  We consider the efficient outcome of a canonical economic market model
involving buyers and sellers with independent and identically distributed
random valuations and costs, respectively. When the number of buyers and
sellers is large, we show that the joint distribution of the equilibrium
quantity traded and welfare is asymptotically normal. Moreover, we bound the
approximation rate. The proof proceeds by constructing, on a common probability
space, a representation consisting of two independent empirical quantile
processes, which in large markets can be approximated by independent Brownian
bridges. The distribution of interest can then be approximated by that of a
functional of a Gaussian process. This methodology applies to a variety of
mechanism design problems.
