  This paper provides closed-form formulas for a multidimensional two-sided
matching problem with transferable utility and heterogeneity in tastes. When
the matching surplus is quadratic, the marginal distributions of the
characteristics are normal, and when the heterogeneity in tastes is of the
continuous logit type, as in Choo and Siow (J Polit Econ 114:172-201, 2006), we
show that the optimal matching distribution is also jointly normal and can be
computed in closed form from the model primitives. Conversely, the quadratic
surplus function can be identified from the optimal matching distribution, also
in closed-form. The closed-form formulas make it computationally easy to solve
problems with even a very large number of matches and allow for quantitative
predictions about the evolution of the solution as the technology and the
characteristics of the matching populations change.
