---
# System prepended metadata

title: '總經CH03 - Productivity, Output and Employment'
tags: [總經, 110-1]

---

###### tags: `總經` `110-1`

# 總經CH03 - Productivity, Output and Employment

## Production Function
### Factor Income
```
Land -> Rent
Labor -> Wage
Capital -> Interest
Entrepreneur -> Profit/Loss
```
### Shape of the Production Function
$Y = AF(K, N) = AK^{\alpha}N^{1-\alpha}$
 
```
A: Total Factor Productivity = 總要素生產力
```
- 斜率為正
- 隨著資本投入，逐漸平緩(資本邊際產出與勞動邊際產出**遞減**)
- 任一點的斜率為MPK or MPN
    - 資本邊際產出 $MPK = \frac{\Delta Y}{\Delta K}$
    - 勞動邊際產出 $MPN = \frac{\Delta Y}{\Delta N}$

### Supply Shock
供給面衝擊 -> $A$的改變
可能有正面或負面衝擊

## The Demand of Labor - ND
> 廠商想要雇用多少勞動力


### 四假設
- 資本額固定
- 勞工都一樣
- 勞工市場是競爭的
- 廠商追求最大化利潤

$W$: 名目工資
$w = MPN$: 實質工資
$w = W / P$
$MPN = \frac{\partial Y}{\partial N}$
$MRPN = MPN * P$: 勞動邊際產值

**Firm's profit maximization: $w = MPN$**

### Facotrs shifts the Labor Demand Curve
Supply shock



## The Supply of Labor - NS
### Income - Leisure trade-off
勞動休閒取捨
SE：替代效果 - 我要賺更多！$\Delta {NS} > 0$
> 更高的實質工資會吸引勞工增加工時

IE：所得效果 - 賺夠了！ $\Delta {NS} < 0$
> 勞工因實質工資提高，便減少工作時數

$SE + IE = TE$

後彎勞動供給線：勞動供給線可能出現兩段式方向

---
財富增加或是預期未來實質工資上漲 -> 當下之勞動供給線左移

## Labor Market Equilibrium
$\bar w$：市場結清實質工資
$\bar N$：充分就業雇用量
$\bar Y$：充分就業產出(GDP)

景氣衰退
$\bar w, \bar N, \bar, Y$皆下降

## Unemployment
```
POP = 總人口
WAPOP = 工作年齡人口 (15-64)
N = 就業人口
U = 失業人口
LF = N + U = 勞動力
```

```
u 失業率 = U / LF
p 勞動參與率 = LF / WAPOP
就業比率 = N / WAPOP
```
### Employment Flow

---
### Discourage Workers
unemployed -> not in labor force

---
### How long are people unemployed?
失業時期：unemployment spell

---
Four possible reasons for increase duration:
- Measurement issue
- Unemployment benefit
- large job lost
- weak economic recovery

---

### Why there always are unemployed peolpe?
> 自然失業率 $\bar{u}$
> when output and employment are at full-employment levels

- Frictional umployment 摩擦性失業
    - 各種態度的異質性, eg:薪水、工時
    - Matching process takes time
- Structural umployment 結構性失業
    - 商品週期改變 - 季節性失業
    - 經濟結構轉變 - 被機器取代，工廠外移
---
> 循環失業率 ${u}$ - $\bar{u}$
- Cyclical umployment 循環性失業
    - 因景氣衰退造成的失業。${u}$ - $\bar{u}$ > 0
    - 景氣繁榮時可能額外雇用員工，造成負值。${u}$ - $\bar{u}$ < 0
    - 充分就業：${u}$ = $\bar{u}$。${u}$ - $\bar{u}$  = 0

---
## Okun's Law - Relating Output and Unemployment
- 第一種
    $\bar{Y}$：充分就業時的產出，長期的產出平均值
    $Y$：當期的產出

    $-2(u - \bar{u}) = \frac{Y - \bar{Y}}{\bar{Y}} \sim \ln{Y} - \ln{\bar{Y}}$（產出缺口）
    
    $\bar{Y} = \frac{Y}{-2(u - \bar{u})+1}$

    - 不同景氣的反應
        - 景氣衰退：${u}$ - $\bar{u} > 0$，$\frac{Y - \bar{Y}}{\bar{Y}} < 0$
        - 景氣繁榮：${u}$ - $\bar{u} < 0$，$\frac{Y - \bar{Y}}{\bar{Y}} > 0$
        - 充分就業：${u}$ - $\bar{u} = 0$，$\frac{Y - \bar{Y}}{\bar{Y}} = 0$
- 第二種

    $\Delta{Y}$：$Y_{last} - Y_{pre}$
    
    $\frac{\Delta{Y}}{Y_{pre}} = 3\% - 2\Delta{u}$

    
## 數學補充
取自然對數後相減 = 成長率
$\ln{12456} - \ln{12345} = \frac{12456 - 12345}{12345} = 0.90\%$

[總經04](/SMYfmLCETQ2JVwCH6c5J9A)