I'd like to excise the discussion of the random public goods-related topics from the low content thread. So that this post has some content, a brief summary.

If Mises.org is your primary source for learning economics, you will certainly have some misconceptions. If you reject that possibility, then this thread is probably not for you. Mostly, this should be a place for people who are willing to learn stuff to ask questions.

A brief review of the words in the title -- Wikipedia is as always a decent source.

Public Good -- a good which is non-rivalrous (infinitely consumable) and non-excludable (all have access). Like such ideal goods don't exist, but to the extent that a good is like a "public good" the theory of public goods applies. Note that these are properties of the good. Who produces them is immaterial -- private actors can and do produce public goods, and state can and do produce goods which are not public goods. Also note the possibility that one can make a similar good which is excludable is not always relevant. These are just different goods. (A walled garden is not a public garden.)

Externality -- a property of transactions, this is a cost or benefit which is incurred by a third party.

Free Riders -- people can benefit from stuff without paying for it.

What is the free rider problem? That public goods don't get produced (aren't produced to optimal levels) because people who are willing to pay to have the good produced figure that they can get the benefit without paying, and so don't.

Finally, I'll conclude with these words of Coase:
"All solutions have costs and there is no reason to suppose that government regulation is called for simply because the problem is not well handled by the market or the firm."

That's to get us started...

Originally Posted by Sholar
The value of the externality associated with the production of the public good does not affect how much of the good is produced, but certainly it affects the "socially optimal" level of production of the good?

Also, how is a free rider not someone benefiting from an externality? He is a third party not involved in a transaction benefiting from that transaction.

I've got sort of a cute example/illustration to start things off. And the government is nowhere to be found in it!

Suppose there is afirm looking to provide a particular public good. It can be supplied in different levels (say in hour long increments). Two people in town, Alice and Bob. Their actual values--also known as marginal benefits (and willingness to pay for the good) along with the firm's marginal cost per hour are listed below

Hours........Alice......Bob....Marginal Cost
1...........$18.......$10..........$2
2...........$16........$9..........$5
3...........$14........$8..........$8
4...........$12........$6..........$11
5...........$10........$4..........$14
6...........$8..........$3..........$17

So here, the optimal amount of the public good would be 5 hours, with Alice paying $10 and Bob paying $4. The marginal cost of providing that fifth hour equals the marginal benefit, which is the decision making metric which maximizes social welfare (it maximizes consumer surplus plus producer surplus).

Now suppose Alice is a lying bitch . She under reports her willingness to pay for this public good by $7. Now, the firm can only supply four hours of protection, and collects $5 from Alice and $6 from Bob for their good.

Is this in Alice's best interest? well, she loses the 5th hour of the public good, which means she loses something she values at $10. But instead of paying $50 (5 hours x $10/hr) she pays only $5/hour x 4 hours, or $20. So she is better off by $30, so she has incentive to lie, and to cause underproduction.

Note: the demand curve in this case makes it so the firm may want to under-produce if it is a monopoly (another market failure), but the willingnesses to pay could be adjusted to make the demand curve more inelastic so that the firm--even if it is a monopoly--will want to produce as much of the good as possible (possible meaning that the money/hour it can collect is greater than the Marginal cost)

Also, sholar, do you agree with DrModern when he said in the LC thread that I have the definitions of public good and externality "weirdly tangled?"

Sure. Stuff gets made when people pay for it. How much better off the people who aren't paying for it become doesn't impact how much is made. But it does impact at what cost it would be "better" (in the sense of allocative efficiency) for the item to be produced.

A free rider is someone benefiting from an externality. The "free rider problem" refers to the problem of underproduction of public goods because people anticipate the ability to free ride.

I also agree with what Scolar wrote--I can see where you're coming from. And a lot of Intro Micro books put Externalities and Public goods in the same chapter.

Trouble is that in the Block article, Block either was confused or redefining common economic terms. The definition of a private good has nothing to do with whether or not an externality exists.

Right. I was confused because you said in the other thread if you get people to enter into some sort of assurance contract so the following happens:

Positive externalities associated with the production of the public good are only eliminated if everyone pays in advance for it, and if everyone pays for the public good in advance, none of them can free ride.

Check out the example I gave earlier--Alice is (partially) free riding, even if she pays in advance. I think that's the 'easy riding' which someone mentioned in the LC thread. Though I've never heard of that term being used before, I kind of like it.

In some sense, Alice is paying less than she should, which causes underproduction of the good since she lied in order to pay a smaller amount.

Well, the principle is, first, to keep the ideas separate:
Externality is a property of the transaction.
Public Good is a property of the good.

Second, I don't know if it's a problem of definitions, necessarily. It's also related to how people misuse those terms when discussing "the problem of public goods" which is much, much more about "the problem of free riders" than it is "the problem of externality".

"to the extent that bread is a source of external economies it is a public good" makes the mistake of confusing the two ideas. Talking about the value of the (positive) externality of a public good, for example, in this exchange, is what causes that reaction:

He didn't define public goods in that way. He said that people use the externalities associated with the production of public goods as a justification for government production of those goods. Which seems true enough. He gives a very standard definition of public good later in the paper:

This is a good example.

The problem of free riders doesn't disappear by asking those people to join the transaction (which removed the externality). Compare this to the problem of (negative) externalities, which is solved by incorporating everyone into the transaction (hence the stuff about Coase).

Well, he does get excludability correct--but my beef with the quotes I saw wasn't actually in his definition of public good, but with either how he was confused about private goods not having externalities or how he was redefining common economic terms (defining private goods as things that don't have externailities--in addition to the other parts of the normal definition).

I didn't see his statements about people arguing for government intervention. My own view is that you could come up with at least three alternatives once you know about the problem with public goods.

1. Gubmint provision
2. Ignore the problem (or at least know how big the problem that you've decided to live with is.)
3. Try to come up with novel ways of dealing with the problem.

The third alternative may include second-best solutions, or actually first-best solutions with 'weird' ways of asking and collecting money from people. It's been a while, but I remember some strange rules when asking people how much they're willing to pay and then deciding how much they should pay that result in better allocations.

Well that's only a problem to the extent that the assurance contractor is unable to effectively price discriminate. If I go to Wal Mart and buy a TV that I value significantly more than the price of the TV, no one would say that I am a free rider. They would simply say that WalMart is unable to effectively price discriminate.

Being able to price discriminate or not does not affect the welfare of society. The producer surplus plus consumer surplus will remain unchanged if the number of transactions is unchanged.

And actually, in my example, the firm was able to perfectly price discriminate to determine the optimal level of the good. Alice paid $10 and Bob $4 in the optimum.

Finally, I'd say that price discrimination doesn't really have anything to do with public goods. I replied to you to help, but this is sort of a tangent to the main thrust of the thread.

I'm not sure I understand the point that you are trying to make. If the efficient amount of parkland is 10 acres, but the market only produces 5 acres, we are collectively worse off (by the definition of efficient).

If the market were -- magically, through clever mechanism design, whatever -- able to get everyone to contribute enough to produce the efficient outcome, then we wouldn't speak of a "free rider problem".

If everyone who uses the parkland pays an equal amount for it, it is absurd to say that the underproduction of parkland is due to free riders.

The "everyone pays an equal amount" part here is a completely unnecessary assumption.

I'm not sure why you bring it up. The producer of the public good is welcome to use price discrimination or any other mechanism.

In my example, if everyone had to pay the same price, the good would cost $5.50 each, and four hours would be provided. The good would be under-provided, since 5 is the socially optimal level.

If it were provided at that level, it is because Alice, Bob or both of them lied about their willingness to pay for the good. In other words, one or both of them is not paying their marginal benefit of the last unit of the good. In a perfectly competitive market (with a private good) they are--there are mechanisms built into such markets that ensures this happens. But in the example with Alice and Bob paying $5.50, they aren't.

And that's the crux of the problem...not that they're paying the same or different amounts. Rather, the price that they are paying is not equal to that good's marginal benefit, and in the public goods problem there are incentives making this better for the individual. In a Perfectly competitive market, the incentives cause the price to be equal to the marginal benefit of the last good.

First, let me make an important general comment: how the costs are distributed are completely irrelevant to whether the level of production is allocatively efficient (e.g. no Kaldor–Hicks improvement is possible).

There are a couple of errors here which are confusing your example, the important one for us being describing the marginal cost as if it were the total cost.

To recap: in the original example, the fifth hour would be produced in an efficient outcome because the marginal benefit (A=10, B=4) equals the marginal cost (C=14). (The total cost of provisioning all five hours would be 2+5+8+11+14=40.)

However, if A had a marginal benefit of $7 less in each case (as she was representing), only the fourth hour would be produced in an efficient outcome (A' = 12-7=5, B=6, C=11).

In total, the first four hours cost 26. If A and B paid the same amount, they would pay 13 each. How the costs are distributed are completely irrelevant to whether the marginal production was efficient.

(In addition, the phrasing that they each pay 5.50 for the fourth hour is a bit unfortunate, as paying 5.50 violates the declared incentive constraints for A', who expressed a marginal benefit of 5. I prefer not to complicate the discussion by elaborating.)

As I predicted, Sholar's explanations are better than mine were. This is not super easy to grasp or to explain. I hope this thread is helpful for you, mjkidd (no sarcasm).

This is a problem but I don't see how it could be described as a free rider problem. An identical problem might exist if people systematically overvalue a public good and overpay the assurance contractor, resulting in the overproduction of a public good. This is obviously not a free rider problem. The assurance contractor charging too little or charging too much are two sides to the same problem, namely misspricing the assurance contract relative to the actual true value of the public good.

Scholar and ShaneP:

Have you read that book yet?

Oops, you're right. I should have said the price to both is $5.50. And that does violate what A would say, so if they had to pay the same price the output would be even lower. So one typo, and one legit mistake (violating incentives by saying B would pay $5.50).

IE, I agree with everything Scolar wrote about the example above. So if you were confused by something I miswrote or erred slightly, and you understand what Scolar wrote, well, just go with him, since we are saying the same thing. Or at least trying to


Edit: I was also assuming that A and B will pay the firm the same in aggregate to the firm for each hour purchased. Thus, the price per hour would be determined by the last hour provided, and every hour would cost that amount. In the case of truth telling, the fifth hour would be the last, and the price per hour would be $14. But as you said (and I said earlier as well) regardless of how the price is determined, the welfare gain of society increases. If A and B own the firm (government) and they only pay the firm's cost, then all the gain is by consumers. If the firm is a perfectly price discriminating firm and charges $28 for the first hour, $25 for the second and so on, then all the gain is by the producers. But as long as 5 hours are provided, the producer plus consumer surplus is maximized and will be unaffected by the price.

I've got it, and it's on my list of things to do, but I haven't yet.

BTW, I think/hope the book just falls under my third alternative (figure out what to do about the public goods/free rider problem). From what you said about it, it does.