  In the first part of this paper, we derive an infinite dimensional partial
differential equation which describes an economic equilibrium in a model of
storage which includes an infinite number of non-atomic agents. This equation
has the form of a mean field game master equation. The second part of the paper
is devoted to the mathematical study of the Hamilton-Jacobi-Bellman equation
from which the previous equation derives. This last equation is both singular
and set on a Hilbert space and thus raises new mathematical difficulties.
