###### 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)