ABSTRACT
If an even briefer summary of the chief results is demanded, it may be given as follows. The definition of the basic system turns out to be considerably more complicated in the case of joint production than in the case of single-product systems. However, the definition can be extended to all meaningful systems, although a uniqueness property does not apply to certain exceptions which are akin to one-commodity models in that relative prices are constant (or limited in their movements). Starting from a situation in which prices are positive in a given system in a self-replacing state, the rate of profit may be varied. A (small) class of jointproduction systems share all properties of single-product systems (‘all-productive systems’), but prices do not remain positive for most with ‘large’ variations of the rate of profit, and the wage curve does not fall monotonically in all standards. No basic system (including basic single-product systems) has positive prices at all positive rates of profit (including the range between the maximum rate of profit and infinity). Many systems have neither standard commodity nor maximum rate of profit. However, if the rate of profit is equal or superior to the rate of growth, it can be shown that it is almost always possible to delete one process from the system whenever a price turns negative so that the system consisting of the remaining processes overproduces the commodity that had a negative price. It therefore ceases to be a commodity and there remains a square system with the number of commodities and processes reduced by one. Executing this (and similar) operations wherever necessary, one finds that prices are positive and that the wage in a given standard falls monotonically in the golden rule case as the rate of profit (greater than or equal to the rate of growth at constant returns to scale) rises from zero to a finite maximum. A standard commodity is associated with the system appearing at the maximum rate of profit, and that system is all-productive.
