Simple Commodity Production
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Simple Commodity Production book
Suppose the price vector at which the n goods exchange is p. Agent v wishes to produce goods whose exchange value at these prices will be sufficient to purchase his consumption bundle bV and to replenish the stocks he borrowed to operate his chosen activities. If he chooses to operate an activity vector xv, then his gross revenue must be
PXV ~ pAxv + pb" where the two terms on the right-hand side are his investment costs and his consumption cost. We assume that subject to meeting his costs, the producer wishes to minimize the labor he
expends. His program is:
Choose XV to min LXV} s.t. P(1 - A)xV ~ pbv (P5.l)
If the inequality in Definition 5.1 is met, then total gross production when all producers optimize is sufficient to replace all inputs used and to meet all consumption needs. Thus, each producer can trade at prices p the gross output XV he produces for the bV he requires and the investment goods Axv he used and must replace.