What is the "Baumol Tobin Square root law" ???

Question

Can someone please explain the the concept of Baumol Tobin Square root law?

Answer 1

This is the famous square root rule.2 It has these implications for the demand for
money:
1. The transactions demand for money is negatively related to the interest rate i.
2. The transactions demand for money is positively related to income, but there
are economies of scale in money holdings—that is, the demand for money
rises less than proportionally with income. For example, if T0 quadruples in
Equation 1, the demand for money only doubles.
3. A lowering of the brokerage costs due to technological improvements would
decrease the demand for money.
4. There is no money illusion in the demand for money. If the price level
doubles, T0 and b will double. Equation 1 then indicates that M will double as
well. Thus the demand for real money balances remains unchanged, which
makes sense because neither the interest rate nor real income has changed.
Tobin Mean-Variance Model
Tobin’s mean-variance analysis of money demand is just an application of the
basic ideas in the theory of portfolio choice. Tobin assumes that the utility that
people derive from their assets is positively related to the expected return on
their portfolio of assets and is negatively related to the riskiness of this portfolio
as represented by the variance (or standard deviation) of its returns. This
framework implies that an individual has indifference curves that can be drawn as
in Figure 21A-1. Notice that these indifference curves slope upward because an
individual is willing to accept more risk if offered a higher expected return.