There existed a few theories of externality before Coase's. In general the goods are produced if the value of the goods are more than their manufacturing cost, but if their value is less than the goods are not manufactured. Here the cost of the manufacturing includes the direct costs like raw material, labor, electricity etc (The Swedes Get it Right, 1)
Now when the steel manufacturer makes his balance sheet he won't include these external costs into profit and loss statement for he pays nothing for that. The solution in this case may be that the government tells the company how much it can pollute air or it may impose the taxes depending upon the amount of the pollution it causes, called Pigovian taxes. This was the general theory followed before Coase came up with his theory (The Swedes Get it Right, 1).
Coase approach: Coase begins by giving the example of straying cattle, which destroys the crops in the neighborhood land. In this case we get more cattle i.e. the meat at the expense of the crops. Thus we can get either the crops or the meat. The answer lies simply in deciding the value of what we obtain at the expense of value of what is sacrificed. Thus Coase gives prime importance to the value of the product (1).
In this example Coase considers various options. Suppose if the value of the meat is more than the value of the crops in that case the cattle raiser may give some compensation to the farmer by mutual understanding. If the value of the crops on the other hand is more than the value of the meat in that case the farmer may build the fencing to protect its crops from the cattle and demand some compensation for doing so. ...