There are several definitions of externalities, with small variations, but these variation can have important impacts on the interpretation that could be made.
We will retain this one:
An impact, positive or negative, on any party not involved in a given economic transaction or act.
From the beekeeper’s point of view, no transaction takes place, and his power of decision on the investment choices of his farmer neighbor is nil.
In the first situation, he can hope to sell a honey of better quality (thanks to the fruit trees), but also have a higher yield and thus sell 11kg of honey at 12 € per kilo (per hive and per year). The externality can therefore be evaluated at 11kg x 12 €/kg – 100 = 22€ / hives and per year.
In the second situation, the insecticide (gaucho) can decimate the hives, so the negative impact is: 100 € / hives and per year. Nevertheless, this can be compensated by a compensation / fine that the farmer has to pay to his neighbor. In the case of an indemnity of 80 € per hive per year, then the net balance of externalities is 20 € per hive per year of losses (negative externality).
The second example shows that the first complexity of the notion of externality is the linkage of the externality to events (transactions), that could lead to its evaluation. It is therefore necessary to group together certain impacts in order to evaluate them properly.
According to Coase, externalities can be transformed into tradable goods (the externality is thus included in a negotiation and can disappear if the transaction relates to a known event), has two conditions :
If we take again the examples from above The beekeeper and the farmer: we can in this case (in the absence of neighbors and third parties), imagine that a negotiation takes place and that the additional profits obtained by the beekeeper and the farmer are distributed in an equitable way (via a cooperative for example), but this supposes that there are no other stakeholders in this decision, and that the additional profits are known and stable,