From: Ian Wright (iwright@GMAIL.COM)
Date: Fri Sep 23 2005 - 14:57:29 EDT
Hi Ian Before thinking about "race horses" I need to explain the full generality of the problem as described in the literature. I mentioned a single "self-reproducing non-basic", such as "beans", only for simplicity, and to follow Sraffa's original mention of the problem. But in general, if the maximum eigenvalue of the non-basic subsystem is less than that of the basic subsystem then "complications arise". In essence, this is the case when the limiting factor of the whole input-output structure is not a property of the basic subsystem, but the non-basic. So we don't need to identify a particular non-basic commodity that enters into its own production. On 9/22/05, Ian Hunt <ian.hunt@flinders.edu.au> wrote: > > Clearly, a good deal of labour and other resources go into the production > of racing horses - just ask the trainers. Production of race horse stock > also requires much labour and resources - just ask the breeders. > Yes, I agree. But Sraffa doesn't quite agree with us. For example, the surplus portion of the real wage consumed by the labour force that works in the production of racing horses is not counted as an indirect cost by Sraffa. So if workers consume "cake", and cake is a non-basic good, then cake is not considered as an input to the "race horse" sector. In these circumstances, why would the rate of profit in the industry be set > by the natural reproduction rate of horses? > It wouldn't. The rate of profit is assumed uniform and varies with the real wage. The rate of profit can range from zero to G, where G is the maximum growth rate of the basic sector. A problem arises when the maximum growth rate of the non-basic sector G* is less than G. For profit rates less than G* everything is ok. Speaking a little loosely, for profit rates equal to G* the price of non-basics is undetermined, for profit rates greater than G*, prices are negative. In this example, the natural reproduction rate of horses is a limiting factor on the amount of race horses that can be produced in a given period, i.e. it is a datum that determines G*. -Ian.
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