If we label consumption as Trainspotting characters Friends TV show shirt spending paid for out of current income, and investment as spending paid for by money acquired in a previous time period, we have derived the “Savings equals Investment identity”. With these definitions the “Savings equals Investment Identity” is a true identity, that is easily understood, and is always true “by definition”. It is not an “equilibrium” that the economy is always tending towards. It is something that, for any defined time period, will always be exactly true. Above we have shown a model where savings equal investment is an identity true for any given specified time period, not just an equilibrium that the economic system tends towards. Now I wish to show how adapting this model we can also show that not only is Savings equal to Investment but the money saved by the end of the given time period is actually the SAME money as the money used for the investment spending.
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Although ALL spending can be Trainspotting characters Friends TV show shirt classified as EITHER consumption spending ( paid for with money acquired as income in this period) OR investment spending (paid for with money previously owned), spending cannot be classified as BOTH consumption or investment at the same time. They are mutually exclusive categories. If spending is categorizable as investment spending it cannot be categorized as consumption spending. If spending is categorizable as consumption spending it cannot be categorized as investment spending. All spending is categorizable as one or the other, but never both at the same time. Looking at investment spending, it must be spending paid for using money being spent for the first time in the given time period. If, in the given time period, it had previously been used for spending, then that spending would have caused income for the recipient, and any further spending of that same money, would be spending paid for out of current income and that would make it consumption spending.