Talk:Baumol–Tobin model

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"Using the fact that average money holdings are equal to Y/2N we obtain a demand for money function: $$M= \left ( \frac {CY} {2i} \right )^{\frac {1} {2}}$$ "

If the average money holdings are equal to Y/2N, then a demand for money would be Y/N, so: $$M= \left ( \frac {2CY} {i} \right )^{\frac {1} {2}}$$

And only average long-run demand for money will be: $$\overline {M}= \frac {M} {2}= \left ( \frac {CY} {2i} \right )^{\frac {1} {2}}$$

Deisik (talk) 11:55, 30 November 2009 (UTC)

Dr. Faig's comment on this article
Dr. Faig has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"The exposition is very good. The only things missing is a little note to the effect that one may want to restrict N* to be an integer. In this case, the formula given is just an approximation"

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Faig has published scholarly research which seems to be relevant to this Wikipedia article:


 * Reference : Miquel Faig & Belen Jerez, 2006. "Precautionary Balances and the Velocity of Circulation of Money," 2006 Meeting Papers 457, Society for Economic Dynamics.

ExpertIdeasBot (talk) 15:11, 24 June 2016 (UTC)

Unclear formula, need to improve
After the sentence: "Using the fact that average money holdings are equal to Y/2N we obtain a demand for money function:"

the article is unclear: you didn't define P and you just repeat the same formula, it's useless. Besides you didn't show how you got that repeated formula. As it's connected with Fisher formula, N = V (MV=PY), so I don't see what did you do. I think your Y equals PY in Fisher's equation. Pawel.jamiolkowski (talk) 01:24, 4 September 2022 (UTC)

Error in formula
I analysed once again your formulas and papers in references and I see the last formula is wrong. Now it is:

M/P = (C*Y/(2*i))^0.5

And it should be:

M = (C*Y/(2*i))^0.5

or, equivalently:

M/P = (C*Q/(2*i*P))^0.5

where Q is the quantity of goods purchased and P is the average price of these goods (Y = P*Q). So Q can be thought as the real GDP and Y is the nominal GDP.

You say "Using the fact that average money holdings are equal to Y/2N "

So

M = Y/(2*N)

Hence:

N = Y/(2*M)

Also from Baumol's formula you have:

N = (Y*i/(2*C))^0.5

So

Y/(2*M) = (Y*i/(2*C))^0.5

From this we have

M = (C*Y/(2*i))^0.5

which is correct formula. If you divide it both sides by P, we have

M/P = (C*Y/(2*i*P^2))^0.5

and then

M/P = (C*(Y/P)/(2*i*P))^0.5

hence

M/P = (C*Q/(2*i*P))^0.5

which is exactly the same as the last formula shown in Baumol-Tobin's paper "The Optimal Cash Balance Proposition: Maurice Allais' Priority" (1989) on p. 1162 (to which you also refer) where the authors denote F = C * Q and R = P.

However, Baumol-Tobin define F as a total cost of transactions (cost of investing money, see p. 1161), so that formulas will be consistent when Q = N. This will be met when a single product is purchased in each individual transaction.

So please correct it.

Also consider changing the status "to quite relevant", because it allows you to not only look for the optimal distribution of cash over periods, but also the optimal cost of investment. Moreover, Baumol's article, for example, has been cited 3774 times according to google scholar. Pawel.jamiolkowski (talk) 09:11, 23 September 2022 (UTC)