Is the use/consumption of natural resources considered an externality per se? On a finite planet natural resources are rival goods by definition, i.e. if one agent uses/consumes a natural resource it becomes unavailable for other agents.

Mankiw defines an externality as "the uncompensated impact of one person’s actions on the well-being of a bystander".

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EDIT:

To illustrate my question imagine an isolated island that hosts two agents: Alice and Bob. Every year the agents are replaced with new agents Alice1 and Bob1, Alice2 and Bob2, etc. The only natural resource on the island is a tree that yields three fruits per year. The agents need two fruits as sustenance and plant the third one to grow a tree for Alice1 and Bob1 to enjoy the following year.

A third agent, Chris, visits the island and offers a massage. Alice values the massage at \$50 and Bob at \$40. The market clears at \$40.01 and Alice receives the massage. Even though the massage is a rival good, Bob can hardly argue that the massage given by Chris to Alice causes a negative externality since it does not affect him other than that he would have liked to have a massage at a lower price point.

However, during his visit Chris also needs to eat. 

Case 1: Alice who is harvesting the fruits sells Chris the fruit that Bob would have eaten.
Does the sale of the second fruit by Alice to Chris cause a negative externality for Bob?

Case 2: Alice sells Chris the third fruit available that year and shares the proceeds with Bob. Consequently Alice and Bob cannot plant it and when Alice1 and Bob1 arrive at the island the following year there is no fruit tree and they perish.
Does the sale of the third fruit by Alice and Bob to Chris cause a negative externality for Alice1 and Bob1?
Use or consumption of natural resources is not in mainstream economics considered as an externality per se.

First of all the quote from Mankiw is probably from undergraduate textbook and taken out of context as it is incomplete. 

For example according to Economics by Mankiw and Taylor (2014) 3rd ed the externality is defined as:


  the cost or benefit of one person's decision on the well-being of a bystander (a third party) which the decision maker does not take into account in making the decision.


Moreover, if you consider the above definition somehow 'tainted' because it is not just Mankiw but Mankiw and Taylor then consider the following quote from Mankiw (2018) Principles of Microeconomics 8th edition:


  An externality arises when a person engages in an activity
  that influences the well-being of a bystander but neither pays nor receives
  compensation for that effect. If the impact on the bystander is adverse, it is called
  a negative externality. If it is beneficial, it is called a positive externality. In the
  presence of externalities, society’s interest in a market outcome extends beyond
  the well-being of buyers and sellers who participate in the market to include the
  well-being of bystanders who are affected indirectly. Because buyers and sellers
  neglect the external effects of their actions when deciding how much to demand
  or supply, the market equilibrium is not efficient when there are externalities. That
  is, the equilibrium fails to maximize the total benefit to society as a whole. 


These more complete quotes bring necessary context into the discussion. First as is clear from the both first and second quote, not any decision that has effect on third party causes externality. As both of the quotes above clearly state for the third party effect to qualify as an externality the third party's well being and cost for the third party must not be taken into an account.

However, assuming perfect market the cost that is created by the fact that if rivalrous good is consumed other person cannot enjoy it is taken into account through supply and demand interactions. Consider the following simplistic model:

We have single buyer offering some commodity, lets use an egg sandwich as example - clearly rivalrous good - also if we would replace the egg sandwich by wood or stone or iron the result would not change. Now lets assume there are two people Aria and Ceresi. Aria values sandwich at \$50 and Ceresi at \$40. Also for the sake of simplicity lets assume that the sandwitch was produced at no cost to seller (its purely simplification assumption to make the problem easier to solve) - it was just an endowment. Also I will assume for simplification total informational symmetry so we dont need to go through some game theory to solve the problem. In such situation there will be a bidding war between Aria and Ceresi, and since Ceresi values the sandwich at \$40 but Aria which values the sandwich more will bid \$40.01 and gets the sandwich. Now it is true that this can be considered as a negative effect to Ceresi as now she missed opportunity to consume sandwich that would give her utility equal to \$40 dollars, but is this an externality? No! Why? Because the fact that Ceresi is not going to enjoy the sandwich is already captured in the market price that Aria payed for the sandwich! Hence here we cannot say that the condition that the effect on the third party was not taken into account applies.

In order to create negative externality in this case, the egg sandwich would have to make Aria fart which would create additional disutility to Ceresi which was not captured in the market transaction because if Ceresi would knew that the sandwich would create fart she might be willing to bid the price more in order to avoid that disutility but this was not captured by market. 

Now replace egg sandwich with a natural resource - oil - and you get the same effect. If the oil is bought just to be consumed as a part of some art installation there would be no externality, the fact that the oil is consumed and so other people cant enjoy it is already reflected in the market through supply and demand interaction. However, if the oil is burned which creates pollution which then harms people, and this harm is no longer captured by the market interactions we get the negative externality.

This is also clearly expressed by Mankiw in his principles of economics where he says:


  In the
  presence of externalities, society’s interest in a market outcome extends beyond
  the well-being of buyers and sellers who participate in the market


However, the condition for an externality is even stricter because to truly satisfy the condition that the well-being of the bystander is not taken into account there cannot be any other market effect that would result in internalizing the effect on a bystander. 

For example, consider a factory that processes oil and during the production process spills some oil waste on a nearby ground where some rancher herds his cattle. If the rancher has no property rights over the land this would create externality as the well being of the rancher would not be taken into an account. However, if the rancher owns the land and the oil refinery creates a damage to it through the oil waste he can sue for the damages which forces the factory to internalize the externality and making it disappear. 

Consequently, the rivalrous property does not cause in itself externality. In fact most often the externalities have nothing to do with whether the good is rivalrous or non-rivalrous but with whether the good is excludable or non-excludable. Most often externalities arise due to the fact that some good is non-excludable. 

Furthermore, Mankiw is an excellent economist but he writes textbooks for undergraduates. Any undergraduate text will have to sacrifice some precision in order to make the text more accessible. According to the more advance texts, like for example MWG - the bible of microeconomics, the externality is defined as a situation where as a result of makret failure the joint surplus of actors is not maximized. For example in our Aria - Ceresi example I gave above the joint surplus is maximized even though Ceresi did not received anything as Ceresi's surplus was zero while Arias's surplus was \$9.99, the 'producer surplus is \$40,01 and hence total surplus is \$50. Moreover, it is easy to see that given that no other allocation of sandwich would increase the total surplus, if the sandwich is not sold everyone gets zero, if Ceresi gets sandwich maximum total surplus would be \$40 in this situation. 

Hence even though I personally consider Mankiw's textbook superb and I use them when I teach microeconomics to undergraduates as a TA, you have to keep in mind that undergraduate books always have to sacrifice some accuracy for the sake of accessibility. Even I had to do that here, the full formal mathematical description of externality in MWG is more nuanced still but I hope that all of the above already provided enough clarity that I don't need to present it here.



In response to @KennyLJ,  it is true that in the past the definition of externality was quite vague. Moreover, it is also true that there might not be consensus on what externality is between different schools of economic though. However, I dont know of any textbook or mainstream paper that works on externalities that would define externality in a broad term as any rivalous good as @KennyLJ using the definition: 

"A decision's effects are called external if they fall on someone other than the decision-maker(s). A positive (negative) external effect is called an external benefit (cost)."

Here is the list of different definitions given in different widely used textbooks:


Mankiw and Taylor (2014) Economics 3rd ed:


the cost or benefit of one person's decision on the well-being of a bystander (a third party) which the decision maker does not take into account in making the decision.


concept more narrow then what @KennyLJ claims 


Mankiw (2018) Principles of economics. 8ed.




  An externality arises when a person engages in an activity that influences the well-being of a bystander but neither pays nor receives compensation for that effect. If the impact on the bystander is adverse, it is called a negative externality. If it is beneficial, it is called a positive externality. In the presence of externalities, society’s interest in a market outcome extends beyond the well-being of buyers and sellers who participate in the market to include the well-being of bystanders who are affected indirectly.


which is again much more narrow than what KennyJL claims and also it disproves the claim of KennyJL that "My guess is that Mankiw would agree that his quoted definition is the same as the above." - Clearly Mankiw does not agree with KennyJL definition - to the extend that his own textbook shows.


Mas-Colell Whinston Green (1995) Microeconomic theory states:



  "Definition "11.B.1 An externality is present whenever the well-being of a consumer or the production possibilities of a firm are directly affected by the actions of another agent in the economy." .... "When we say 'directly,' we mean to exclude any effects that are mediated by prices.


Again inconsistent with what KennyJL claims to be the "standard" definition. 


Varian Microeconomic Analysis 3rd edition:



  When the actions of one agent directly affect the enviroment of another agent, we will sa that there is an externality.  ... the first theorem of welfare economics does not hold in the presence of externalities. The reason is that there are things that people care about that are not priced. 


Hence again even Varain's definition which is arguably less precise is clarified by Varian's statement that the reason why externalities exist is that "The reason is that there are things that peoole care about that are not priced." 

Moreover, all examples given in Varian on chapter on externalities indicate that his definition is basically consistent with previous sources.

Varian distinguishes between consumption externalities and production externalities and gives examples such as smoking tobacco or having loud music or smoke affecting a production of clean laundry. None of the examples he gives an no fair reading of the chapter suggest he means that any external effect qualifies.


Cowen \&amp; Tabarok Modern Principles of Economics 3rd ed:



  Externalities: external costs or external benefits. External cost: a cost borne by people other than the consumers or the producers trading in the market. External benefit: a benefit recieved by the people other than the consumers or producer trading in the market.


Hence yet again this definition is more narrow as it specifically mentions it has to occur outside the market.

Hence, I cant understand how @KennyJL can claim his interpretation is standard. Of course nobody can prove negative, but all this points to the fact that such interpretation is not standard.



Moreover, I think that @KennyJL grossly misrepresented his quotes that I would like to point out:


  Scitovsky (1954):


The concept of external economies is one of the most elusive in economic literature. … full clarity has never been achieved. Definitions of external economies are few and unsatisfactory.

yes but the same source also says this:


  It is
  agreed that they mean services (and disservices) rendered free (without compensation) by one producer to another;
  but there is no agreement on the nature
  and form of these services or on the
  reasons for their being free. It is also
  agreed that external economies are a
  cause for divergence between private
  profit and social benefit and thus for the
  failure of perfect competition to lead to
  an optimum situation


It is true that Buchanan and Stubblebine (1962) say:


  Externality has been, and is, central to the neo-classical critique of market organisation. … Despite this importance and emphasis, rigorous definitions of the concept itself are not readily available in the literature.


but the same paper also says:


  "Pigovian discussion concerning the divergence between marginal social cost (product) and marginal private cost (product). By saying that such a divergence exists, we are, in the terms of this paper, saying that a marginal externality exists


Hence again the authors here do not even claim that anything goes or that the broad definition of KennyJL would be valid. In fact the paper itself suggests that externality is something that happens outside price system.

I did not double checked books as due to current coronavirus with my university proxy I can only check papers and not books but the two above sources are clearly misrepresented.