EBF 200
Introduction to Energy and Earth Sciences Economics


A Tale of Two Roommates


Here is a story about two guys sharing an apartment. We’ll call them Bert and Ernie. It turns out that Bert is a big fan of Megadeth, and can't get enough of their music. However, Ernie does not like this music so much. Ernie likes quiet. So, we have a bit of a problem: two people sharing the same apartment, one who likes loud, raucous, heavy metal, and one who cherishes peace and quiet. Is there a solution? This being an economics course, we are inclined to ask, is there some application of “economics” that would allow us to define just how much music can be played and keep both people happy? Is there some way we can "optimize the social wealth" in the apartment, some way to maximize happiness in the entire in-apartment community, which consists of Bert and Ernie. (We'll not worry about any externality effects the music might have on the neighbors for now.)

Well, in economics we are fond of stating things, especially utility and happiness, in terms of money, if only for the ease of accounting and measurement it allows us, so we have to define Bert and Ernie’s “happiness” in numbers. These numbers represent happiness in money terms. Let us suppose that the happiness for between zero and 5 songs is given on the following table:

Table 7. 1 Bert and Ernie example - # of songs played and happiness
Number of songs played Bert's Happiness Ernie's Happiness
0 0 0
1 10 -2
2 18 -6
3 24 -13
4 28 -20
5 30 -32

The above table contains the "total" amount of happiness for each number of songs. As you can see, the more songs played, the happier Bert gets and the more unhappy Ernie gets. We can assume, for simplicity, that all of the "happiness" numbers are denominated in dollars.

What is the “best” number of songs? Well, we want to know at which number total social happiness is maximized. Since our society here consists of two people, it's pretty easy to do - we add together everybody’s happiness and find out what the highest total is for everybody added up:

Table 7.2 Bert and Ernie example - Total Happiness
Number of songs played Bert's Happiness Ernie's Happiness Total Happiness
0 0 0 0
1 10 -2 8
2 18 -6 12
3 24 -13 11
4 28 -20 8
5 30 -32 -2

So it appears that 2 is the “best” number of songs played. It is the “socially optimal” amount.

Now, how do we get to this amount?

Let us assume that this apartment belongs to Bert, and Ernie is his guest. So Bert has the “property right” to play music. Since he has the right, and he is happiest when playing 5 songs, then this is how much he will play in the beginning.

This being economics and all, Ernie decides that maybe he can buy a little bit of peace and quiet. So, he offers Bert some money to go from 5 songs to 4. If we go to 4, Ernie's happiness increases from -32 to -20, so he is 12 dollars better off. So, he would be willing to offer up to 12 for one less song. If we go from 5 to 4, Bert's happiness decreases from 30 to 28. He will be giving up 2 dollars of happiness to listen to one less song. So, if he is being offered more than $2 to not play the 5th song, he should accept if he is a rational utility maximizer, and, of course, we assume that he is. For this drop in music, he must gain back at least $2 to be better off. So, we will have a trade. Ernie will pay less than 12, but more than 2, to go from 5 songs to 4. Both guys are happy with between 2 and 12 dollars being exchanged for one less song.

We can repeat the same thing for 4 to 3 songs and 3 to 2 songs.:

From 5 to 4 songs, the payment is between $2 and $12

To go from 4 songs to 3 a payment of between $4 and $7 will satisfy both Bert and Ernie.

Now, if we have negotiated a total of three songs, and Ernie wants to go down to 2, he will offer up to 7, and Bert will accept anything over 6.

So, to date, we have had three opportunities to make trades where both people are better off - Bert is willing to give up music if he is compensated more than the happiness he is losing from not hearing music, and Ernie is willing to pay if he pays less than the amount of happiness he gains from each less song. These trades are mutually beneficial, and are "wealth generating" - both guys are better off if these "trades" are made.

So, what about going from 2 to 1 song? Well, to do this, Bert needs to get at least $8, because that's how much value he places on the second song. However, Ernie is only willing to offer 4, since that is how much he values the extra silence. Since there is no number that is above 8 AND below 4, this trade will not be made. We will stop at 2. So, if we add up the trades, we can say that:

“We will go from 5 songs to 2 for an exchange of between $12 and $26.”

Note that we stop at 2 songs, which is the “socially optimal” amount.

OK, now what if we assume that the opposite is true: that Ernie owns the flat, and Bert is his guest. In this case, Bert is happiest with 0 songs. So, that is where we start. In this case, Bert is willing to offer Ernie some money in order to be able to play some music. To go from 0 songs to 1 song, he will offer up to 10. Ernie will be happy with anything more than 2.

So, we will go from 0 to 1 songs with a payment between $2 and $10. This will be a mutually beneficial trade, so both are willing to make it.

Now, if we want to go from 1 song to 2 songs, Bert is willing to offer up to $8, and Ernie is willing to accept anything over $4. Once again, there is an opportunity for a trade to be made, and it will be made.

So, what about going from 2 to 3 songs? Well, Ernie needs to get at least $7 to want to do this trade. However, Bert is only willing to offer $6. Since there is no number that is above 7 AND below 6, this trade will not be made. We will stop at 2. So, if we add up the trades, we can say that:

“We will go from 0 songs to 2 for an exchange of between $6 and $18.”

Note that we stop at 2 songs, which is the “socially optimal” amount.

You will notice that we started in two different places - in one case we started with 5 songs being played and, with voluntary exchange, we got to 2. In the other case, we started at 0, but with mutual, wealth-generating trades, we also got to 2. No matter where we start, we end up at the same place, and that place happens to be the socially optimal amount of Megadeth tunes.

OK, so this example seems a little silly. But let’s say I changed the table above to “Tons of Hideous Guck Emitted into Stream by Steel Plant Near Your House,” “Payoff to Steel Plant,” “Payoff to People in Your Town.”

Another Example

Table 7.3 Paris Hilton and Nicole Ritchie example
Number of Junior Whoppers PH Total Value NR Total Value
0 0 0
1 9 8
2 16 14
3 21 18
4 24 20
6 25 20

Paris Hilton and Nicole Ritchie are stuck in a room at the Motel 6 for the next 3 hours. Both are hungry. Paris has a bag of 5 Junior Whoppers, while Nicole has no food. Nicole does have money. Here are their TOTAL value of Junior Whoppers. All values are in $ million

Assuming that Nicole does not use force, and that neither party acts out of spite (ok, let’s pretend), explain any deal that will take place. Some hints: 1) Calculate marginal values; 2) Remember, don’t have the sum of Junior Whoppers that Paris and Nicole eat exceed 5!

Some more problems for you to do at home:

Eric and James are locked in the locker room at the Jordan Center for the next five hours. Eric has 6 “mini-Mac” burgers in a bag. James has money. Each of them has total value of mini-Macs consumed (in shekels, of course) as outlined below.

Table 7.4 Eric and James example
# of Macs Eric's Valuation James's Valuation
1 40 90
2 70 160
3 95 216
4 116 265
5 131 301
6 140 333

A: (14 points) Assume that neither party acts out of spite, and all trades are voluntary, explain what trades will be made.

B: (6 points) Let us make this a little harder. Assume that every time Eric sells a mini-Mac to James, Eric has to pay 50 shekels to the government authority. How many shekels will the government collect from Eric, and why?

Click here for answer


Part A

1st Step: Reorganize remembering that total Macs must = 6

Table 7.4b Eric and James example: 1st Step
Macs for Eric Macs for James Eric's TOTAL HappINESS (TH) James' TOTAL HappINESS (TH)
0 6 0 333
1 5 40 301
2 4 70 265
3 3 95 215
4 2 116 160
5 1 131 90
6 0 140 0

2nd step: Calculate Eric’s Marginal Cost (MC) for giving up Macs and James’s Marginal Value (MV) for gaining Macs

Table 7.4c Eric and James example: 2nd Step
Macs for Eric Macs for James Eric's TH Jame's TH ERIC MC [TH(X+1)-TH(X)] james' mv [TH(X)-TH(X+1)
0 6 0 333 40 32
1 5 40 301 30 36
2 4 70 265 25 50
3 3 95 215 21 55
4 2 116 160 15 70
5 1 131 90 9 90
6 0 140 0 - -

What trades will take place?

As long as James has a higher marginal value, or marginal happiness for each burger that is greater than Eric's marginal cost, they will trade.

To trade 1, Eric has MC of 9, James MV of 90. So, they will trade in the range [9,90].

To trade a 2nd mac, Eric has MC of 15, James MV of 70. So, they will trade in the range [15,70].

To trade a 3rd mac, Eric has MC of 21, James MV of 56. So, they will trade in the range [21, 56].

To trade a 4th mac, Eric has MC of 25, James MV of 50. So, they will trade in the range [25, 50]

To trade a 5th mac, Eric has MC of 30, James has MV of 36. So, they will trade in the range [30,36]

But for the 6th mac, Eric has MC of 40, James MV of 32. No Trade!

So, Eric will trade 5 macs to James for a price in the range [9+15+21+25+30=100, 90+70+55+50+36=301]

They will reach the maximum net happiness of 341 – all by themselves, using the “invisible hand.”

Here, trade creates wealth by moving assets to higher valued uses.


Part B:

Add 50 to Eric’s margins. Now only 2 trades make sense, where the net gain>50. So, the government collects 2*50=100 shekels.

So instead of trading 5 units, Eric and James trade only 2.

Taxes reduces trading in goods – which is bad!

But, later, we’ll see how to use taxes to reduce the production of bads – which is good!

The Coase Theorem:

If transactions costs are not “too high,” the market will find the optimal (best, wealth maximizing) solution.

But what constitutes “transactions costs?”

What could be a transactions cost?

  1. Spite. Perhaps not so much in business, but often in divorce (“The War of the Roses” (1989))
  2. Government Regulation and taxes; say a tax on trading
  3. Public goods problem. Instead of having only Ernie being affected by the toxins in the stream, let us have 100,000 residents in your hometown being affected. Now, fighting pollution becomes a public goods problem. (So, the problem with externalities is that they create public good problems.) Here the government could come in and impose a solution. The government could say: Don’t pollute so much; or pay us X dollars every time you pollute. What is the difference?

This theory was first elaborated by a professor by the name of Ronald Coase, who won the Nobel Prize in Economics for his work in 1991. He was the first person to observe that if property rights were well defined, and could be enforced, it was possible for a society to move to the socially optimal equilibrium in cases of pollution, or other externalities. In his honor, this has become known as the "Coase Theorem," and is the foundation of a large part of environmental legislation in the United States.

Want to learn more?

If you are a little bit more interested in this, you can read the article at the following link, which was written at the time of Coase being awarded the Nobel Prize. It is written at a slightly higher technical level than most of the course content, but is not so obtuse that anyone taking this course should have difficulty reading it.

"The World According to Coase" by David D. Friedman

The most important underlying assumption of using a "Coasian" solution to an externality problem is that property rights need to be well defined and enforceable. That means that we have to know who owns what, and that the people who own those things should be able to enforce their rights, and stop unauthorized users from using resources that they own. After a little bit of thinking, this becomes self-evident. Externalities arise because an economic actor is able to off-load some of his costs onto another person, and if the afflicted person had well-defined and defendable property rights, this would not happen, or at least, it would not persist. Coase was able to hone in on the underlying, root problem of externalities, and shows how such problems can be solved.


The Coase Theorem states that assigning property rights for the affected resource will result in the socially optimal quantity being produced.

It DOES NOT MATTER to which party the rights are assigned; to get the socially optimal quantity, all that is required is the clear definition of property rights.

When the producer has the property rights:

  • The parties receiving dis-utility from the externality will pay the producer of the externality to reduce production levels.
  • The optimal quantity is reached when the cost required by the producer to reduce by one more unit is higher than the benefit of the reduction.

When the affected party has the property rights:

  • The producer of the externality will pay the affected party to be permitted to increase production.
  • The optimal quantity is reached when the cost required by the affected parties to allow one more unit of production is higher than the benefit of that production.

This can only work with low transaction costs, which is not the case:

  • If there are many affected parties, so it is expensive to coordinate the necessary contracts for the sale of property rights.
  • If one person can block the sale, regardless of the costs actually imposed on them.
  • When enforcement of the contract can be expensive, such as the costs of court proceedings if there is a breach of contract.
  • If the costs of monitoring the offending behavior are high. That is, can we tell if someone is polluting a river?

Another issue facing application of the Coase Theorem is that of equity: it assumes that an affected party has the ability to pay a polluter to pollute less, which is not always the case. There is also a social issue here: the notion of paying a person in order to not perform a "bad deed' seems very wrong to many people. Looked at from the other perspective, allowing a company to make a payment to government in order to be able to emit pollution is seen by some people as wrong. This notion is described in the article at the following link, which I would like you to read:

Reading Assignment

Read the article: It's Immoral to Buy the Right to Pollute by Michael J. Sandel

We will talk a little bit more about this issue later. These are issues that can, and have been, addressed. The difficult part then boils down to the notion of defining property rights. Who has a property right to a river, or to the air, or to peace and quiet?