We’re starting to cover in class the topic of network effects, where goods consumed have positive externalities (e.g. the more people have cellphones, the more utility the people buying them will enjoy). Of course, negative externalities exist as well: imagine a river, a factory upstream and a farm downstream. In this case, the water of the river acts like a good that the factory uses by dumping its industrial waste into, and the farm uses the water to irrigate its plants. One can clearly see that the utility of the farmer is affected negatively by the factory, since polluted water isn’t exactly condusive to watering plants.  In this case, it seems somewhat fair that the factory pays some sort of compensation to the farmer for reducing his utility, and using that intuition, we can examine a theorem that’s used very often in modern law in dealing with matters of negative externalities: Coase Theorem.

A result from classical economics shows that goods with positive externalities are underproduced, and goods with negative externalities are overproduced. In this case, underproduced and overproduced are measured from the standpoint of society. When we say the good is underproduced, we mean that the net benefit to society (measured as the sum of utility of members of the society)  from producing one more good is greater than the cost of producing that good, and conversely for the case of overproduced goods. An intuitive way of looking at this is as follows: In the case of cellphones, if I buy one, than the utility my friends get from having their cellphones increases since they can contact me. Yet the amount they benefit doesn’t factor into the decision of whether I should buy one - the only thing that matters is weighing the cost of the phone versus the amount of utility I get from buying the phone. In this sense, even though I’m increasing the utility of society as a whole, my own increase in utility is less than the overall increase in society’s utility.  This means that there will exist people for which even though their own utility gained from having a phone is less than the cost of buying it, the benefit to society is at least as great as the cost of the phone : This is an outcome where society as a whole would have benefitted if the person bought the phone, but the result is that the phone is not bought, hence the phone is underproduced. The arguement works exactly in the same way for goods with negative externalities.

From that, one can see that the problem arises because the benefits and costs to society are not the same as the benefits and costs to the individual consuming the good. If we had some way to make the two the same, then the problem of overproducing and underproducing would disappear.

In 1960,  economist Robert Coase published his paper “The Problem of Social Cost”, and was awarded the Nobel Prize in 1991 for it, along with his  other work on transaction costs. What Coase basically proposes is that property rights be established as a way of accounting for this negative externality. Setting aside the perhaps impractical nature of this for the moment, suppose we somehow decided that ownership of the river could be assigned totally to either the factory or the farm. Suppose further, for the sake of illustration, that we could quantify a) the amount of utility the factory gets from dumping its waste into the river, and b) the amount of utilty lost by the farm as a result of the factory dumping the waste,

Now, say the ownership of the river was assigned to the farm. If the factory gains $100 in utility from dumping while the farm loses $50 in utility as a result, one can intuitively see that this would result in the factory wanting to pay the farm some amount between $50-$100  for permission for the factory to continue dumping waste into the river. Conversely, assume that the factory gains $50 in utility from dumping while the farm loses $100 in utilty. In this case, the farm would exercise its ownership of the river to stop the factory from dumping its waste into the river, and since the factory gains less from dumping than the farmer does from the factory not dumping, the factory would not be able to rationally compensate an amount to the farm to allow the factory to keep dumping.

This also works in the reverse direction: Assume the ownership of the river was assigned to the factory. If the factory gains $100 in utility from dumping while the farm loses $50 as a result, the factory gains more from dumping than the farm gains from not dumping, hence the dumping will continue. If the factory gains $50 in utility from dumping while the farm loses $100 utility as a result, one can see that the farmer would want to pay the factory some amount between $50-$100 to make it stop dumping.

The interesting result from this is that, regardless of who the property rights of the river is assigned to, the result is that the actions that cause a greater net benefit to society ( measured as the sum of the utility of the farm and the factory)  are allowed to occur. That is to say, if the factory gains more from dumping than the farm does from not dumping, then as a result of the property right established, dumping will occur. The reverse is also true: if the farm gains more from not dumping than the factory does from dumping, than dumping will not occur. Both these results are independent of whoever the river’s property rights get assigned to.

Of course, that is not to say that the Theorem is without its shortcomings. For one thing, notice that we assumed that there were no bargaining costs - it doesn’t cost anything for the factory or farm to negotiate with each other. This is not entirely realistic since we expect most of this bargaining to occur in real life in the presence of lawyers representing the factory and farm, and  who don’t work for free. For another, as we established earlier, the concept of establishing property rights may not make sense entirely either: imagine if the factory dumped its waste into the air instead. Establishing property rights for air would seem like a much less viable solution.

For further reading: http://en.wikipedia.org/wiki/Coase_theorem