  In standard Walrasian auctions, the price of a good is defined as the point
where the supply and demand curves intersect. Since both curves are generically
regular, the response to small perturbations is linearly small. However, a
crucial ingredient is absent of the theory, namely transactions themselves.
What happens after they occur? To answer the question, we develop a dynamic
theory for supply and demand based on agents with heterogeneous beliefs. When
the inter-auction time is infinitely long, the Walrasian mechanism is
recovered. When transactions are allowed to happen in continuous time, a
peculiar property emerges: close to the price, supply and demand vanish
quadratically, which we empirically confirm on the Bitcoin. This explains why
price impact in financial markets is universally observed to behave as the
square root of the excess volume. The consequences are important, as they imply
that the very fact of clearing the market makes prices hypersensitive to small
fluctuations.
