most-expensive thing on a menu. There are a lot of explanations for this, but the simplest term is “extremeness aversion”

As another example of violating IIA, Dan Ariely uses the example of online marketing of The Economist magazine:



(Predictably Irrational, page 1)

Nonlinear pricing (“second-degree”)
“Nonlinear pricing” is a catch-all term for any price regime which doesn’t have (Total expenditure = $$p$$ X $$Q$$) with a constant $$p$$. In other words, it’s any price regime which wouldn’t have a stragith-line-from-the-origin plot of total expenditure versus quantity purchased. (That’s quantity purchased by one buyer, not the complete market quantity.)

(Draw pictures)

There are lots of ways this can happen. One we’ll focus on is the two-part tariff.


 * Two-part tariff
 * A two-part tariff is a price regime in which a customer pays a flat fee ($$F$$) for access to a product, and then pays a constant per-unit price ($$p$$) to purchase the product.

(Draw pictures)

It’s important to notice that we’re doing something different here with $$Q$$ and demand generally. Instead of $$Q$$ being the market demand, $$Q$$ is someone’s individual demand. So, here the firm is maximizing revenue for an individual customer, but assuming there are many customers (we’ll start off assuming that there are many customers with identical demand).

Without deciding on the flat fee $$F$$ yet, suppose the consumer has decided to purchase the product. When the firm sets the per-unit price $$p$$, the consumer decides how much to purchase. Once they’ve decided to purchase more than zero, they follow their regular demand in deciding how much to purchase. This leaves the consumer with some consumer surplus ($$CS$$).

Now what the firm does is set the flat fee equal to that consumer surplus, $$F= CS$$. (Of course, this means it’s not really consumer surplus anymore.)

= Price discrimination methods =

Two-part tariffs

 * Two-part tariff
 * A two-part tariff is a price regime in which a customer pays a flat fee ($$F$$) for access to a product, and then pays a constant per-unit price ($$p$$) to purchase the product.

(Draw pictures)

It’s important to notice that we’re doing something different here with $$Q$$ and demand generally. Instead of $$Q$$ being the market demand, $$Q$$ is someone’s individual demand. So, here the firm is maximizing revenue for an individual customer, but assuming there are many customers (we’ll start off assuming that there are many customers with identical demand).

Without deciding on the flat fee $$F$$ yet, suppose the consumer has decided to purchase the product. When the firm sets the per-unit price $$p$$, the consumer decides how much to purchase. Once they’ve decided to purchase more than zero, they follow their regular demand in deciding how much to purchase. This leaves the consumer with some consumer surplus ($$CS$$).

Now what the firm does is set the flat fee equal to that consumer surplus, $$F= CS$$. (Of course, this means it’s not really consumer surplus anymore.)

A way to think about a two-part tariff is that the monopolist lowers the price in order to give the consumer more consumer surplus, but then takes all that consumer surplus back as the flat fee.

The revenues are the same as if firm was perfectly price discriminating over all the units the consumer purchases. There are two advantages over perfectly price discriminating:


 * 1) First, it’s much easier to administrate, and harder to cheat.
 * 2) Second, it can work better when knowledge of demand is approximate—as long as the firm has some ideas about consumer demand, they can choose an $$F$$ close to $$CS$$ and the process works approximately.

…We’ll come back to two-part tariffs

Bundling (Tie-in sales)

 * Bundling
 * A firm bundles two or more products together when it either requires them to be purchased together, or makes an appealing price to purchase them together instead of separately.

For the purposes of this class, we’ll ignore “mixed bundling” in which the firm tries to price so that some buy the bundle and some buy the individual products. That’s because we’re concentrating on (near) zero marginal cost products, for which mixed bundling isn’t profitable.

In practice, for instance, you can purchase Microsoft Word separately from Excel, but Word along costs almost as much as the Microsoft Office suite.

Suppose that there are two products, and two different kinds of consumers. This table gives each type of consumer’s value for each product:

1.0


 * l | c | c |

Consumers &amp; Value for A &amp; Value for B

Type I &amp; $50 &amp; $80

Type II &amp; $90 &amp; $20

We want to know if the firm could do better by bundling the products, selling them grouped together in a “suite”. To do that, we need a series of “what-ifs”.

What if the firm sold the items unbundled?


 * For product A, they could choose a price of $50 or $90.
 * With a price of $90, they will sell to only Type II consumers, for a revenue of $90.
 * With a price of $50, they will sell to both kinds of consumers, for a revenue of 2 X $50 = $100.
 * So, they’ll set a price of $50 for product A.
 * For product B, they could choose a price of $20 or $80.
 * With a price of $80, they will sell to only Type I consumers, for a revenue of $80.
 * With a price of $20, they will sell to both kinds of consumers, for a revenue of 2 X $20 = $40.
 * So, they’ll set a price of $80 for product B.
 * So, their total revenue (unbundled) would be $100 + $80 = $180.

If the firm sells the products bundled, then:


 * Type I consumers value the bundle at $50 + $80 = $130.
 * Type II consumers value the bundle at $90 + $20 = $110.
 * So, for the bundle, they would choose a price of either $110 or $130.
 * With a price of $130, they will sell to only Type I consumers, for a revenue of $130.
 * With a price of $110, they will sell to both kinds of consumers, for a revenue of 2 X $110 = $220.
 * So, they’ll set a price of $110 for the bundle.

Since the revenue when the products are bundled is greater, that’s what the firm would want to do.

(leave this one up)

This won’t always be the case:

1.0


 * l | c | c |

Consumers &amp; Value for A &amp; Value for B

Type I &amp; $90 &amp; $50

Type II &amp; $30 &amp; $60

We want to know if the firm could do better by bundling the products, selling them grouped together in a “suite”. To do that, we need a series of “what-ifs”.

What if the firm sold the items unbundled?


 * For product A, they could choose a price of $90 or $30.
 * With a price of $90, they will sell to only Type I consumers, for a revenue of $90.
 * With a price of $30, they will sell to both kinds of consumers, for a revenue of 2 X $30 = $60.
 * So, they’ll set a price of $90 for product A.
 * For product B, they could choose a price of $50 or $60.
 * With a price of $60, they will sell to only Type II consumers, for a revenue of $60.
 * With a price of $50, they will sell to both kinds of consumers, for a revenue of 2 X $50 = $100.
 * So, they’ll set a price of $100 for product B.
 * So, their total revenue (unbundled) would be $90 + $100 = $190.

If the firm sells the products bundled, then:


 * Type I consumers value the bundle at $90 + $50 = $140.
 * Type II consumers value the bundle at $30 + $60 = $90.
 * So, for the bundle, they would choose a price of either $140 or $90.
 * With a price of $140, they will sell to only Type I consumers, for a revenue of $140.
 * With a price of $90, they will sell to both kinds of consumers, for a revenue of 2 X $90 = $180.
 * So, they’ll set a price of $90 for the bundle.

In this case, the optimal revenue for the bundle is less than that for the products separately.

Several things to notice:


 * All of these decisions are trade-offs between selling to more people at a lower price and selling to fewer people at a higher price.
 * That’s just like the decision of a firm with market power to move up or down the demand curve.


 * One way to think of bundling is that it makes consumers more homogenous.
 * By adding products up, the values of the bundles may become more similar between consumers.
 * If this occurs, there is more likely to be a “right” price which includes all the consumers, rather than excluding some of them entirely.


 * A second way to think of bundling is that it’s price discriminating by self-selecting consumers for each product in the bundle.
 * In essence, it’s asking Type II consumers to pay $90 for product A, when a Type I consumer wouldn’t be willing to do so.
 * While we can’t say exactly how much Type I consumers are paying for product B, it’s certainly more than Type II consumers.

Examples of bundling
What are some examples of bundling in information markets?


 * Cable channel packages
 * Record albums
 * Netflix
 * Newspaper
 * Performance rights organizations—ASCAP / BMI

= Price discrimination methods =

Two-part tariffs (with more than one kind of consumer)
What if all consumers of the product aren’t exactly alike? (duh!)

Setting a two-part tariff isn’t as clear-cut if there are different kinds of consumers.


 * If consumers have different demand, they will most likely have different consumer surplus.
 * If they have different consumer surplus, then trying to extract all the consumer surplus from all the consumers will backfire. The consumers with lower consumer surplus will just decide to sit out the market entirely.

So, how to figure it out? Usually like this:


 * Figure out who will have the lower consumer surplus at any price. That will be the flat fee charged to all consumers.
 * Then, simply solve for $$MR = MC$$.
 * Actually, not quite so simply, we’ll see below how to do it.
 * And, similar to what we saw with bundling, will also need to to some checks to see if it’s better to price some consumers out of the market entirely.

example 1—use for lecture
Two types of consumers:


 * Type I consumers
 * $$Q_{I} = 100 - p$$


 * So the inverse demand function is $$p = 100 - Q_{I}$$


 * Type II consumers
 * $$Q_{II} = 200 - 2 p$$


 * Since both types of consumers are buying at the same price, …
 * …$$Q_{II} = 200 - 2 (100 - Q_{I}) = 2 Q_{I}$$

It might help to draw the demand functions. (Draw them). With these functions we should be able to see whose $$CS$$ the firm will use for the flat fee.

If the firm set $$F=CS_{II}$$, then the Type I consumers would just quit the market.

So, if the firm wanted to sell to both types, they would need to use $$F=CS_{I}$$.

Now, how do we go about finding the marginal revenue to use the $$MR = MC$$ condition? There’s a trick to it.


 * In order to sell another unit to a Type I consumer (increase $$Q_{I}$$), the firm needs to lower $$p$$ …
 * …but if they lower $$p$$, they will also sell some extra amount to Type II consumers …
 * …and if they sell more to Type I consumers, that additional revenue must also be included in $$MR$$.

$$\begin{aligned*} R     &= 2 CS_{I} + p\left(Q_{I} + Q_{II}\right) \\ &= 2 \frac{1}{2}Q_{I}(100-(100-Q_{I})) + p\left(Q_{I} + 2 Q_{I}\right) \\ &= Q_{I}^2 + p\left(3 Q_{I}\right) \\ &= Q_{I}^2 + \left(100-Q_{I}\right) 3 Q_{I} \\ &= Q_{I}^2 + 300 Q_{I} - 3 Q_{I}^2 \\ &= 300 Q_{I} - 2 Q_{I}^2\\ MR  &= 300 - 4 Q_{I}\\\end{aligned*}$$

Solving for $$MR = 0$$ gets $$Q_{I} = \frac{300}{4} = 75$$, which implies that $$p = \$25$$ and that $$Q_{II} = 150$$.

What’s revenue there? $$R = 2 \frac{1}{2}Q_{I}^2 + p\left(Q_{I} + Q_{II}\right) = 5625 + 25 \cdot 225 = 11,250$$

Then, the question is: is it better to sell to just one type of consumer?


 * A little intuition helps here.
 * If it is more profitable to sell to only one consumer, which kind will that be?
 * It will be the consumer who values the product more—Type II consumers.
 * Then, how should we price for those consumers?
 * If we rule out serving Type I consumers, then we can exploit Type II mercilessly, set $$p=MC$$ and $$F=CS_{II}$$.

If we do that here, then $$p=0$$ gets $$Q_{II} = 200$$ and $$CS_{II} = \frac{1}{2}(200)(100) = 10,000$$.

So, it turns out this monopolist is better off selling to both kinds of consumers with the single two-part tariff.

example 2—extra, not for lecture
Two types of consumers:


 * Type I consumers
 * $$Q_{I} = 100 - p$$


 * So the inverse demand function is $$p = 100 - Q_{I}$$


 * Type II consumers
 * $$Q_{II} = 200 - p$$


 * Since both types of consumers are buying at the same price, …
 * …$$Q_{II} = 200 - (100 - Q_{I}) = 100 + Q_{I}$$

It might help to draw the demand functions. (Draw them). With these functions we should be able to see whose $$CS$$ the firm will use for the flat fee.

If the firm set $$F=CS_{II}$$, then the Type I consumers would just quit the market.

So, if the firm wanted to sell to both types, they would need to use $$F=CS_{I}$$.

Now, how do we go about finding the marginal revenue to use the $$MR = MC$$ condition? There’s a trick to it.


 * In order to sell another unit to a Type I consumer (increase $$Q_{I}$$), the firm needs to lower $$p$$ …
 * …but if they lower $$p$$, they will also sell some extra amount to Type II consumers …
 * …and if they sell more to Type I consumers, that additional revenue must also be included in $$MR$$.

$$\begin{aligned*} R     &= 2 CS_{I} + p\left(Q_{I} + Q_{II}\right) \\ &= 2 \frac{1}{2}Q_{I}(100-(100-Q_{I})) + p\left(Q_{I} + 100 + Q_{I}\right) \\ &= Q_{I}^2 + p\left(100 + 2 Q_{I}\right) \\ &= Q_{I}^2 + \left(100-Q_{I}\right) \left(100 + 2 Q_{I}\right) \\ &= Q_{I}^2 + 10000 + 200 Q_{I} - 100 Q_{I} - 2 Q_{I}^2 \\ &= 10000 +100 Q_{I} - Q_{I}^2\\ MR  &= 100 - 2 Q_{I}\\\end{aligned*}$$

Solving for $$MR = 0$$ gets $$Q_{I} = 50$$, which implies that $$p = 50$$ and that $$Q_{II} = 150$$.

What’s revenue there? $$R = 2 \frac{1}{2}Q_{I}^2 + p\left(Q_{I} + Q_{II}\right) = 2500 + 50(50 + 150) = 2500 + 10000 = 12,500$$.

Then, the question is: is it better to sell to just one type of consumer?


 * A little intuition helps here.
 * If it is more profitable to sell to only one consumer, which kind will that be?
 * It will be the consumer who values the product more—Type II consumers.
 * Then, how should we price for those consumers?
 * If we rule out serving Type I consumers, then we can exploit Type II mercilessly, set $$p=MC$$ and $$F=CS_{II}$$.

If we do that here, then $$p=0$$ gets $$Q_{II} = 200$$ and $$CS_{II} = \frac{1}{2}(200)(200) = 20,000$$.

So, it turns out this monopolist is better off selling to just Type II consumers.

Menus of two-part tariffs
Two-part tariffs (and other nonlinear pricing regimes) are frequently offered as options:


 * All-you-can-eat buffet or standard menu
 * Alternative cell-phone plans

Offering a “menu” of optional two-part tariffs essentially combines the two-part tariff with versioning. The same ideas which apply to versioning apply to these:


 * The goal of offering different plans is having consumers self-select into the plan which is most profitable.
 * The different plans compete with each other.
 * So you want to make sure no plan is so appealing it draws customers you wanted in a different plan.
 * You can tune this by making a plan more or less appealing—it’s a bit simpler with two-part tariffs since you do that just by changing prices.
 * You tune this not one plan at a time, but the entire menu.

''Solving for the profit-maximizing menu of two-part tariffs is a pretty intensive process. I’d like you to understand what’s going on, and to be able to work with these a bit. However, I can’t honestly imagine giving you such a thing on an exam unless it was the whole of the exam.''


 * If setting up a successful menu of two-part tariffs, the trade-offs are different than one two-part tariff for multiple types. The goal is to keep the consumers sticking to the preferred plans.


 * And advantage of price discrimination by “menu” is that the firm doesn’t strictly need to know how many of each type of consumer there are.

Suppose again two kinds of consumers—this time given them different prices:


 * Type I consumers
 * $$Q_{I} = 100 - p_{I}$$


 * So the inverse demand function is $$p_{I} = 100 - Q_{I}$$


 * Type II consumers
 * $$Q_{II} = 200 - 2 p_{II}$$


 * So the inverse demand function is $$p_{II} = 100 - \frac{1}{2}Q_{II}$$
 * Now both types of consumers will not be buying at the same price, so we can’t cleanly relate $$Q_{I}$$ and $$Q_{II}$$ as we did with a single two-part tariff.

The firm will aim to exploit the type with the higher overall demand (bot won’t completely succeed), so one plan on the menu is:


 * Plan II
 * $$p_{II} = 0$$, $$F_{II} = \text{(? Wait and see ?)}$$—give this type a lot of surplus, since it’s worth the most to them and the firm wants to take it back as a flat fee. But they’ll be limited in their flat fee by the other plan.


 * Plan I
 * $$p_{I} = 50$$, $$F_{I} = 1250$$—here, the firm is taking all of Type I’s consumer surplus. However, they aren’t “fully exploiting” Type I consumers because they could get more out of them by lowering $$p$$ and raising $$F$$.

Now we need to think about how much the consumers would want to switch plans.


 * Type I consumers have zero consumer surplus under Plan I. $$F_{II}$$ needs to be chosen so that they get at best zero surplus under Plan II. Their surplus (prior to the flat fee) under Plan II would be $$5000$$, so we know $$F_{II} \geq 5000$$.
 * Type II consumers need to have at least as much consumer surplus remaining under Plan II as under Plan I. Their consumer surplus under Plan I (after paying the flat fee) would be $$\frac{1}{2}(100)(50) - 1250 = 1250$$.
 * So, the flat fee $$F_{II}$$ needs to be such that $$10000 - F_{II} \geq 1250$$.
 * The firm might as well get as much as possible, so selects $$F_{II} = 8750$$.
 * This is enough that Type I consumers are (strictly) better off with Plan I.
 * It’s also enough that Type II consumers are indifferent between Plan I and Plan II, so we’ll assume they choose Plan II.
 * …about the indifference …obviously a bit extreme, so there would be a bit more wiggle room in practice.


 * Plan I
 * $$F_{I} = \$1250$$, $$p_{I} = \$50$$


 * Plan II
 * $$F_{II} = \$8750$$, $$p_{II} = \$0$$

= Price discrimination methods =

Two-part tariffs and tie-in sales

 * “Tie-in” sales are generally things which require in some way the purchase of different things together.
 * So, bundling is one kind of tie-in sale—book refers to it as a package tie-in.
 * But another kind is called a requirements tie-in—requiring that customers who purchase A from the firm need to thereafter purchase all their B from the firm—presumably with A and B related somehow.


 * Sometimes a requirements tie-in is just a tricky way to impose a two-part tariff—World of Warcraft, for instance.
 * Sometimes it can be contractual—cell phone plans (usually actually three-part tariffs).
 * Sometimes it’s built into the hardware—razors &amp; razor blades, printers and ink catridges.

One of the things to notice is that the price of the product which is the “flat fee” may wind up being either greater or less than that item’s marginal cost, depending on demand.

Menus of two-part tariffs
Offering a “menu” of optional two-part tariffs essentially combines the two-part tariff with versioning. The same ideas which apply to versioning apply to these:


 * The goal of offering different plans is having consumers self-select into the plan which is most profitable.
 * The different plans compete with each other.
 * So you want to make sure no plan is so appealing it draws customers you wanted in a different plan.
 * You can tune this by making a plan more or less appealing—it’s a bit simpler with two-part tariffs since you do that just by changing prices.
 * You tune this not one plan at a time, but the entire menu.
 * And advantage of price discrimination by “menu” is that the firm doesn’t need to know as much about how many of each type of consumer there are.

= Durable goods =

Studying durable goods is putting an emphasis on time, which means there are a lot of complexities to consider. We’ll need to use ceteris paribus a lot to think about just one or a few elements at a time.

Important things:


 * Possibly most important: Think of demand as demand for the service which the good provides. Potentially the demand for this service is constant over time, but demand for the good will rise and fall as more consumers own the good.

Doctrine of first sale

 * In the U.S. most copyrighted works are subject to the “doctrine of first sale”, which says (more or less) that the owner of a legally-acquired copy of a copyrighted work is allowed to give away or sell that copy without permission from or payment to the copyright holder.
 * So, if you get a book, you’re allowed to resell it or give it away.
 * There are a few interesting kinks in the law. While it’s always legal to sell a copy you own:
 * If what you have purchased is a license, then you cannot necessarily resell that license. Many times digital works are structured so that they are “licensed” rather than “sold”.
 * For certain goods (music recordings, some computer software), you are allowed to resell, but not to rent to item to someone else.
 * Interestingly, you are not allowed to rent out audio recordings (CD’s) but you are allowed to rent out video recordings (DVD’s).

In many other countries, some arts are subject to some version of “droit de suite”, which means the original artist is always entitled to some royalties when the artwork is resold. (California has a similar state law.)

= Durable goods =

Studying durable goods is putting an emphasis on time, which means there are a lot of complexities to consider. We’ll need to use ceteris paribus a lot to think about just one or a few elements at a time.

Important things:


 * Possibly most important: Think of demand as demand for the service which the good provides. Potentially the demand for this service is constant over time, but demand for the good will rise and fall as more consumers own the good.
 * So, a durable good can be thought of as a good which provides a flow of services over a fairly long period of time.
 * And it’s often more meaningful to think of demand for the service than demand for the good.

What’s a durable good?
I have said that information goods tend to be durable goods. Let’s try to figure out which are really durable, which aren’t durable, and which are somewhere in-between.


 * Are any information goods clearly not durable goods?
 * Pharmaceuticals


 * Are any information goods clearly extremely durable?
 * Some creative works (books, movies, music) are clearly durable goods, but there’s also a lot of qualifications
 * But there’s a lot of uncertainty about which ones will retain their commercial value.
 * And there’s format changes over time—compatibility issues.


 * Software, particularly, tends to be durable in a technical sense but much less durable from a consumer demand point of view.
 * Many information goods are perculiar in that it is the very consumption of the good which reduces its value to the same consumer in the future.
 * While information goods do not “wear out” and are not “consumed” in the same ways that other goods do, there is frequently a decrease in their value over time. Notice that this is a matter of the value decreasing as the time from the work’s development increases, not as the time from sale increases.
 * Timeliness (news, popular arts)
 * Tastes (popular arts)
 * Compatibility (software)


 * A lot of the economics study of durable goods is commercial goods—factory equipment and similar. This is obviously different in many important ways from information goods.
 * In government statistics on durable goods, most information goods are not counted—DVD’s, books, etc. Business software is counted as a durable good, with a depreciation rate of ~ 55% and a 3-year useful life (for non-custom-built, non-in-house software). So, just a little durable.

Durability decision—quickly
A fair amount of the study of durable goods focuses on the business’s decision on how durable to make the product. Why is that?

For a lot of the goods which are counted as durable goods, durability goes along with marginal cost—more careful manufacturing, using higher-quality parts, etc. can make a tractor more durable.

For information goods, the marginal cost has much less relationship to the product’s durability—information goods are, by their nature, very durable.

If there is a cost with increasing the “durability” of an information good, it is primarily in the sunk cost or development cost for the good. Sometimes it is possibly to extend the value-life of an information good by making a greater up-front investment.

Residual demand

 * Suppose there is no discounting.
 * A good is useful over two periods, with demand for the service the good provides being $$Q(p) = 100 - p$$, with $$p$$ being the rental rate (We’ll need to be careful about rental versus sales, but I won’t be using the notation $$R$$ for rental price.)
 * In the second period, the firm

Model
For this we’ll be using backward induction.


 * When looking at decisions which take place over time, what decisions are possible at time 4 will depend on what decisions were made in times 1, 2, and 3.
 * A good way to figure out the best decision in time 1 is to think about what conditions that will set for times 2, 3, 4, and what the best decisions in those times will be.
 * So backward induction is starting at the end time by looking at the best decision we could make in any conditions we might find for the final period.
 * Then we “roll back” that part of the decision to the previous period with the reasoning, “if this is what I’ll do in period 4, what do I do in period 3 to set me up best for period 4?”

Often in decision theory and game theory, backward induction is done on decision trees or game trees. This will look different, but is the same idea. We’ll have a two-period model of selling a durable good. We’ll start the analysis by thinking about the second period, and ask “Conditional on what the seller decided to do in the first period, what would be their best decision in the second period?” Once we have an answer to that question (conditioned on the period 1 decision), we’ll “roll back” to period 1 and ask, “What should the seller do in period 1, knowing both how the decision will immediately affect profits and also how it will set them up for another decision in period 2?”

= Durable goods =

Studying durable goods is putting an emphasis on time, which means there are a lot of complexities to consider. We’ll need to use ceteris paribus a lot to think about just one or a few elements at a time.

Important things:


 * Possibly most important: Think of demand as demand for the service which the good provides. Potentially the demand for this service is constant over time, but demand for the good will rise and fall as more consumers own the good.
 * So, a durable good can be thought of as a good which provides a flow of services over a fairly long period of time.
 * And it’s often more meaningful to think of demand for the service than demand for the good.


 * Discounting, interest rates, time preference
 * Price discrimination over time
 * Credible vs. incredible threats and commitment
 * Expectations

What’s a durable good?
I have said that information goods tend to be durable goods. Let’s try to figure out which are really durable, which aren’t durable, and which are somewhere in-between.


 * Are any information goods clearly not durable goods?
 * Pharmaceuticals


 * Are any information goods clearly extremely durable?
 * Some creative works (books, movies, music) are clearly durable goods, but there’s also a lot of qualifications
 * But there’s a lot of uncertainty about which ones will retain their commercial value.
 * And there’s format changes over time—compatibility issues.


 * Software, particularly, tends to be durable in a technical sense but much less durable from a consumer demand point of view.
 * Many information goods are perculiar in that it is the very consumption of the good which reduces its value to the same consumer in the future.
 * While information goods do not “wear out” and are not “consumed” in the same ways that other goods do, there is frequently a decrease in their value over time. Notice that this is a matter of the value decreasing as the time from the work’s development increases, not as the time from sale increases.
 * Timeliness (news, popular arts)
 * Tastes (popular arts)
 * Compatibility (software)


 * A lot of the economics study of durable goods is commercial goods—factory equipment and similar. This is obviously different in many important ways from information goods.
 * In government statistics on durable goods, most information goods are not counted—DVD’s, books, etc. Business software is counted as a durable good, with a depreciation rate of ~ 55% and a 3-year useful life (for non-custom-built, non-in-house software). So, just a little durable.

Durability decision—quickly
A fair amount of the study of durable goods focuses on the business’s decision on how durable to make the product. Why is that?

For a lot of the goods which are counted as durable goods, durability goes along with marginal cost—more careful manufacturing, using higher-quality parts, etc. can make a tractor more durable.

For information goods, the marginal cost has much less relationship to the product’s durability—information goods are, by their nature, very durable.

If there is a cost with increasing the “durability” of an information good, it is primarily in the sunk cost or development cost for the good. Sometimes it is possibly to extend the value-life of an information good by making a greater up-front investment.

Residual demand

 * Suppose there is no discounting.
 * A good is useful over two periods, with demand for the service the good provides being $$Q(p) = 100 - p$$, with $$p$$ being the rental rate (We’ll need to be careful about rental versus sales, but I won’t be using the notation $$R$$ for rental price.)
 * In the second period, the firm

Rational expectations

 * Generally, rational expectations is a condition which is required by some models
 * Rational expectations requires that if people expect an outcome, they will act in a way which brings about that outcome …
 * …because what if they didn’t? If everyone expects there to be a lot of holiday traffic on Christmas Eve, and so everone drives two days earlier, then the model isn’t very good—the very existence of the model causes it to be wrong.
 * There are lots of places where it can be shown the rational expectations condition fails, but it’s the best place to start.

Resale if the consumers who value the good change but overall demand doesn’t
= Network externalities =

We’re going to go to stuff which is clearly the demand-side now, looking at goods which are networked (in a literal or figurative way).

This will remain pretty technical, but a lot of the technical stuff will be manipulating graphs instead of manipulating algebra.

Externalities
Externalities might be best described by what they are not. Economists put a lot of emphasis on the idea of gains from trade:

<dl> <dt>Gains from trade</dt> <dd> If two people decide to exchange with each other, then each person must be made (weakly) better off by the exchange, or they wouldn’t do it. So, any voluntary exchange creates value. Trade is good. </dd> <dt>Externality</dt> <dd> If some people do something which harms or benefits someone who isn’t involved in the decision, the effect on the person involuntarily involved is an externality. The logic of gains from trade break down, and it is possible too much or too little trade could occur. </dd></dl>

A lot of economic discussion focuses on the negative externalities: pollution, traffic congestion, etc.

We’ll mostly be talking about positive externalities, where someone is involuntarily helped by the decisions others make.


 * Network externalities
 * The benefit (or harm) that a member of a network receives when someone else joins that network.


 * We’ll mostly be concentrating on the benefits part of that, with positive network externalities, but negative network externalities certainly exist also.

Another way to phrase positive network externalities—and we’ll use both expressions is:


 * Demand-side economies of scale
 * The benefit to each consumer increases as more consumers purchase the good.

Compare that to:


 * Supply-side economies of scale
 * The average cost of producing each unit decreases as more unites are produced.


 * Most often this is simply called “economies of scale”, so if I just say “economies of scale” I probably mean supply-side economies of scale, but the two will have some things in common.

Classic (though somewhat dated) example is a fax machine.

What’s a network?
We’re going to primarily stay vague about what’s a network for this course. A network can be something like:


 * a physical road network
 * a data network
 * people who connect through a common database
 * people who use a similar product

When does the structure of the network matter?



For most purposes, we’ll just say that both of the networks above have size=5, and ignore that they have different properties.


 * A network may be closed or open.
 * This is very much like the idea of excludability.
 * An open network is one that anyone (person, product) can connect to. Nobody can deny access.
 * A closed network is one which has someone who’s the gatekeeper, who can keep people from joining even if the gatekeeper chooses to allow access fairly freely.


 * A network may be sponsored or not
 * A sponsored network has someone (probably an organization) who is, in some fashion “in charge” of the network, perhaps promoting or maintaining the network.
 * Often that means that the sponsor can benefit from the network.
 * Frequently, sponsored and closed go together, but it is possible to have a network which is sponsored and open.


 * A network may be one-sided or two-sided (or maybe more-sided) …

Two-sided networks
We’ll also talk about these as “two-sided platforms” or “two-sided markets” (or abbreviate as something like “2SP”).


 * A one-sided network has network externalities simply as above—when more people join the network it benefits everyone in the network.
 * A two-sided platform connects two different kinds of users:
 * (A) users benefit when there are more (B) users.
 * (B) users benefit when there are more (A) users.


 * Issues of standards very often have to do with 2SP’s.
 * Example: MP3 is a two-sided platform which connects music makers and music listeners. MP3 is the standard which allows that connection to work with different players. (There are other audio standards.)
 * For the purposes of this course, we’ll use this idea as the near-definition of a standard:
 * Standard
 * A standard defines what belongs to a network.

With a two-sided platform, does an (A) user benefit when there are more (A) users? This is a little messy:


 * Indirectly, yes: More (A) users will likely mean an increase in the number of (B) users, which will then benefit the (A) user.
 * Often not pure: The Windows operating systems are primarily two-sided-platforms for connecting software developers and users. However, there is also some one-sided-network aspect to ease in sharing files and similar.

If you’re wondering if something is a 2SP, make sure you can clearly identify a graph like this, with the platform connecting two kinds of users:



Sorta aside for now: Besides network externalities, two-sided platforms and similar standards-based products can be seen to have a lot in common with complementary goods, and often one side’s users are well-described as “complementors”.

Random example:

A shopping mall is a 2-sided platform connecting shoppers with retailers. It is a closed network, since it can deny retailers space and can eject shoppers if it wants. Usually a mall will persue an “openness” approach on the customer side even though it is a closed network.

Discussion:


 * Clump into groups ~ 4 people.
 * Designate a talker.
 * Figure out 5 networks. Is each …
 * …1-sided or 2-sided (or more-sided)?
 * …sponsored or not?
 * …closed or open?

Pecuniary externalities
There’s often a confusion which arises like these when talking about network externalities:


 * “There are externalities when more people buy coffee because when a lot more people buy coffee it pushes the price up and so it harms the other people who want to drink coffee.”
 * “There are externalities when more people buy software because that makes it cheaper to produce which makes it better for other people who want to buy it.”

The first of these is reasonable and sorta fits the definition of an externality, but we exclude things like that from our discussion of externalities. It’s called a “pecuniary externality” meaning that any externality effect is due to the movement of equilibrium prices. We don’t pay much attention to these things because they don’t cause markets to go wrong—they’re necessary for markets to work correctly. (The second of these has the same problem, plus is confused in other ways, as well.)

Examples
Education:


 * There seems to be, in most cases, a positive externality to education. The educated person benefits, but having more educated people also helps the overall economy. (Is this a network externality?)
 * There may be a negative pecuniary externality to education: More educated people means more competition for jobs requiring an education, so lower wages. (Notice that this harms the already-educated job seekers, but helps the employers.)

Cities:


 * There often seem to be positive network benefits to having many people in a city. That’s a real (non-pecuniary) positive network externality.
 * However, more people living in a city will push up rent, which is a negative pecuniary externality.

More two-sided platform examples




Again, do side (A) users benefit from more (A) users? Yes, indirectly. We’re going to concentrate on the “Yes” for now and sidestep the “indirectly” for later. As long as we’re concentrating on the “Yes”, we can treat two-sided networks and one-sided networks similarly, which isn’t too far wrong.

Network externalities =


 * Network externalities
 * The benefit (or harm) that a member of a network receives when someone else joins that network.


 * We’ll mostly be concentrating on the benefits part of that, with positive network externalities, but negative network externalities certainly exist also.
 * We’ll also be using the term “Demand-side economies of scale”.

Classifying networks: We talked about closed vs. open networks, sponsored vs. unsponsored networks, and one-sided vs. two-or-more-sided networks. Issues of whether a network is open or sponsored won’t enter into the theory we cover very much yet. The two-sided platforms are different in important ways, but we’ll overlook those for a while and just pretend the theory we’re working on for one-sided networks applies to two-sided networks as well.

= Graphs for goods with network externalities =

We want, as much as possible, to use standard economics approaches even if a product has network externalities. That’s likely to mean demand curves.



What does a demand curve show?


 * 1) Looking at it one way, it answers the question, “At any given price, how much can be sold?”
 * 2) Looking at it the other way, it answers the question, “At any given quantity sold, what is the marginal willingness to pay for the last unit?”

We’ll focus on #1 for now.

For goods with network externalities, demand can be very odd.

Why?


 * The demand depends on how many others have the good.
 * If I expect to be the only person to ever own a telephone, then would I want to buy a phone for $10? Probably not.
 * If I expect everyone I know to own a telephone, then I probably would think that’s a fine price.
 * Trying to draw this kind of thing is tricky.

Rather than try to figure it out right on the $$p-vs-Q$$ graph, I’m going to do some graphical mechanics on other kinds of graphs and then work toward the $$p-vs-Q$$ demand curve.



This is not the demand curve yet—one way to see that is to look at the axis labels. There’s no price axis.


 * $$Q^X$$
 * The expected number of customers


 * Expectations are vital.
 * “number of customers” not “amount sold”—we’re going to be generally assuming discrete choice.


 * $$Q(Q^X, p)$$
 * The quantity demanded given some expected number of consumers and a particular price.

With positive network externalities, what happens to $$Q(Q^X, p)$$ (with ceteris paribus $$p$$ held constant) …


 * …as $$Q^X$$ increases?
 * …as $$Q^X$$ decreases?

What happens to $$Q(Q^X, p)$$ (with ceteris paribus $$Q^X$$ held constant) as $$p$$ increases?



The overall shape of the curve …


 * The $$Q(Q^X, p_1)$$ curve slopes upward with positive network externalities. Since greater network size makes the product more valuable, more people are willing to purchase at any given price if they expect a larger network.
 * It curves downward (meaning slopes upward, but not as steep) for 2 reasons:
 * diminishing marginal returns to network size
 * The $$1,000,001^{st}$$ extra person using the network doesn’t add as much value as the $$11^{th}$$ extra person using the network does.
 * saturation
 * Eventually all the people who have much interest in the network are already in it. (Some people will just never want to join Facebook.)


 * Possible flat bit along the horizontal axis—the quantity demanded doesn’t go negative, but it can be zero.

Aside on rational expectations in general

 * Generally, rational expectations is a condition which is required by some models.
 * Rational expectations requires that if people expect an outcome, they will act in a way which brings about that outcome …
 * …because what if they didn’t? If everyone expects there to be a lot of holiday traffic on Christmas Eve, and so everyone drives two days earlier, then the model isn’t very good—the very existence of the model causes it to be wrong.
 * There are lots of places where it can be shown the rational expectations condition fails, but it’s the best place to start.
 * We will also use the expression “fulfilled expectations”.

Fulfilled expectations and network externalities
On the 45-degree line: $$Q(Q^X, p) = Q^X$$




 * We’re concerned about how expectations and actual quantity interact. Along that line, realizations and expectations are the same.
 * I’ve labeled 3 important points, (L), (C), and (H)
 * At each of these and only these the expected quantity equals the realized quantity
 * At other points fulfilled expectations fails. If the consumers expect a different quantity than one of those three, the very fact that they expect that quantity will cause them to choose a different quantity.

At these three points:


 * (L)
 * Zero! Nobody is using the product (so “L” is for “Low demand”).


 * (C)
 * Small number are using the product.


 * (H)
 * A lot of people using the product (so “H” is for “High demand”).

So, at (L), (C), and (H), $$Q(Q^X, p) = Q^X$$. Each of these points shows a demand equilibrium.


 * Demand equilibrium
 * In a market with network externalities, there is a demand equilibrium if the quantity demanded (given prices and expected quantity) equals the expected quantity.


 * i.e. $$Q_{e}^{X}$$ is a demand equilibrium at price $$p_1$$ if $$Q(Q_{e}^{X}, p_1) = Q_{e}^{X}$$.

Dynamics around the demand equilibria
However, which of the three is a likely outcome?

There are stable and unstable equilibria:

Aside: What’s an equilibrium? It’s a state of a system where forces pushing (pulling) in different directions are equal so the system doesn’t move.



Apply the idea to our graph:


 * Between (L) and (C)
 * [[Image:NetEffects-QvsQX-dynamics-part3-01.PNG|frame|none|alt=image]]


 * $$Q < Q^X$$
 * Fewer people actually want to buy it than are expected to buy it. People will figure this out, and then the expected number of people will drop.
 * When the expected number of people drops, even fewer people want it.
 * Overall the system moves down and left.


 * Between (C) and (H)
 * [[Image:NetEffects-QvsQX-dynamics-part1-01.PNG|frame|none|alt=image]]


 * $$Q > Q^X$$
 * More people actually want to buy it than are expected to buy it. People will figure this out, and then the expected number of people will rise.
 * When the expected number of people rises, even more people want it
 * Overall the system moves up and right.


 * Between (H) and $$+\infty$$
 * [[Image:NetEffects-QvsQX-dynamics-part2-01.PNG|frame|none|alt=image]]


 * $$Q < Q^X$$
 * Fewer people want it than are expected.
 * Again, overall it moves down and left.



So, for the three demand equilibria:


 * (L)
 * is stable. Forces are pushing down and left into the corner.


 * (C)
 * is unstable. Forces on either side are pushing (pulling) away from (C). A slight deviation away from the equilibrium in either direction will pull the system farther away.


 * (H)
 * is stable. Forces from both sides are pushing toward (H). If the system moves a little bit away, it will be pushed back to (H).

= Network externalities =

So, at (L), (C), and (H), $$Q(Q^X, p) = Q^X$$. Each of these points shows a demand equilibrium.


 * Demand equilibrium
 * In a market with network externalities, there is a demand equilibrium if the quantity demanded (given prices and expected quantity) equals the expected quantity.


 * i.e. $$Q_{e}^{X}$$ is a demand equilibrium at price $$p_1$$ if $$Q(Q_{e}^{X}, p_1) = Q_{e}^{X}$$.

Apply the idea to our graph:


 * Between (L) and (C)
 * [[Image:NetEffects-QvsQX-dynamics-part3-01.PNG|frame|none|alt=image]]


 * $$Q < Q^X$$
 * Fewer people actually want to buy it than are expected to buy it. People will figure this out, and then the expected number of people will drop.
 * When the expected number of people drops, even fewer people want it.
 * Overall the system moves down and left.


 * Between (C) and (H)
 * [[Image:NetEffects-QvsQX-dynamics-part1-01.PNG|frame|none|alt=image]]


 * $$Q > Q^X$$
 * More people actually want to buy it than are expected to buy it. People will figure this out, and then the expected number of people will rise.
 * When the expected number of people rises, even more people want it
 * Overall the system moves up and right.


 * Between (H) and $$+\infty$$
 * [[Image:NetEffects-QvsQX-dynamics-part2-01.PNG|frame|none|alt=image]]


 * $$Q < Q^X$$
 * Fewer people want it than are expected.
 * Again, overall it moves down and left.



So, for the three demand equilibria:


 * (L)
 * is stable. Forces are pushing down and left into the corner.


 * (C)
 * is unstable. Forces on either side are pushing (pulling) away from (C). A slight deviation away from the equilibrium in either direction will pull the system farther away.


 * (H)
 * is stable. Forces from both sides are pushing toward (H). If the system moves a little bit away, it will be pushed back to (H).

So, meaning of the third label, (C), “critical mass”.


 * Critical mass
 * In a market with network externalities, there may be a critical mass. The product will succeed (have relatively high use) if and only if it can achieve a greater use than the critical mass.


 * There won’t always be a critical mass. We’ll be giving the circumstances where there is critical mass a lot of attention, though.

Here’s an example without a critical mass. What might look like this? (show stand-alone demand)




 * Sometimes there will be a critical mass at some prices and not at other prices.
 * Or there could be a critical mass when there’s a competitive substitute but not when there’s no competitor.

Positive and negative feedback
We’ve already seen positive and negative feedback, we just didn’t call them that.


 * Positive feedback
 * The strong get stronger and the weak get weaker.


 * Negative feedback
 * The strong get weaker and the weak get stronger.


 * These might be very different than your intuitive use of the terms! For instance, it’s not like positive and negative reinforcement.


 * Negative feedback tends to stabilize systems. When there is negative feedback around an equilibrium, the system will tend to return to that equilibrium.
 * Positive feedback tends to lead to extremes and to unstability. When there is positive feedback around an equilibrium, the system will move away from that equilibrium.
 * It is often said that products with network externalities exhibit positive feedback—that’s largely, but not entirely true. Around the critical mass there is positive feedback, so that a failing product will fail even more, while a successful product will succeed even more.
 * However, assuming there is a limit to how high (H) can be—that it’s not infinite—then around (H) there is negative feedback.
 * So, for this particular kind of network externalities, there’s positive feedback around (C), and negative feedback around (L) and (H), but in casual talk about network externalities, this system mught be described as having “positive feedback” in general.

= Multiple equilibria and path dependence =

In economics, we’re most used to systems where there is a single, stable equilibrium.



When we do have such a system, we can often ignore time.

Basic idea: With a single, stable equilibrium, we know where the system will wind up eventually. For a lot of purposes we can ignore how it gets there. Comparative statics, for example, compares multiple end states ignoring the adjustment process.





With strong network externalities (at least, these specific ones), there are multiple stable equilibria. We don’t know which of these is the likely end state without thinking about how things happen.


 * Path dependence:
 * How things happen can determine what happens.

Whenever this is true, we need to think about dynamics as well as statics.

= Trying to get to a demand curve =

Demand curves are very useful. So far, we chose to hold price constant but allow $$Q^X$$ and $$Q$$ to vary. We obviously aren’t going to describe a demand function very well if price can’t change. So, now let’s think about what happens when price changes.

just plot $$Q-vs-Q^X$$ at first at different price levels …

Now, we’ll combine two plots, we’ll combine the $$Q-vs-Q^X$$ plot at different price levels with a $$P-vs-\left(Q, Q^X\right)$$ plot. Notice the horizontal axis label on the $$P-vs-\left(Q, Q^X\right)$$ plot. It has both $$Q$$ and $$Q^X$$ on it. In fact, all the pints we’re plotting there are demand equilibria—we’re assuming an equilibrium before it even gets to this plot. One thing that will imply is that the system doesn’t have to be on the demand curve all the time, but that if it strays off of the demand curve it will come back to it.



Looking at the demand curve alone:



It slopes UP?!

Sorta—it’s dotted for a reason. The upward-sloping section of demand are the critical mass points for each price level. It’s part of the demand structure, we don’t want to forget about it, but we never really expect that much to be demanded.

On the upward-sloping section: as the price goes up, the user is giving up more in money to use the good, so they neet greater compensation with network size to make it worth buying. So $$Q^X$$ has to be greater to overcome critical mass.

Again, let’s think about time:




 * In the classic market model, we see everything we need to predict quantity demanded.
 * Without network externalities, we can see that at the price $$p_1$$, there is $$Q_D$$ demanded of the good. We’re not sure exactly how or when all those consumers will purchase the good, but we can be pretty confident about the quantity which will be purchased.


 * With network externalities, there are two different strong possibilities.

We can copy the dynamics from the $$Q-vs-Q^X$$ plot to the demand curve.




 * At $$Q_1^X$$:
 * People expect the product won’t be very popular, so the value from network externalities isn’t enough to make it worth the price.


 * At $$Q_2^X$$:
 * People expect the product to be popular, so the value from netowkr externalities makes it worth purchasing.


 * At $$Q_3^X$$:
 * People expect the product to be very popular, but that’s still not enough to convince that many people to actually buy it.

Notice that critical mass depends on price. If the price is lower, that can compensate for fewer people using the product and make it worthwhile to buy. (This will be important for strategy.)