The Arrow–Debreu (1954) extension of the fundamental theorems of welfare economics has cast new light on the role of governments as economic agents, especially in developing countries. In a pure Walrasian economy, or Arrow–Debreu economy, competitive equilibrium will lead to Pareto optimality as long as there is a sufficient number of markets to span the commodity space. This is an exacting condition and goes beyond the exceptions to the static version of the fundamental theorems of welfare economics that were discussed in Chapter 2. In effect, the dynamic version of the theorems requires that a complete set of futures markets exists in time, space, and uncertainty.

In an Arrow–Debreu world, combinations of other goods or contingent claims can span missing or incomplete markets and thus achieve a Pareto-efficient, competitive equilibrium. Competitive equilibrium can obtain, for example, in the wool–spinning–yarn sector, despite the fact that historically only two out of the three markets have been observed, those for wool and yarn. Processing margins implicit in the price of yarn have often made the spinning market redundant. Similarly, there are four possible markets that link the present with the future in the foreign exchange market of dollars in terms of yen: the spot foreign exchange market, the forward foreign exchange market, the spot lending market, and the spot borrowing market. Of the four, three markets are sufficient to span the commodity space: a Japanese exporter can convert yen into dollars in the spot market and lend dollars to a future date, thus hedging the dollar risk of his exports to the U.S. This makes redundant the forward market for dollars.