Stockholder Unanimity in Making Production and Financial Decisions

Grossman, Sanford J.; Stiglitz, Joseph E.

We show that "spanning" does not imply stockholder unanimity if there is trading in the shares of firms. Each basis vector of the space spanned by all firms' output vectors can be treated like a composite commodity. If, in addition to spanning, firms act as price takers with respect to prices of composite commodities, then there is unanimity. We analyze the spanning assumption for the vector space of contingent claims generated by firms' choices of debt-equity ratios. We show that there is a strong relationship between the Modigliani-Miller theorem, spanning, and the existence of a complete set of markets.



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Quarterly Journal of Economics

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July 2, 2012