A0, A1, A2, A3, … , An
B0, B1, B2, B3, … , Bn
· · · · · ·
X0, X1, X2, X3, … , Xn
Y0, Y1, Y2, Y3, … , Yn
· · · · · ·
where "A, B, ... are different kinds of inputs, X, Y, ... are different kinds of outputs, and the entrepreneur is supposed to make his plan for a period of n future weeks." Inputs to the production process are simply things that the entrepreneur buys for his enterprise, and outputs are those things that he sells. The author points out that the model is general enough to handle the case in which the entrepreneur plans to shut down the enterprise and sell off all the equipment at some future date. In this case, "the plant he plans to have left over ... [is] a particular kind of output (say Zn), a kind which is only produced in the last week." All outputs are then zero for all time periods after the enterprise is sold.
The general dynamic problem for the enteprise is to select the optimal production plan from among all those that are technically feasible. The author points out the similarity of this problem to the static problem of choosing the set of quantities of factors of production and products. He explains that the technical limitation on production plans (or the "production function") will give the maximum possible quantity of a given output on a given date, if all inputs, and all outputs but the given one, are fixed in magnitude. Similarly, "if all outputs, and all inputs but one, are given in magnitude, [the production function] will give the minimum input necessary on the remaining date." Given this limitation, all changes between production plans reduce to (1) "substituting some amount of one output for some amount of another, (2) ... substituting [some amount of] one input for another," or (3) "increasing or diminishing one input and one output simultaneously" or some combination of these "elementary variations." The author concludes the section by noting that this is "exactly as in statics."
The general dynamic problem for the enteprise is to select the optimal production plan from among all those that are technically feasible. The author points out the similarity of this problem to the static problem of choosing the set of quantities of factors of production and products. He explains that the technical limitation on production plans (or the "production function") will give the maximum possible quantity of a given output on a given date, if all inputs, and all outputs but the given one, are fixed in magnitude. Similarly, "if all outputs, and all inputs but one, are given in magnitude, [the production function] will give the minimum input necessary on the remaining date." Given this limitation, all changes between production plans reduce to (1) "substituting some amount of one output for some amount of another, (2) ... substituting [some amount of] one input for another," or (3) "increasing or diminishing one input and one output simultaneously" or some combination of these "elementary variations." The author concludes the section by noting that this is "exactly as in statics."
