Time in the Economic Equations of Prices and Production

We begin with a simple example which will soon be generalized. Consider time as a sequence of points t₀, t₁, t₂ etc. which follow one another in a given distance which we shall call a time step. All events in the world last for a minimum of one time step, which may be arbitrarily small. Consider first the process of producing a consumption good whose quantity is represented as C. This consumption good is produced in three successive steps, each of which lasts one time step (so that the time step is our elementary period of production). Assume that production in the first stage requires only raw materials taken from nature in quantity R₁ plus human labor in quantity L₁; to produce intermediate outputs in quantity X₁. The product X₁ is then combined with raw materials R₂ and labor L₂ in the second stage of production I₂ to produce new intermediate products X₂. In the final stage of the process, I₃, C units of the consumption good itself are produced by combining X₂ with new inputs of raw materials and labor R₃ and L₃. Employing the symbol ⊕ to connote combination in production as determined by the available technology, we may represent this three-stage process as follows (see Bliss (1977)): $$\begin{array}{*{20}{c}} {{{I}_{1}}:} \hfill & {{{R}_{1}} \oplus {{L}_{1}}} \hfill & \to \hfill & {{{X}_{1}}} \hfill \\ {{{I}_{2}}:} \hfill & {{{R}_{2}} \oplus {{L}_{2}} \oplus {{X}_{1}}} \hfill & \to \hfill & {{{X}_{2}}} \hfill \\ {{{I}_{3}}:} \hfill & {{{R}_{3}} \oplus {{L}_{3}} \oplus {{X}_{2}}} \hfill & \to \hfill & C \hfill \\ \end{array}$$