While this concept of market clearing resonates well in theory, the actual execution of markets is very rarely perfect. Markets demonstrate consistent shifts of supply and shifts of demand based on a wide spectrum of externalities. Even in static markets there is competitive consolidation that allows companies to charge differing price points than that of the equilibrium. The concept of monopolies provides a good example for this experience, as monopolies (see example) can control price and quantity simultaneously.
Another classic criticism of market-clearing is the way in which the labor market functions. In the 1930's, during the worst depression recorded in the United States, the labor market did not clear the way economic theories of market clearing would assume it would. Instead, there seemed to be what John Maynard-Keynes (father of Keynesian Economics) called 'stickiness,' which preventing the market from normalizing. The importance of raising these concerns is the understanding that while the concept of market clearing, equilibrium and supply/demand charts are highly useful in understanding the basic functioning of markets, reality does not always conform with these models.