a)The factory is producing a bad smell, but nobody is seen affected in this case. Hence, in this scenario, there is no presence of externality.

b) Under coase theorem, any arising conflict would be settled by the involving parties on the sets of inputs and outputs.

1. If the first scenario is considered, then the family has full property rights to a pleasant smelling environment, it is not their fault, and they have a full right to clean the environment. They have to give up $8000 in order to have a clean environment. Therefore, the factory should compensate them $5,000 because this externality is created on the part of the factory.

2. In the second scenario, the factory has the full right to emit the bad smell, and it's the moral responsibility of the factory to look into this matter. Therefore, the factory should install the cleaning system so that this externality could be removed.

The second scenario would provide the efficient outcome because in both scenarios, the factory needs to compensate for this externality. Hence, the factory should install the cleaning system on its part so that it could manage with its social responsibility. The differences between these scenario is that it is clearly an externality for the family because it does not get any benefits on part of creation of this externality but they only get harm.