In my previous two columns I compared the economy to a 1 billion-piece jigsaw puzzle with a twist.

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In fact, if the puzzle is assembled randomly — without any guiding logic — the resulting picture will almost certainly be ugly visual gibberish. It'll be a worthless outcome. Plenty of hard work put into assembling the puzzle will prove to have been for naught.

Such a huge puzzle can't possibly be assembled into a meaningful picture by a central planner.

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But suppose that each piece is equipped with a monitor that beeps whenever that piece connects with another piece in a way that is productive — that is, in a way that contributes toward making the final outcome a beautiful picture. And suppose that the more important is any particular connection of two pieces toward producing a beautiful overall outcome, the louder is the beep.

Now, finally, imagine each of these billion puzzle pieces having a mind of its own, as well the ability to move. Each piece loves hearing these beeps — and the louder the beep, the happier the piece.

This puzzle — strange as it is — will assemble itself into a configuration that results in a meaningful and beautiful picture.

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As long as the loudness of the beeps corresponds to ways of connecting that result in a meaningful, beautiful picture, such a picture will be produced without any person (or any puzzle piece) intending to produce it.

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Of course, no real-world jigsaw puzzle has pieces that move on their own in search of beeping sounds.

But carry this puzzle analogy over to the real-world economy. Each owner of private property has incentives to use his or her property in ways that produce the greatest return — the "loudest beeps," if you will.

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Likewise for the individual worker, who might own only his own labor services. He will combine that labor with the labor and assets of those other private-property owners who promise him the largest return on his work effort.

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And because this unintended outcome emerges from the self-interested actions of owners of private property, each of these owners is made better off. No one is forced to do business with those whom he'd prefer to avoid, and — being free to take advantage of any and all existing opportunities — each person chooses those opportunities that improve his lot in life by the greatest degree.

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Responding to prices in this way doesn't produce heaven on earth. But it does encourage millions of people to interact peacefully with each other in ways that are mutually beneficial.

And that's a beautiful picture.