A market is simple - it's just the word used for the aggregate of people buying and selling things. If you buy your friend's old furniture or hire a babysitter, that is a "market" for furniture or babysitting. That's it. The "market" is simply the collection of all the individual decisions made in the exchange of goods. There's no complexity or size required to be a "market".
But from those very simple simple beginnings, complex systems develop, with simple signals. Those signals are prices. As each individual makes the choices that are best for them, they influence the prices of the things they buy, or choose not to buy.
As people choose not to buy something they have previously purchased, sellers have to unload what they currently possess to minimize their losses, and stop stocking replacement supplies. These result in price drops as people turn away from purchasing a particular thing. The lower prices encourage people to buy the excess supplies, reducing the loss to the merchants who carried it, and allowing new customers to experiment with the things being cleared out, possibly creating new demand.
As people start buying something new, the sudden surge in interest drives up prices as supplies do not meet the new demand, or supplies of a pre-existing thing become scarcer or harder to create. The price increases divert some customers away from purchasing the thing, leaving some of it available to those who have a greater need or desire for it. It also encourages other suppliers to begin supplying more product, which reduces the price of the goods, helping dampen the price increase.
But these are not "supply" and "demand" in some general sense, but rather they are the collective decisions of each individual person making an individual choice.
A Large Market
To control a market of any size, you'd need to know and understand all the intricate details of each individual choice in each individual transaction.
And that's where the problem comes in - no single person or group of people can assess or evaluate the needs or choices of the people involved in any market of any size. While the price signaling can direct people to spend their money in a way that is most efficient for them and beneficial for society at large, the people or committee could only make choices that they believe would benefit society, but not the benefit of the individual people or even the society at large for the most part.
Only by allowing the different people with separate agendas to pursue their own goals can any problems be sorted out. Otherwise, only problems come into being.
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I have been invited to the Young Republicans National Federation Convention and need to work out some of the expenses. I need to arrange transport and incidental expenses. This would easy, except I would also like to visit my sister, who is on the way. I need some help getting everything paid for, not much, though.
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