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We consider the efficient outcome of a canonical economic market modelinvolving buyers and sellers with independent and identically distributedrandom valuations and costs, respectively. When the number of buyers andsellers is large, we show that the joint distribution of the equilibriumquantity traded and welfare is asymptotically normal. Moreover, we bound theapproximation rate. The proof proceeds by constructing, on a common probabilityspace, a representation consisting of two independent empirical quantileprocesses, which in large markets can be approximated by independent Brownianbridges. The distribution of interest can then be approximated by that of afunctional of a Gaussian process. This methodology applies to a variety ofmechanism design problems.

Approximating welfare in large efficient markets