From Cambridge to Eternity: “Dimension Algebra 04”

 

<Questions for Review of “Money Demand”>

1.     What was “money” historically?

- Commodities: shells, stones, copper, nickel, silver, gold and so on

- Classical economists: a veil

- David Hume among others ³⁾: the annual average ²⁾ of monetary outstanding             

- John M. Keynes among others: the outstanding balance as at a moment of interest

- John R. Hicks among others ⁴⁾: something that is a “constant” fraction (or multiple) of                                                                       the annual “nominal” income: i.e. M= k∙I = k∙( P∙Y)

2.     How do we calculate the average?          

<A> There are indefinitely many. For more, please refer to:

Average (Wikipedia).

 

3.     What is the quantity “equation” M∙V= P∙Y meant with? 

<A> First of all, the name might well be corrected because it is not exactly an equation but a “definition identity” which must always and everywhere hold true.

      Suppose a tiny economy “Yap” in the steady state with a purchasing party on one side and a retailing party on the other side of the market. For the sake of convenience, we assume that the money of the retailing party (as the collective employer) recycles to the purchasing party (as the collective employee) when the latter’s hands are empty. For simplicity, we put on hold all the trade in intermediate goods, old assets and anything else other than the final goods, services and assets which are created in the year and only in that year. In addition, we choose the most popular way of averaging. ²⁾

      We take, for example, in Yap: 600 stones current as money legally valued one ducat each (M); trade worth 4,800 ducats (P∙Y) taking place over the year in a nicely-differentiable distribution. Then, the average money balance of the spending (demanding) party is a half (1/2) of the initial balance. 

Accounting for the Yapean economy:

       - The monetary balance outstanding: M= 600 ducats all through the year

       -The nominal GDP P∙Y= 4,800 ducats per annum

      - The economy-wide velocity of money V= 4,800/ 600= 8 turns per annum 

      - The average liquidity preference of the spending party M_p= (1/ 2)∙M= 300 ducats

      - The “constant” of the Cambridge Quantity equation k= 300 ducats/ (4,800 ducats  per year)                = (1/ 2)∙(1/ 8 turns per year)= 0.0625 year = 22.5 days.

       “Yep, k is a ‘constant’ in Yap, either 0.0625 year or 22.5 days.” (Q.E.D.)

4.     What in the reality will the individual “constant” k of John R. Hicks be?

<A>Please come back to yesterday.

5.     Would there be any realistic way to come up with an estimate of the “constant” k as for the national economy of modern times?

<A> We would not know until the end of time if in Here save Yap.

 

Yap, the Island Where People Pay in Stone Money