Step 1: Understand market failure.
Market failure occurs when the allocation of goods and services by a free market is not efficient. It may happen in the presence of externalities, public goods, or market power.
Step 2: Analyze each option.
- Option (A) is correct because externalities, such as pollution, cause market failure as they result in unaccounted costs or benefits to third parties.
- Option (B) is correct because public goods are non-excludable and non-rivalrous, which often leads to market failure because private firms will not produce them in sufficient quantity.
- Option (C) is correct because market power, such as a monopoly, can lead to inefficiency in the market as monopolists can set prices above the competitive equilibrium, reducing overall welfare.
- Option (D) is incorrect because private goods do not cause market failure; they are typically efficiently allocated by the market.
Final Answer:
\[
\boxed{\text{Market failure occurs in the presence of externality, public goods, and market power.}}
\]