The transactions cost for alternative exchange mechanisms for the household exchange problem can be characterized by the computational complexity of the exchange process. The computational complexity for any exchange mechanism is at least nH, where n is the number of goods and H is the number of households. Imposing the conditions of conservation, nonnegativity and quid pro quo results in a command exchange mechanism whose computational complexity is nH. Multiparty barter exchange, formalized using graph theory, has computational complexity equal to the minimum of (nH2, n2H). Introducing an auxiliary good, money, reduces the computational complexity to nH. A problem with decentralized information is demonstrated.

[A new formulation of the linear quadratic control, LQC, problem with known coefficients, called the LAG, is presented. The LAG generally does not generate a recursive Ricatti system. For models with long lags an important issue is whatformulation leads to an efficient algorithm both with respect to storage and speed. At present the most efficient known formulation is the minimum state variable representation, MSV. The LAG requires much less storage than the MSV as the LAG does not require conversion to state space representation. For short time horizons the LAG is computationally faster than the MSV. As the time horizon increases, the efficiency of the LAG relative to the MSV declines. Numerical comparisons of the Theil, Chow, MSV, and LAG formulations are shown.]