A market left alone produces the quantity where the last unit's private benefit equals its private cost. Regulation exists where the private and social accounts diverge, and there are only five such places worth naming.
What are externalities and public goods?
An externality is a cost or benefit landing on somebody outside the transaction. A dyeing unit discharging into a river pays for its dye and its labour and not for the fish, so private cost sits below social cost and the market makes too much cloth at too low a price. The instruments are a tax set at the marginal external damage, a tradable permit that fixes the quantity and lets the price emerge, a technology mandate specifying the equipment, or a liability rule that makes the polluter pay after the fact.
Each of the four is a different answer to one question: who is made to hold the cost the market dropped.
A public good is non-rival and non-excludable: my use does not reduce yours, and I cannot be kept out. A lighthouse, a legal system, a clean-air standard and a systemic-risk buffer are all in this family. No private seller can charge for something nobody can be excluded from, so the state provides it or mandates it.
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What are informational frictions and weak competition?
Informational frictions come in two shapes that regulators treat differently. Adverse selection is hidden characteristics before the deal: the seller of a used car knows something the buyer does not, so the buyer bids the average and good cars leave the market. Moral hazard is hidden actions after it: an insured driver drives worse. Disclosure, licensing and mandatory audit attack the first; deductibles, retention requirements and capital rules attack the second.
Weak competition is the failure the market-structures work taught you to measure. Where scale economies are large enough that one firm serves the whole market more cheaply than two could, you have a natural monopoly, and the choice is a regulated private monopoly, a state-owned one, or a franchise auctioned to the lowest bidder. Where competition merely deteriorates rather than being impossible, the instrument is antitrust: merger review before the fact, conduct enforcement after it.
Regulation without a market failure, and overlapping failures
The fifth reason is not a market failure at all, and honesty requires saying so. Some regulation pursues a distributional or social objective that the market would satisfy efficiently and unacceptably. A minimum wage, a rural service obligation on a telecom licence, a lending quota to priority sectors, a rule that a bank may not refuse a basic account: none of these is justified by an externality argument. They are choices about who bears what, made through politics.
The correct model of a distributional regulation is therefore a political one, and it does not go away because the economics is unfavourable.
Two failure modes almost always coexist in the interesting cases. A bank run is an externality (my withdrawal raises your risk) resting on an informational friction (nobody can tell a solvent bank from an insolvent one at the counter), which is why bank regulation carries both a disclosure regime and a liquidity buffer.
Naming both is what stops you predicting that one will be dropped when the other is strengthened.