Procrustean Art of Backtracking: “Equation of William Baumol”

 According to a Korean maxim in Chinese characters, “The darkest is right under the lamppost” (燈下不明). Often times, the answer to an age-old trouble is of simple or rather naïve ideas around us for long, sometimes even longer than the trouble in hands.

             Getting out of the popular framework of reference tangled with vested interests, we often find an incredibly short answer as in:

1)     “Eppur si muove.”

2)     “The Emperor in naked!”

3)     The “equation of monetary inventory” by William Baumol (1952) is all that we might refer to at the very beginning of an economic downturn.

 

To “keep things simple,” we copy the following from somewhere else:

             (Quote) The household has to conduct cost-benefit analysis for the decision how much money to hold (M^d): the marginal benefit is in saving financial transaction costs and the marginal cost is from forgone interests. In this regard, the American economist William Baumol suggests a clue in the 1952 article. We borrow from him and slightly revise the equation so as to represent the annual average of the optimal balance of money at the typical household:

M^d= (b∙T/ 2i)^1/2,

where b is the financial transaction costs per transformation

T is the annual total of uniformly-distributed monetary expenditures, and

i is the interest rate (of reference).

This equation represents the balance of money required of, not preferred by, the household.   

            When we aggregate this equation to the economy where individual differences wash out, the equation in the same form effectively represent the money stock (M^d≡ M^s) at a seasonally adjusted typical moment of the year. The interest rate will now become the market-wide level of interest rate instead of the typical household’s reference rate. …

             It may additionally be noted that the dimensions of terms match and that the nominal interest rate is from the aggregate asset market as opposed to “the real interest rate controlled by the central bank.” This Baumolite equation [M^d= (b∙T/ 2i)^1/2] is immune from all the defects in popular macroeconomic models…. (Unquote)

             We are sooner or later to realize that the simple-most equation is more effective in giving answers to economic troubles than the IS-LM and the AS-AD models. Even more superb, the equation is pertinent to prevention of recession while the models are to “recovery.”