In http://mises.org/story/3424 , George Reisman says:"Thus imagine that initially spending for consumers' goods in the economic system was 500 units of money, the spending for the capital goods to produce those consumers' goods was 250 units of money, the spending for the capital goods to produce those capital goods, 125 units of money, and so on, with each succeeding amount of spending for capital goods being half of the spending for the capital goods it helps to produce. Now imagine that spending for consumers' goods falls from 500 to 400 units of money. Here is how at the same time spending for capital goods can increase from 500 (i.e., the sum of 250 + 125 + 62.50 +…) to 600 units of money. The mechanism is that the spending for the capital goods required to produce consumers' goods falls from .5 x 500 to .6 x 400, i.e., from 250 to 240."
I just don't understand where that .6 comes from.
this is my tentative approach.
i belive Reisman doesnt want to go straight from 'the money supply is an invariable 1000 money and so 100 less spent on consumption is a 100 more to uinvest in capital', so he simply wanted to illustrate that the asusmption that 100 less spent on consumption will not necessarily mean a reduction in what is spent on capital , even if the amount spent on the capital used in the state closes to producing the consumption goods declines.
so in the scenario
spending on consumption goods fell from 500 to 400.in the economy a geometrical series of payments 250 + 125 +62.50 etc.buys all the capital that has progressively brough about the consumption goods
(notice the ratio is 0.5) and so this sum of total capital expenditure is 500 since s=a/(1-r) => s=250/(1-.5)=250/.5=500Reisman needs to show how despite the number of $ spent on the capital that would produce the new 400 of consumer goods dropping from 250 to some lower amount, yet the geometric series of money spent on the capital structure (as a whole) might still sum to a higher figure.(something higher than the initial 500 sum) (i.e. it needen't necessarily decline)to do this he needs the capital stage closest to the production of the consumer goods to have cost some amount less than 250.he picked 240 to do this job. now what geometric ratio would it take for the sum of the geometric progress to add up to some number above the initial 500?any fraction above .52 would do the job. .6 is such a number and geometrically sums to a nice round number of 600.so this illustrates how it is possible for the total sum invested in the capital structure to be the larger even when consumption spending is reduced and the capital stage closest to production costs less (e.g 240 rather than the initial 250)i hope i understood it right, but anyhow, it occasionally takes a clumsy response to encourage more refined answers
least i tried!
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