The good mess in supply and demand analysis

–I have a fantasy about supply and demand, provoked by all those graphs like the one below from Wikipedia:

That is: Imagine demand and supply curves shifting downwards, say, with equilibrium price P* and quantity Q* shifting down with them. At some point, the two curves intersect the horizontal axis (as with the dotted Supply 1 curve in the figure), producing two quantities, Qs < Q*.

–But at that point, Qs must be the quantity supplied even when price is zero. To put it another way, a portion of the quantity demanded is actually provided at no price because of, say, intrinsic motivation, or suppliers are confused, or everyone was just lucky.

I’d like to think that is the good mess waiting in every partial (!) equilibrium analysis.

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