Financial Markets & Money

Money Demand & Traditional LM

coreExam · medium

Money demand is Mᵈ = €Y·L(i), proportional to nominal income and decreasing in the nominal interest rate. With exogenous money supply Ms, the LM relation Ms/P = Y·L(i) gives an upward-sloping LM curve — higher Y raises money demand, requiring higher i to re-equilibrate. The modern Grassi framework replaces this with a flat LM (CB targets i directly), but the traditional story remains the foundation.

Derivation

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Money Demand

Money is held for transactions. Demand rises with nominal income and falls with the nominal interest rate (the opportunity cost of holding cash rather than bonds):

M^d = \$Y \cdot L(i), \quad L'(i) < 0

In real terms:

\frac{M^d}{P} = Y \cdot L(i)

Two Regimes

Traditional (exogenous $M$ ): Central bank sets $M$ ; $i$ adjusts to clear the market.

\frac{M^s}{P} = Y \cdot L(i) \implies \text{LM upward-sloping in } (Y, i)

Modern (targeted $i$ ): Central bank sets $i = i^T$ ; $M$ adjusts passively.

i = i^T \implies \text{LM horizontal}

Grassi uses the modern framework throughout — LM is flat. The traditional LM still matters for understanding the history and for explaining what $M$ does in the modern regime (it moves endogenously to support the target $i$ ).

Velocity

V \equiv \frac{\$Y}{M} = \frac{1}{L(i)}

Velocity rises with $i$ . At the ZLB ( $i \to 0$ ), $L(i)$ expands and velocity falls sharply — money demand becomes nearly insatiable (liquidity trap).

Why Fiscal Policy Differs by Regime

| Regime | $\uparrow G$ effect | |--------|--------------------| | Traditional LM | $Y$ rises; $i$ rises; partial crowd-out of $I$ | | Modern (flat) LM | $Y$ rises by full multiplier; $i$ unchanged |

This is why modern presentations (and the Grassi course) emphasise the flat-LM case: under an interest-rate-targeting CB, there is no financial-market crowd-out, only the direct multiplier.

Worked Example

L(i) = 0.2 − i. P = 1. Nominal income €Y = 1000. Money supply M = 150.

Equilibrium: M = €Y·L(i) → 150 = 1000·(0.2 − i) → 0.15 = 0.2 − i → i = 5%.
If €Y rises to 1100 (fiscal expansion, P unchanged): 150 = 1100·(0.2 − i) → 0.136 = 0.2 − i → i ≈ 6.4%.
Interest rate rises by 1.4 pp — crowding out the private investment response.

At €Y = 1000: i = 5%. At €Y = 1100: i ≈ 6.4%. Higher output raises money demand, pushing up the equilibrium rate.

Common Mistakes

—Forgetting that nominal income €Y is the scale — real money demand is proportional to real Y only after deflating by P.
—Confusing money demand with wealth: wealth = money + bonds; demand for money is a portfolio choice given wealth.
—Applying the traditional upward-sloping LM to the Grassi framework, which uses flat LM (targeted i).
—Assuming M and €Y move one-for-one — they do only when i (and hence L(i)) is held constant.

Exam Cues

→Money demand: Mᵈ = €Y·L(i). Proportional in nominal income, decreasing in i.
→Traditional LM: Ms/P = Y·L(i), upward-sloping. Modern LM: i = iᵀ, horizontal.
→Velocity = 1/L(i). Higher i → lower L → higher velocity.
→Fiscal expansion: traditional → partial crowd-out via ↑i. Modern → full multiplier, i unchanged.