Quantifying inefficiency in incomplete asset markets∗

It is known that the incompleteness of asset markets causes inefficiency in almost every equilibrium. Yet unexplored is the ”size” of this inefficiency. The size of a Pareto improvement is the total willingness to pay for it, out of current consumption. Inefficiency is the maximum size of any Pareto improving reallocation. Inefficiency of US consumption in middle age is computed to be 10-11% of total consumption in youth, for CRRA parameters 1.5-3.25, in a calibrated economy. The inefficiency of a general economy is approximated. A natural approximation, based on marginal rates of substitution (MRS), is preposterously crude in the calibrated economy, owing to a law of diminishing willingness to pay. Alternative approximations end up being functions of a classical notion, weighted social welfare maximized subject to resource constraints. They are simple, sharper in general and accurate in the calibrated economy.