A POSTSCRIPT TO DYNAMIC PROBLEMS IN THE THEORY OF THE FIRM
A POSTSCRIPT TO DYNAMIC PROBLEMS IN THE THEORY OF THE FIRM
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DOI：
10.1002/nav.3800070103
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发表时间：
1960-03
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影响因子：
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通讯作者：
H. M. Wagner
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文献类型：
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作者：
H. M. Wagner
INTRODUCTION In a previous paper [31 the combined use of traditional economic constructs and dynamic programming was suggested for solutions to several intertemporal problems in the theory of the firm (that produces a single commodity.) 1 As a specific application of these techniques, a method was presented for solving a dynamic version of the economic lot size model [4]. The purpose of this postscript is:(i) to demonstrate that the algorithm suggested for the dynamic economic lot size model is also applicable to situations in which the cost curves (which may differ from period to period) have nonincreasing marginal costs as a function of output, algorithm for solving optimal pricing and output problems in which the cost curves have nondecreasing marginal costs as a function of output. 3 As in 31, the approach emphasizing the use of analytical techniques familiar to economists is continued. Throughout we assume that each marginal revenue relation is a nonincreasing function of the corresponding period sales and that initial and ending inventory are zero. eg, because of quantity discounts, and (ii) to describe a forwardWe consider finding a sequence of output qo (t) and prices, which in turn determine sales qs (t), that maximizes total profits over the entirety of periods t= l, 2,..., T. The period marginal revenue and cost functions are denoted by MR [qs (t)] and MC [~(t)], and the unit cost of carrying an item of inventory from period t to period t+ 1 is denoted by it. We postulate that at each period t, MR [qs (t)] 5 M (finite); that for qs (t) sufficiently large, MR [qs (t)] 5 0; and MC [qo (t)]> O for all qO (t). It will be helpful to recall the previous system of diagrams [3, p. 571, arraying each period's marginal revenue and cost curves, constructed such that the second period's curves are shifted downward by the amount il, the third period's by the amount il+ i2,..., and the T th period's by the amount il+ i2+...+ iT-1. All geometric arguments throughout the paper
