>    The introductory economics story of how minimum
> wages lead to unemployment is not well-grounded in
> either model. 

Right.  The introductory economics story is a 
partial equilibrium story augmented by a story
of how single markets react to price floors.  The
story is coherent.  It (the augmented story) just 
is not the A-D model, though the unaugmented
partial equilibrium story is.

> This story relies on a model of the labor
> market with monotone supply and demand functions.
> An equilibrium in this story is supposed to lead to
> constancy in wages and employment across dates. 

Not true.  Exogenous changes leading to higher 
labor productivity, for example, lead to a
shifting demand curve and higher wages.

> Thus,
> the labor demand function in this story cannot be
> identified with factor demand functions in the Arrow-
> Debreu model. 

Yes, they can.  Partial equilibrium analysis is a
special case of the general A-D model.

> If long period equilibria were compatible
> with supply and demand theories, they would provide
> the rational foundation of the textbook story. 

So what?  Do you think the above statement is the same
as the statement "If long period equilibria were not
compativel with supply and demand theories, they 
would prove that supply and demand theories have
no rational foundation?"