Market inefficiencies occur when the free market does not allocate resources efficiently. Four sources of market failure are
1. Monopoly power: example would be telephone services, because there are only a few major providers they are able to charge a price higher than is optimal.
2. Negative externalities: This is when there is a large impact e.g. pollution that is not taken into account by the free market.
3. Property rights: when property rights are not properly established e.g. on inventions, then the free market will produce lower than the optimal quantity.
4. Public goods: fewer public goods than optimal may be provided, because of the lack of incentive for individual firms. E.g. Public Education.
Perfect Competition: While true perfect competition is rare, it can be seen when there are an infinitely large number of suppliers and demanders. In this case they will both act as price-takers. An example would be the wheat farming industry. But let me know if you need something more here. If you clarify the question a bit I might be able to help more.
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