LM - Money Market

Money

$M^d$ is the money demand.

There are three reasons why money is demanded:

• Transactional
• Precautionary Motive
• Speculatory

Transactional Motive

Traditional approach: It’s a cumbersome affair to go to the bank so I will just withdraw a large amount of money and hold it for my personal use.

• It depends on the level of income (how much you hold)

$$T^d=\varphi (y{)}_{+}$$

Precautionary Motive

• Its not about emergency
• Money demanded by the individual to meet his day-to-day expenditure (unexpected expenditure)
  • Suddenly if I see Jamuns being sold, I might want to buy it but I will not withdraw cash from the bank, rather I will just always keep some cash on me.
• It too demands on the level of income

$$P^d=\varphi (y{)}_{+}$$

Speculative Motive

An individual has wealth $W=1000$, split into two parts $M=700$ and $B=300$, out of which he allocates $M=700=(T^d=400)+(P^d=100)+200(?)$

He wants to participate in investments in the secondary market. Say, he buys a perpetual bond:

$$P_B=\frac{A}{r}$$

So, as

$$r\downarrow ⟹P_B\uparrow ⟹M^d\uparrow$$ $$r\uparrow ⟹P_B\downarrow ⟹M^d\downarrow$$

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Liquidity Trap is a situation where the interest rates don’t drop beyond this point. Any amount of money that you try to pump in is getting trapped.

$$M/P=l(r)+R(y)\text{\hspace{1em}(5)}$$ $$M/P=m(r_{-},y_{+})\text{\hspace{1em}(6)}$$

Money Market

Let us assume that money supply, $M^s$ is held constant, which is a function:

$$\overline{M^S}=M^d=c_0+c_{1}y-c_{2}r$$

Suppose that the level of income goes up $y\uparrow$,

$$y\uparrow ⟹M_{(T)}^d\uparrow ⟹\text{DisEQ}⟹M^d\downarrow ⟹r\uparrow$$

On the contrary,

$$y\downarrow ⟹M^d\downarrow ⟹\text{DisEQ}⟹M^d\uparrow ⟹r\downarrow$$

Equilibrium

Why when $y\uparrow ⟹r\uparrow$?

• Money market Equilibrium, where the money supply is fixed exogenously at $M_0^S$ and the money demand curve is sloping downwards which depends on the level of income ($y$) and the rate of interest ($r$).
• Now, originally $M_S$ and $M_d$ were in equilibrium
• and if the level of income rises from $y_0$ to $y_1$ to $y_2$, the money market equilibrium interest rate should also increase from $r_0$ to $r_1$ to $r_2$ in order to equilibriate the money market.
• Thus, for every rise in the level of income The interest rate needs to rise or increase.

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The LM curve represents the pace of $r$ and $y$ that will keep the money market in equilibrium with a given level of money supply.

Thus, the LM curve slopes positively upwards

Derivation

The four quadrant approach gives us the money market equilibrium and thereby helps us to derive the $LM$ curve.

Quadrant	Contents
SE	It reflects the transaction demand for money
NW	It reflects the speculative demand for money
SW	It reflects the money market equilibrium $M^d=M^S$: In this quadrant, we use a $45°$ triangle where $T^d+S^d=M^d=M^S$ ($M^S$ is fixed exogenously)
NE	It houses the pairs of $r$ and $y$ which maintains the money market equilibrium and helps us to derive the LM curve.

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Explanation

Given $y_0$, we can find the $T^d$ from $k(y)$

• We subtract this $T^d$ from the total money demand to see what level of speculative demand implies given the money supply
• this level of $S^d$ shows us in turn the level of interest rate, $r_0$ that will maintain the money market in equilibrium with the level of income $y_0$.
• Thus, the money market equilibrium pairs are $r_0$ and $y_0$ leading to / deriving the $L-M$ curve