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A problem is considered where jobs arrive at random times and assume random values, or importance. These must be assigned to a fixed set of men whose qualities are different but known. As each job arrives, its value is observed and the decision-maker must decide which man, if any, to assign to this job. If a job arrives at time t and its value is observed to be x, then by assigning man i with quality pi, a reward r(t)pix is received, where r(t) is a discount function. The object is to find an assignment policy which maximizes the expected reward from the available men. The problem is analyzed for different arrival distributions and for different discount functions, but in all cases, the optimal policies are shown to have fairly simple forms, independent of the actual qualities of the men, the pi's. Other interpretations of the model, besides the men and jobs interpretation, are also given. The paper concludes with a similar model which does not, however, include time as an explicit parameter.

Choosing the maximum value from a sequence ofN independent values is a well known problem often called the candidate problem or secretary problem. This paper treats the above problem with a discount penaltyα (0

This paper presents a problem which I believe has not heretofore been analysed2 and provides a theory to explain, under different circumstances, three related phenomena: (1) spendthriftiness; (2) the deliberate regimenting of one’s future economic behaviour— even at a cost; and (3) thrift. The senses in which we deal with these topics can probably not be very well understood, however, until after the paper has been read; but a few sentences at this point may shed some light on what we are up to.

This chapter highlights the question whether second-best saving is greater or smaller than first-best saving when given future saving is non-optimal from the standpoint of the present generation. The chapter presents the postulation that all generations expect each succeeding generation to choose the saving ratio that is second-best in its eyes. This somewhat game-theoretic model leads to the concept of an equilibrium sequence of saving-income ratios having the property that no generation acting alone can do better and all generations act so as to warrant the expectations of the future saving ratios. The chapter presents a comparison of this equilibrium and the first-best optimum. The concept and calculation of the second-best optimum is of interest even if that analysis does not explain actual national saving because society as a whole has no notion of such an optimum.

Estimates a yield curve using a cubic spline approximation to the discount function, as described in McCulloch (1971), "Measuring the Term Structure of Interest Rates", Journal of Business, vol 44, pp 19-31.(This abstract was borrowed from another version of this item.)