Knowledge that Transforms

[This paper discusses the existence of a competitive equilibrium when the assumption of perfect divisibility is not fulfilled for all the goods involved in the economy; we limit ourselves to the case of a pure exchange economy with a finite number of traders. Section 2 is devoted to the proof of an existence theorem when assuming that only two goods are exchanged in the economy; in Section 3 we build a counterexample to show the restrictive nature of the assumptions one has to make in order to generalize the above theorem.]

In an economy with an arbitrary number of consumers and an arbitrary number of commodities, some public and some private, I propose a generalization of Lindahl's equilibrium solution, and prove an existence theorem for it. A particular generalization of the of an exchange equilibrium to an economy with public goods is proposed, and it is shown that a Lindahl equilibrium allocation is also a core allocation.

SINCE KOYCK'S pioneering work, distributed lag models have come to play an important role in econometrics and much work has been done to develop methods for analyzing them-see e.g. Koyck [15], Klein [12], Solow [20], Fuller and Martin [5], Malinvaud [18], Hannan [9], Liviatan [17], Amemiya and Fuller [1], Zellner and Park [25], Thornber [21], Waud [23], Dhrymes [3], and Griliches [7]. In the present paper we present maximum likelihood and Bayesian estimation procedures for estimating the parameters of a typical distributed lag model under four alternative sets of assumptions regarding disturbance terms' properties. Then these procedures and assumptions are employed in analyses of a sample of United States quarterly consumption data to illustrate their application and to show the sensitivity of inferences to the assumptions made about disturbance terms' properties. We also compute posterior probabilities associated with four alternative models. The plan of the paper is as follows. In Section 2, the model to be analyzed is described and alternative assumptions about disturbance terms are introduced. Section 3 contains a discussion of maximum likelihood techniques and application of them in the analysis of U.S. quarterly consumption data. Then in Sections 4 and

J. Frank Sharp, James C. Snyder, James H. Greene, A Decomposition Algorithm for Solving the Multifacility Production-Transportation Problem with Nonlinear Production Costs, Econometrica, Vol. 38, No. 3 (May, 1970), pp. 490-506