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...

A classic characterization of competitive equilibria views them as feasible allocations maximizing a weighted sum of utilities. It has been applied to establish fundamental properties of the equilibrium notion, such as existence, determinacy, and computability. However, it fails for economies...

R&D investment are an important engine of growth and development. Yet economists have often claimed under-investment, also due to the asymmetric information between inside investors and outside investors and financiers, and the consequent capital and financial market imperfections. Some recent...

A classic characterization of competitive equilibria views them as feasible allocations maximizing a weighted sum of utilities. It has been applied to establish fundamental properties of the equilibrium notion, such as existence, determinacy, and computability. However, it fails for economies...