Money Market

Money Demand

definition

Money Demand Function

$$M^D=P[L(Y,i)]$$

$P:$ price level

$Y:$ real income or output

$i:$ nominal interest rate on nonmonetary assets

$L:$ function relating $M^D$ to $Y$ and $i$

can also write like this:

$$\frac{M^D}{P}=L(Y,r+{\pi }^e)$$

$\frac{M^D}{P}$: Real Money Demand

$r:$ real interest rate on nonmonetary assets ${\pi }^e:$ expected inflation rate

Factors that affect Money Demand

Nominal interest rate on nonmonetary assets

• Higher nominal interest rate $⟹$ larger cost of holding money
• Nominal interest rate $\uparrow ⟹M^D\downarrow$

Real income

• Higher real income increases desired consumption

Number of desired transaction increases

• Real income $\uparrow ⟹M^D\downarrow$

Price Level

• Higher price level means more money needed for transactions
• Price Level $\uparrow ⟹M^D\uparrow$

and also

• Risk of nonmonetary asset returns
  • Risk $\uparrow ⟹M^D\uparrow$
• Liquidity of nonmonetary assets
  • Liquidity $\uparrow ⟹M^D\downarrow$
• Expectations of nonmonetary asset returns
  • Expected return $\uparrow ⟹M^D\downarrow$

Money Supply

Definition

Money Market Equilibrium

given by: $M^D=M^S$

$$M^S=P\times L(Y,i)$$

$P:$ price level

$i:$ nominal interest rate on nonmonetary assets

At aggregate level for nonmonetary assets:

$$M^D+N{M}^D=M^S+N{M}^S$$ $$EQ⟹(M^D-M^S)+(N{M}^D-N{M}^S)=0$$

$M:$ money

$NM:$ nonmonetary assets

Price Level increases with Money Supply if Y flat

$M^S\uparrow ⟹P\uparrow$ if $Y$ unchanged

Quantity Theory of Money

$$MV=PY$$

$M:$ Money supply

$P:$ Price level

$Y:$ real income or real GDP of economy

$V:$ Velocity of money $\left(V=\frac{PY}{M}\right)$

Equation is also Log Linear:

$$\begin{array}{r}\log M+\log V=\log P+\log Y\\ \frac{\Delta M}{M}+\frac{\Delta V}{V}=\frac{\Delta P}{P}+\frac{\Delta Y}{Y}\end{array}$$

Quantity theory implications

• Assumes real money demand proportional to real income
• Assumes V is constant
• If change in M doesn’t affect Y $⟹$ Y determined by tech and resources
• P changes same percentage as M

Factors that affect Money Supply

determined by FED

Open-Market Operations

• Purchase and sale of treasuries by the FED
• primary tool of FED to control $M^S$

Sale of Bonds

• Public buys bonds
• decreases money supply

Purchase of Bonds

• Fed pays public using newly created money
• increases money supply