# 貨幣銀行學 Chapter 20
###### tags: `貨幣銀行學`
## Preview
1. quantity theory of money and demand of money
2. interest rates and the demand of money objective
3. relationship between money growth and inflation
4. budget deficit :arrow_right: inflation
5. three motives of liquidity preference theory of money([流動偏好](https://wiki.mbalib.com/zh-tw/%E6%B5%81%E5%8A%A8%E5%81%8F%E5%A5%BD))
6. portfolio choice theory of money demand
## Quantity theory of money
### 1.
$$
V=\frac{P\times Y}{M}
$$
V : velocity(流通速度)
P : price level
Y : real output
M : money aggregate
P * Y =aggregate nominal output
:::info
example:
P * Y = 10 trillion
M = 2 trillion
V =5(each dollar is spent 5 times)
:::
### 2. Equation of exchange
$$M\times V = P \times Y
$$
* we want to know M:arrow_up:(PY:arrow_up:? , V:arrow_down: PY?)
### 3. velocity fairly constant in the short run
$$
V = \bar V
$$
Money demand interpretation of quantity theory
$$
M \times V= P \times Y
$$
1. Cambridge view (Marshall and Pigou)
money demand is proportional to nominal income
b/c 1.medium of exchange
2.store of wealth
2. In this theory money demand is not a function of interest rate
v = bar v
:::info
ex
v = bar v = 5
M= 2 trillion PY= 10 trillion
M= 4 trillion PY= 20 trillion
:::

3. Belief of classical economists price and wage are completely flexible
output remain at fall-employment level
4. Quantity theory of money and the price level
$$
M\times\bar V = P\times\bar Y
$$$$
P=\frac{M\bar V}{\bar Y}
$$
:::info
ex
Y =10 apples
M = 5
V = 2 :arrow_right: 4
P = 1 :arrow_right: 2
money double :arrow_right: price level double
:::

5. Quantity theory and inflation
* x.y :arrow_right: xy(percentage change) = x (percentagechange)+ Y(percentage change)
* MV=PY
MV((percentage change) = PY(percentage change)
M(percentage change)+V(percentage change) = P(percentage change)+Y(percentage change)

6. Empirical evidence
* long run :
1. time series data
2. cross countries data good
* short run :
* not that good
7. Budget deficit and inflation
* ordinary people(earn/borrow) v.s government(heavy tax/issue bound/print money)
* government budget constraint
* G-T = ΔMB + ΔB
MB : money base
B : bound
G-T = DEF
:::info
ex:
DEF = 100 million
=100(MB) + 0 = 0 + 100(B)
* When DEF > 0,and ΔB=0
:arrow_right: ΔMB>0 :arrow_right:M^s^:arrow_up:
:::
**It is called monetizing the debt**([債務貨幣化](https://wiki.mbalib.com/zh-tw/%E8%B4%A2%E6%94%BF%E8%B5%A4%E5%AD%97%E8%B4%A7%E5%B8%81%E5%8C%96))
8. In practice government issues bounds to the public, and them the central bank purchase bounds from public
### Keynesian of money demand
1. liquidity preference theory (流動性偏好理論) b/c he thought
2. 3 motives of money demand
* transaction motive payment technology matters
ex credit card
* precautionary motive(預防性動機)unexpected want
* speculative motive
3. nominal interest of bonds =
opportunity of holding money i :arrow_up =
B:arrow_up: M^d^:arrow_down:Putting three motives together
$$
\frac{M^d}{P} = L(i,Y)
$$
rewrite :
$$
\frac{P}{M^d} = \frac{1}{L(i,Y)}\\
frac{PY}{M^d}
$$