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intermediate goods and services

As long as we maximize the Hamiltonian expression over all control variables, including intermediate goods and 7 services, it does not matter whether I is directly controlled, as in the compact formulation here, or whether it is indirectly controlled by an arbitrarily large collection of intermediate control variables. In the most abstract formulation, any number of control variables, subject to any number of intermediate-materials-balancing constraints in the background may be simultaneously determining consumption C and net investment I. The intermediate control variables are like dummy variables here ñwe are no more interested in them per se than we are interested in the details of intermediate goods like metallic ores or chemical feedstocks. We are ultimately interested only in the netted-out reduced-form attainable possibilities set A(K) setting out feasible combinations among C and I as a function of K. None of the background detail about control variables representing intermediate goods or about intermediate control sets really matters. The only thing that matters is that NDP is being maximized over the reduced-form attainable possibilities set A(K) (as if at Öxed investment prices) for each instant of time. The second condition of the maximum principle is the di§erential equation , which holds everywhere along an optimal trajectory. Unlike which is a description of a perfectly competitive static economy, condition is a uniquely dynamic description of a capitalstock market in competitive equilibrium. This kind of dynamic competitive equilibrium is sometimes called an ìequilibrium in price expectationsîor a ìperfect foresight equilibrium.î To understand this dynamic competitive equilibrium interpretation, we need to begin with the concept of ìarbitrage.î Arbitrage is the simultaneous purchase and sale of equivalent securities in order to make pure positive proÖts from price discrepancies. Condition is essentially saying that in a perfectly competitive capital market no pure proÖts can be made from arbitrage. Condition is a dynamic version of the basic static principle that prices in competitive equilibrium are determined where supply equals demand ñbecause otherwise someone could make pure proÖts from arbitrage