Knowledge that Transforms

[This paper considers an M/M/s queuing model in which customers who arrive when k customers are present in the queuing system obtain a net benefit of a?k. The a?-sequence is assumed to be a decreasing one. If it is left to the individual customer to decide whether to join the queue or not, he will balk whenever the queue length is greater than some number, say n1. It is shown that if a balking level n2 extless n1 is enforced, then the customers as a group can generally expect a larger net benefit per time unit than when the balking level n1 is applied. One way to ensure social optimality is to impose a toll on the customers who join the queue. In the discussion of a possible economic interpretation of the model we point out the similarities between such a toll and a shadow price in a more conventional optimization model. It is also demonstrated that in a stochastic optimization model capacity utilization is not a sufficient price criterion.]

[Sufficient conditions (in terms of restrictions on individual preferences) have been already established in the literature for transitivity of simple majority decisions when individual preferences are quasi-transitive (but not necessarily transitive) and also for transitivity of multi-stage majority decisions when individual preferences are transitive. This paper establishes sufficient conditions for transitivity of multi-stage majority decisions when individual preferences are quasi-transitive, but not necessarily transitive. This constitutes a generalization of several results proved earlier.]

[This paper is concerned with the so-called k-class estimators of structural parameters in a simultaneous system. The structural equation being estimated is assumed, as is common in other small-sample investigations, to consist of two endogenous variables; and the number of the exogenous variables (included or excluded) as well as the number of equations in the system are arbitrary so long as the identifiability condition of the estimated equation is satisfied. Moreover, we assume that the system contains no lagged endogenous variables and disturbance terms of each period are independently distributed as multivariate normal. The exact finite-sample moments of the k-class estimators are evaluated for 0 @ extless k extless 1. For k extgreater 1 it is proved that the estimator does not possess even the first-order moment. The exact moment functions are expanded in terms of the inverse of the noncentrality (or concentration) parameter. This expansion sheds more light on the comparative study of alternative k-class estimators. Numerical calculations of the mean square error and the bias for some specific cases are also given for illustrative purposes.]

Gramlich and Galper (hereafter referred to as GG) indeed have performed a useful service by pointing out that an erroneous equation was included in my paper [3]. The corrected inventory change equation, the equation with all lagged orders included, was almost identical with the results obtained by applying GG's method (ii) to the order-inventory stock equation presented in Column (2), Table IV of my paper [3, p. 161]. The results are consistent when GG's methods (ii) and (iii) are applied on the correct equations. In any case, GG's methods (ii) and (iii) are well known and deserve no debate here. However, the same cannot be said of their method (i). GG's method (i) is based on two crucial assumptions concerning the pattern of the production process and inventories of defense products. The validity of using the method to derive the coefficients of an inventory change equation from an order-shipment relationship depends directly on these assumptions. If the assumptions describe exactly the actual patterns of the production process and of inventory build-up, then method (i) can be used for GG's purpose. Unfortunately, both of these assumptions are very unrealistic, and the use of method (i) yields misleading results. In their derivation of method (i), GG assume that the production process is rectangular. Furthermore, the authors claim that the method is valid regardless of what is assumed about the shape of the production process-a rectangular assumption serves as well as any.' This claim is faulty, as the following example demonstrates.