Belief: Agents are rational self-interested utility or profit maximisers and act in accordance with relevant constraints … this leads to an optimal allocation of resources.
Policy recommendation: The government should take a laissez-faire approach and leave the economy to work by itself … unless they have to correct market failure.
Neoclassical economics is meta theory, it is an approach to economics that is scientific, relying on a set of assumptions and making various hypotheses. Mainstream microeconomics owes much to neoclassical economics, as this school of thought essentially spurred the Marginal Revolution in the 1870s and now forms the framework by which micro-economists study the behaviour of individual agents and markets.
The Neoclassical vision involves agents (households and firms) optimising their behaviour in a rational manner, subject to relevant constraints. For instance, consumers maximise their utility subject to their budget constraint, and firms maximise their profits subject to their production constraints.
Moreover, Neoclassical economics contends that decisions are made at the margin. For example, a consumer maximises their utility of a good by buying that good until the marginal benefit of buying that good equals the marginal cost; that is, until what they gain from buying the last unit is equal to the cost of obtaining that good.
However, time and time again, the Neoclassical school is criticised for making too many assumptions and, in particular, assumptions that do not accurately reflect the behaviour of individuals or the workings of the economy.