One of my Ph.d. students asked me that question. Similarly, you might wonder whether Hayek adds to the Arrow-Hahn-Debreu equilibrium framework. Joe Stiglitz insists no; my answer ran as follows:
The invisible hand theorem assumes some (possibly weakened) version of perfect markets. It suffices for everyone to simply maximize utility or profit, and then all supply and demand curves will cross. Under spontaneous order, cross-market externalities are more significant. Markets are imperfect, so people look to institutions — and other markets — to orient their behavior and to predict the unknowable future. Market choice is a game of interpreting symbols, drawing inferences, and mapping an understanding of context to the appropriate situations. The resulting order is greater and more complex than the partial equilibrium story we might tell about any single market.
As for Adam Smith, he was closer to Hayek…But the dilemma of the Austrian School is whether it can tell this story without economic analysis collapsing into pure context-dependence. How much do we really know about how people interpret economic signals? So far experimental economics — as exemplified by Vernon Smith — has done the most to bridge these gaps.
Another question I heard this week: "Why is it that older people start going deaf, yet still object more to loud music?" I couldn’t really answer that one either.