Does indeed sound like this is someone's homework assignment, but I'll bite.
An externality in economics is a cost or benefit that spills over from the parties involved in a transaction to third parties who had no part in consenting to the transaction. In the context of security I can see several example of this kind of thing:
1. Companies hosting personal data might choose to save money by not implementing proper security precautions. If a security breach occurs and the data is stolen and misused, the data subjects could suffer loss. In many countries this issue is addressed using data protection laws.
2. Users of computers may choose not to bother taking security precautions and this may result in their computers being herded into a botnet. As a result, third parties may become victims of DoS attacks or other criminal actiity.
3. Manufacturers and users of computer systems might forego security measures in order to keep costs down. A security breach might then result in a loss to third parties that cannot be fully recovered, e.g. a compromised control system might lead to an environmental disaster.
4. On the other side of the coin, if manufacturers and users do spend money to make their computer secure, this is money that could have been spent developing and growing their businesses. As a result, there is a knock-on effect for the whole economy of having to attend to security.
5. In the big picture, computers have become so ubiquitous and so critical to almost all aspects of life that developed countries simply could not function without them. This creates a risk of huge loss to everyone and is impossible to mitigate.
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