Price Signals - Signalling What and Why?

I must confess that I fail to grasp the import of Hayek's oft-repeated point about "prices communicating information". Hayek says that thanks to the existence of "price signals", a consumer or an entrepreneur need not enquire as to whether the demand for a given good increased or its supply decreased - he simply knows that a rise in its price means that it has to be economized. But why should prices be particularly effective in communicating this kind of information?

Imagine that instead of prices, market participants were to rely on short bits of verbal communication such as: "supply down, demand the same" or "supply the same, demand up". Would such a system work as effectively as the one we are familiar with? No, but not because the relevant information regarding "the specific circumstances of time and place" would not be communicated sufficiently smoothly, but because the form in which it would be communicated would not allow for performing cost-benefit calculations. The usefulness of prices does not stem from the fact that they communicate information (since everything communicates information), but from the fact that they embody consumer choices and entrepreneurial anticipations expressed in the form of intersubjective, numerical exchange ratios.

Sometimes Hayek is more precise and talks about prices communicating "decentralized information". But from the above example it clearly follows that the benefits of decentralization could be utilized in a system without prices as well, even though in their absence those "knowledge benefits" would not translate into economic efficiency. There is no question that quick and reliable transmission of information that results from decentralization is one of the great strengths of the free market economy, but it is logically independent of its other great strength - its reliance on the price system.

Still, it has to be noted that one is of no use without the other - from the catallactic point of view, decentralized information not expressible in terms of prices is as worthless as "prices" issued by a centralized, monopolistic agency.

Many of the points touched upon above were of course made in the dehomogenization debate, but I am not sure whether it specifically addressed the concept of "price signals".