“Neoclassical”, as it’s commonly used, refers to the orthodox school of economics. This first arose in the 1870s with W. S. Jevons, Karl Menger and Leon Walras, and has been the dominant school of thought in economics since it was revived in the 1970s by Milton Friedman. In short, this type of economics places great significance on prices and value, and devotes its energies to explaining the relative prices we see around us.
To do this, it studies economics at the margin: by looking at the points at which we are undecided, we can infer what the limits of our wants are. Only an individual can make a decision in this way, or be undecided, so this is an individualist theory that takes subjective wants as the ultimate cause of everything. As well, it makes great use of maths and must therefore make a number of assumptions about human nature and economics in order to produce neat results, rather than messy indeterminacy.
A number of economists, such as the great A. K. Dasgupta (mentor of Amartya Sen) and the economic sociologist Tony Lawson (a long-term critic of the school) think the term ‘neoclassical’ misleading: they prefer the term “marginalist”. Why? Well, in essence it just doesn’t revive the Classical Political Economy of Smith, Ricardo and Marx.
That school was focused on big questions: “Will the capitalism system continue to grow?”, “Will we produce enough to feed our population?”, “What are the underlying social relations of this system?”. Coming, as they did, at the very of capitalism, it’s pretty natural that they would want to focus on understanding the system as a whole, the age-old struggle between humans and nature.
A century later, and people had adapted somewhat; some thought it was brilliant, others found it problematic, but it was hard to deny that it had a certain stability. Scholars were less interested in the big, existential questions – nature, it seemed, had been conquered – and turned instead to understanding the minute relations between the parts of the system.
In essence, the classical school is dynamic – it is interested in the long term path of the economic system. The marginalist school takes this for granted, and gives up the ability to study the dynamic path of the economy, in exchange for managing to learn a lot more about a stationary economy. Neoclassical, in this sense, should refer exclusively to those such as Alfred Marshall who attempted to combine the two – a true resurrection of the classical school.
Finally neoliberalism is, in a sentence, a political movement centred on an acceptance of the conclusions of marginalist economics and a faith in free markets. It’s not a school of economics in its own right, but a political coalition around pro-market policies that holds that, essentially, big questions are resolved. The market is the route to our happiness, an interference with it leads to ruin, no matter how well-intentioned.