a) market failure, b)government failure, c)external cost, d)public cost
Of the choices you offer here, the best answer is A, market failure.
A market failure occurs when there is something wrong with the market that causes it not to produce efficient results. These tend to result in resources being either overallocated or underallocated to the production of some good or service. For example, if there are negative externalities that go along with the production of that good, its market cost will not reflect the costs of those externalities. Therefore, its price will be too low and people will buy too many of that good. This is not efficient or optimal.
None of the options B through D is correct. Government failure is not a breakdown in the market mechanism. It is something that occurs outside that mechanism. External costs are one aspect of one kind of market failure. They are not “any imperfection.” Public costs are similar to external costs.
For these reasons, A is the only right answer. It is the only answer that refers to a variety of imperfections in the market mechanism.