An interesting short cut way of thinking about neoclassical economics and how it derives form classical economics is to imagine the following formula:
necoclassical = classical + Keynes + Fisher
The classical story is one where a market's supply and demand characteristics drive the equilibrium price of a good (including commodities, manufactured goods, services, and the price of labour, namely average wages).
Keynes pointed out that there are nominal price rigidities which prevent certain markets form clearing, a point in case being the labour market. Nominal prices are sticky upwards - they don't like down adjustments.
Fisher pointed out that debt was also a rigidity in certain points during the economic cycle. The debt is expressed in nominal terms, but during deflationary periods, for example, the borrower may find it increasingly hard to make their debt payments.
They're both therefore, pushing forward the classical economic view by highlighting the need for more structure in the too simplistic classical view of a market driven economy.
I think that some time in the next one hundred years, real (as opposed to nominal) debt contracts will be the norm. This will take the sting out of so-called debt-driven deflationary periods. I.e. the nominal rigidity of debt will become a solvable economic problem.
In today's highly politicised world of academic economics, I'd be obliged to refer to the classical + Keynes + Fisher as 'post-Keynesian'.
