Spanning and Financial Intermediation with Incomplete Markets
Spanning conditions are given for an economy where individuals exchange shares of firms indirectly through financial intermediaries rather than directly in stock markets. Allowing for short sales, securities offered by financial intermediaries will span if there are as many linearly independent securities as states of the world. If the spanning conditions hold, unanimity of investment decisions of firms and ownership policies of financial intermediaries follow. Unconstrained Pareto optimality will obtain with the former spanning condition and constrained with the latter.
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