Economics: Applying the Coase Theorem

coase theorem

12/18/2012

~ bschulz

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Let's do another example of the Coase Theorem that will help us see when government actions may be necessary. Let's change the numbers a little bit. Suppose the box maker can still sell his boxes for 50 cents a piece and let's suppose the brewer can still sell her beer at $1.00 per brew. But let's change the cost of pollution now. Let's suppose that the cost for cleaning up the pollution for the box maker is 50 cents. That is, every box he produces creates pollution and if he has to stop the pollution from going into the lake, it's going to cost him 50 cents per box.
Let's suppose the cost to the brewer of cleaning up the pollution, once she takes the water in to her brew factory that it only costs her 25 cents to clean it up and make it fit for beer. So, we've changed the costs of dealing with the pollution. The brewer now has a lower cost of dealing with the pollution. The outcome in this case is going to be different. If we have independent operations, the brewer is still going to have to deal with polluted water, because the boxer is going to choose to dump the pollution into the lake, rather than incur the 50 cent cost of cleaning it up. So, his profits from making a box are now 50 cents, because he's dumping the pollution in the lake.
The brewer now, in order to clean up the water, is going to have to incur a cost of 25 cents. So her profits from making a brew, after she incurs the 25 cent cost of cleaning up the water is $1.00 minus 25 cents or 75 cents. The total profit of the operation now is 50 cents for the box, 75 cents for the beer or a total of $1.25. Now, if the boxer and the brewer get together and want to try to improve upon this situation, the brewer is only willing to offer the boxer 25 cents to stop polluting the lake. Well, 25 cents is not going to cover his cost of having to bottle the pollution, remember, that's 50 cents. So, the brewer and boxer will be unable to reach an agreement that would result in the lake staying clean.
Now, this is an important point. The value in this particular case is maximized when the brewer cleans up the water, because her cost of cleaning it up are lower than the boxer's cost of cleaning it up. In this case, the outcome that maximizes profits for the two parties involved will be for the boxer to pollute the lake and for the brewer, then, to clean up the lake before she makes the beer. So, the lake gets used as a sink before it gets used as a drink. Now, if you don't believe me, consider how much profit would be created if in fact the boxer had to go to the trouble of protecting the lake. If he had to go to the trouble of blocking the pollution himself, in this case, he'd sell the box for 50 cents, it costs him 50 cents to make it, you get zero profit out of the box operations. The brew, now, is made with clean water and with the clean water there's no cleaning costs, so the brewer makes $1.00 per beer.
The total economic profit from one box and one beer is now only $1.00, which is less than $1.25. You get less total economic profit from these two operations when the boxer cleans up than when the brewer cleans up. So, the Coase Theorem, once again, results in the outcome that maximizes value. However, we're only considering value for the two players in the story. Let's suppose I introduce another player.
Suppose, here's a swimmer who likes to swim in the lake. And let's suppose that not only one, but hundreds of people come to swim in this lake on a regular basis. If the water gets polluted, all of these swimmers may decide that it's not worth swimming. It's not worth getting ear infections. It's not worth getting nauseated. Or the water may be so dirty it's not even enjoyable to get in. In that case, the value of the lake to the swimmers may be destroyed. So, will the swimmers get together with the boxer and the brewer and reach an agreement about the pollution? Well, they could, but if there are a whole lot of swimmers, the transaction cost of getting everybody to the bargaining table may be so high that it wouldn't pay them to go to the trouble of trying to protect the lake.
Rather they would just let the lake become polluted, they would complain, they would be unhappy and they would go look for someplace else to swim or stop swimming altogether. When the transaction's cost of organizing an agreement like this become very, very high, it may be less expensive for society to have a government come into the picture and declare that the lake must remain clean. If the government represents the interests of all of the swimmers, the government can enter the arrangement on behalf of the swimmers and declare that, in fact, it's better for society if the boxer has to clean up the pollution.
Even though the boxer and the brewer might agree that it's better for the lake to be polluted, that it's better for the brewer to clean it up than the boxer to prevent the pollution, if we introduce a lot of other interests parties, who have a very high transactions cost of making their wishes known, then it may be easier to have a government step in and impose a solution on the problem, to impose a rule rather than simply allowing these two parties to bargain. Again, we go back to the rules of the Coase Theorem. The Coase Theorem assumes that the cost of getting the parties to the table to bargain is relatively low. If that transactions; cost is low, then we can count on bargaining among the parties to maximize economic value, without any kind of extra government involvement.
However, if transactions' cost are high, it may be less expensive to have the government step in and help to solve the problem. So, there you have it. The Coase Theorem challenges the notion that the government is needed in every case to deal with externalities. Some externalities can be solved by private bargaining, or private negotiations between the parties involved. We can expect that if those parties can get together with low transactions cost, they will agree on an outcome that maximizes the size of the pie, that maximizes economic value. Moreover, if there are no wealth effects, then the property rights, the ownership of the lake doesn't influence the outcome. The water will either be clean or dirty and it doesn't matter who owns the lake. The only difference the property rights make is how the profit is divided between the two parties. However, if there are other interested parties and their transactions cost of participating in a bargain are very high, then, it may be less expensive to society to have some kind of government actions, some kind of law or regulation to help manage the externality.
Market Failures
Solutions to Externalities
Applying the Coase Theorem Page [2 of 2]