1. See Money and Banking in Medieval and Renaissance Venice Vol.1, Coins and Moneys of Account Frederic C. Lane and Reinhold C. Mueller, Johns Hopkins University Press, Baltimore, 1985, p.68.
"Double entry was probably in general use after 1400" says Raymond de Roover on page 21 of his very authoritative opus Money, Banking and Credit in Mediaeval Bruges, Mediaeval Academy of America, Cambridge, MA, 1948. This informative book is an exhaustive study of original sources. It is a first rate treatise of scholarship and thoughtfulness.
An excellent summary of the essentials of accounting is given in Thomas Ittelson's book, Financial Statements, Career Press, N.J. 1998. The book is focussed, well presented, very visual, digestible and easy to assimilate. Unfortunately, in the Balance Sheet Chapter, it shows a minus sign where there should be a plus sign near the bottom of each Liabilities and Equities column.
2. Economic unit = Economic entity. Whatever engages in economic transactions. Examples are: for-profit business entities (partnerships, corporations,..), non-profits (charities, cultural, philanthropic..), government entities (cities, counties, water districts, schools), individual persons, families.
We can subsume many units into a single unit, a collective. The grouping follows the rules of addition. Adding all the members' assets together produces the assets of the collective unit. Same for liabilities etc. That an assembly of economic units is itself an economic unit allows talk of 'aggregates'.
3. One may contemplate a society without ownership. Such societies have been the dream of visionaries. A society devoid of individual ownership would require a different mindset than is common in contemporary societies where people rejoice in their possessions.
What is astutely pointed out by Professor Zeno Swijtink is that all contemporary societies put restrictions on ownership; some are more restrictive, some less so. Marxism permits personal ownership but forbids business ownership. Nowhere is everything open to private ownership. Some ownership is always retained by society for the public good. Hopefully a careful and dispassionate study of economics will inform the debate on what restrictions will benefit society.
4. Slaves do not own themselves.
5. Bank multiplier
Here's the easy way to think about it. A reserve ratio 1:5 means the banker need keep only 1/5th or 20% of deposits on hand in cash. i.e. for deposits of $5,000 he need keep only $1,000 on hand. The banker, on receiving a $1,000 deposit says to himself, "Since I only need 20% on hand, I can use the $1,000 that I have as my reserve and proceed to lend out $4,000!" In lending out the $4,000 he has created that much in deposits in addition to the initial $1,000. From $1,000, $5,000 appears in the world. It has been multiplied by a factor of 5 - the multiplier.
Here's the mathematical examination:
If a bank has deposits of amount D it would be imprudent for it to lend out all of this amount. There is a 'reserve requirement', imposed by the Federal Reserve System on all banks, regarding the percent of its deposits that may not be lent out. This percentage (or ratio) is r. It is the fraction of deposits that must be kept in reserve so as to satisfy the depositors' occasional claims on the bank for the money deposited with it. Currently (2005) r is about 0.1; i.e. 10%. If r were 0.2 the bank would be allowed to make loans only up to 80% of D; 0.8 = (1-r).
Suppose initially an amount D is deposited in the bank. A prudent bank may therefore lend out an amount (1-r)D = D1 keeping rD on reserve. Upon lending out D1 this amount is credited to the account of the debtor in the same bank. The debtor may draw on this account; he has money in the bank, the borrowed money. Hence by the act of lending out D1 = (1-r)D the deposits in the bank are increased by this amount. It now has on deposit the original D plus the amount lent out, D1.
The bank now has new money to lend. It can do further lending in the amount of (1-r)D1 = D2 = (1-r)2D. When it does so its deposits further increase by that amount of lending, D2 = (1-r)D1.
Another new loan is therefore enabled in the amount of (1-r)D2= (1-r)3D And this new loan further increases the banks deposits enabling yet another new loan...
As this process of lending continues the amount deposited in the bank grows from the original deposit of D to
D + D1 + D2 + D3 + ... = D[1 + (1-r) + (1-r)2 + (1-r)3 + ...] = D/r
The reason is that the sum of the infinite series shown in brackets is 1/r. The number 1/r is greater than 1. It is a multiple of the original deposit D.
As an example, if the reserve requirement, r is 20% and the original deposit amount is D = $1,000, when the bank succeeds in lending to its limit, it will have loaned out $4,000 and have $5,000 on deposit. It will have created $5,000 of money in circulation from a $1,000 deposit! The multiplier is 1/r if the reserve requirement is r.
6. Money is defined by Kindleberger as "means of payment in actual use". Charles P. Kindleberger, Manias, Panics and Crashes. A History of Financial Crises. Fourth Edition, John Wiley and Sons, N.Y. 2000, Page 50.
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