  We find the explicit expression for the equilibrium wealth distribution of
the Directed Random Market process, recently introduced by
Mart\'inez-Mart\'inez and L\'opez-Ruiz, which turns out to be a Gamma
distribution with shape parameter $\frac{1}{2}$. We also prove the convergence
of the discrete-time process describing the evolution of the distribution of
wealth to the equilibrium distribution.
