I) Consider that by accounting identity the total value of all money used in the exchange of goods in any one period is equal to the value of all goods exchanged in that period.
II) Now cast to the future. The NPV of all money used in exchange from now till point T is by the same identity equal to the NPV of all goods exchanged between now and point T.
III) So consider that credit is issued to finance the production of those goods and is repaid in full at the end of that period. Assuming that production and consumptions plans are correctly anticipated then the addition to the stock of money is exactly cancelled by debt redemption , assume multiple overlapping period of production then it is the same as Clark parable of the forest, there is no net change to the capital stock, there is no net change to prices.
IV) Consider a net addition to credit and a net addition to production (over and above financing a depreciation fund) – then the NPV of the increased stock of money – the effective demand – is increased – and matched by the NPV of the increased stock of goods – the effective supply, providing we include in our definition of effective supply as yet unsold inventory.
V) Then by accounting identity the aggregate demand would be equal (in a closed economy) to income + delta debt. As our definition is one based on money in exchange we could also define it as to income + delta debt – delta savings.
VI) This definition is the same as the real bills or ‘backing theory’ of value – but there are a number of conditions which require to be held for it not to have a net effect on prices, all of which reflect criticisms of the real bills doctrine.
VII) Firstly the anticipated interest on the loan (plus element) must be the same as the profit on the production of the real goods (the mercentile rate of profit to use the classical definition). If it is less then it is inflationary if more deflationary. A ‘cumulative process’. If this is the case then even if there was full security (collateral) on the loan the backing value of the loan would be changed through deflating or inflating the numeraire value of the goods backing the loan.
VIII) Secondly the activity financed by the new loan must be productive not speculation on an asset, (fictitious bill) if not then the additional money will not be backed by additional goods and we have asset price inflation, leading to more demand for credit through the process described at VII. (this is Bentham’s theory of price and Johannsenn’s theory of the cycle)
IX) At all stages if any agent holds more cash than their desired cash balance it will reflux back to the banks, (The reflux theory), but this does not mean that that prices must be stable because of the processes in VII and VIII.
From this we can derive a correct law of markets. I like this alternative way of looking at it because it deduces monetary theory from a flow input/output view of capital, it also includes inventory, capital gain, depreciation and savings. It might even convince Ramanan.
Lets though have an alternative name for it – how about The Credit Theory of Price.
4 thoughts on “Alternative Algebraic Definition of Keen’s ‘Walras -Schumpeter’ Law”
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algebraic with a g not a j !
Corerected, I am dyslexic sometimes, of course the original arabic was phonetic