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Baumol-Tobin Money Demand

Cash management as an inventory problem, the square-root rule for money holdings.

Equilibrium: M* = 63.2, C* = 3.2

Current equations

Trips cost bY/M: C = 200/MForgone interest (i/2)M: C = 0.05·M

How much cash should you carry? Big withdrawals mean fewer trips to the bank (falling blue curve) but more interest forgone (rising amber line). The cheapest point is where the two costs cross.

Shift the curves

Spending needs (bY)0

More spending means more bank trips at any cash level, optimal cash holdings rise.

Interest rate (i)0

Higher rates make idle cash expensive, hold less, visit the bank more.

The Baumol-Tobin Money Demand model, in writing

Definition

The economics of cash management: holding money sacrifices interest, but going to the bank costs time and fees, so optimal money holdings balance shoe-leather costs against forgone interest.

M* = √(c·Y / 2i), c = cost per withdrawal, Y = spending, i = interest rate

The intuition

Withdraw rarely and you hold big idle balances losing interest; withdraw constantly and you waste time and fees. The square-root rule says optimal cash rises with spending but LESS than proportionally, and falls when interest rates rise, giving money demand its interest elasticity from pure optimization rather than assumption.

Exam tip

The square root is the answer to remember: doubling spending raises optimal money holdings by √2, not 2. Money demand falls in i, rises in transaction costs.

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Money Market →Loanable Funds Market →Capital Asset Pricing Model (CAPM) →Term Structure of Interest Rates →