Microsoft PowerPoint - 103Micro_Part2D5.pptx

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1 Part 2D. Consumer Welfare and Policy Analysis 5. Labor Supply Curves 勞動供給曲線 Labor-Leisure Leisure Choice Income & Substitute Effects Shape of the Labor Supply Curve Income Tax Rates & Labor Supply Perloff (2014, 3e, GE), Section

2 Labor-Leisure Leisure Choice Goal of the Labor-Leisure Leisure Choice To maximize utility subject to 2 constraints. Time constraint Income constraint Leisure Demand vs. Labor Supply We can derive the labor supply curve by solving for the leisure demand with the UMP. The price of leisure is forgone earnings, i.e., wage rate, w. 2

3 Labor s UMP Max UC (, ) { C, } s.t. L T... Time constraint pc wl I... Income constraint 0 where C consumption leisure hour L labor hour T total time I 0 non-wage Income w wage rate p price of consumption (If p = 1, w is the real wage rate.) 3

4 Setup the Lagrangian, g L Max L= UCT (, L) ( I wl pc) { CL, } FOCs L U U = p 0 C C L U = ( 1) w 0 L L I wl pc MU MU C = w p real wage rate The optimal solution of the UMP is characterized by MU w MRS C= = MRT C MU p C 4

5 Solutions * C C ( p, w, I 0)... Demand for Consumption Goods * L T p w I0 L p w I0 (,, ) (,, ) Leisure demand... Labor Supply * ( pwi,, ) 0 5

6 Figure: Labor-Leisure Leisure Choice Consumption, C Time Constraint C* e * L* T Leisure, 6

7 Figure: The Demand Curve for Leisure Graphical analysis to determine optimal work hours and leisure hours per day. Perloff (2014, 3e, GE), Figure 5.8(a), p.180 7

8 Figure: The Demand Curve for Leisure When wage falls, it is optimal to work fewer hours and increase leisure: Perloff (2014, 3e, GE), Figure 5.8(b), p.180 8

9 Figure: The Labor Supply Curve The supply curve for hours worked is the mirror image of the demand curve for leisure hours. Perloff (2014, 3e, GE), Figure 5.9, p

10 Income & Substitute Effects When leisure is a normal good, the SE and IE work in opposite directions, so whether leisure demand increases or not depends on which effect is larger. If leisure is an inferior good, both the SE and IE work in the same direction, a wage increase unambiguously causes the hours worked to rise. 10

11 Figure: Labor-Leisure Leisure Choice Consumption, C TE: e e e e C* e SE: e e IE: e e * L* T Leisure, 11

12 Figure: The IE & SE of a Wage Change w TE: e 1 e 2 (work Less) SE: e 1 e * (work more) IE: e * e 2 (work less) IE dominates in this case. Perloff (2014, 3e, GE), Figure 5.10, p

13 Solved Problem Enrico receives a no-strings strings-attached scholarship that pays him an extra Y* per day. How does this scholarship affect the number of hours he wants to work? Does his utility increase? With an increase in income, leisure may increase or decrease. 13

14 Shape of the Labor Supply Curve The labor supply curve can slope upward, bend backward, or have sections with both properties depending on the income elasticity of leisure. At low wages, the SE (work more hours) dominates the IE (work fewer hours). The opposite occurs at higher h wages. 14

15 Figure: Labor Supply Curve That Slopes Upward and Then Bends Backward Different effects dominate along different portions of the labor supply curve. Potentially backward-bending labor supply curve at higher wages. Perloff (2014, 3e, GE), Figure 5.11, p

16 Income Tax & Labor Supply The Effect of Tax on Wage Income An increase in the income tax rate a percent of earnings lowers workers after-tax wages and may increase or decrease hours worked. If labor supply is upward sloping, lowering wages through h higher h income taxes will decrease hours worked. If labor supply is backward bending, lowering wages through higher income taxes will increase hours worked. 16

17 The effect of imposing a marginal tax rate of is to reduce the effect wage from w to (1 ) w. This rotates a worker s budget constraint in and downward. (1 )w... after-tax wage The government s tax revenue, T, is * T wl w L( ( ) By differentiating T w.r.t., we can show how income tax revenue changes as the tax rate increases. dt 2 wl( ) w dl ( w) wl( ) w dl d d d 17

18 The Effect of Increasing Tax Rate on Government Tax Revenue dt 2 dl wl( ) w d d dt 0 d if dl Therefore, L( ) w d 1 dl w 1 dl d L( ( ) d L ( ) 1 dt i.e., e L, 0 d = 25%, (1 )/ = 0.75/0.25 = 3(> e L,w ) = 90%, (1 )/ = 0.1/0.9 = 1/9 (< e L,w ) 18

19 Figure: Relationship of Tax Revenue to the Marginal Tax Rates Income tax revenue is wh, which has a nonlinear relationship to the marginal tax rate,. Two effects from a change in : Government collects more revenue from higher tax rate. Change in tax rate alters hours worked (and direction i cannot be predicted by theory alone). Perloff (2014, 3e, GE), Figure 5.12, p

20 Conclusion Taxes on earnings are an unattractive way of collecting money for the government if supply curves are upward sloping, because the taxes cause people to work fewer hours, reducing the amount of goods that society produces raising less tax revenue than if the supply curve were vertical or backward db bending. 20

21 Table: 主要國家實際每週工時年別台灣韓國新加坡香港日本美國加拿大法國德國 2000 年年年年年年年資料來源 : 我國行政院主計處薪資與生產力統計月報韓國官方網站 ( 新加坡 Yearbook of manpower Statistics ti ti 附註 :(1) 新加坡 2006 年以前僅包括 25 人以上之私部門,2006 年以後則擴及 25 人以上之公私部門 (2) 日本厚生勞動省以 30 人以上事業單位為調查對象 (3) 美國資料來源為 BLS (4) 加拿大資料來源為 ILO, 包含林業及加班工時 (5) 德國資料來源為德國統計局資料來源 : 行政院勞工委員會統計處, 各國法定工時與實際工時比較,2007 年 10 月 21

22 Table: 主要國家製造業受僱員工平均每月 ( 週 ) 工作時數年別中華民國 R. O. C. (1) 日本 Japan (1) 韓國 Korea, R. O. (1) 新加坡 Singapore 香港 Hong Kong 美國 U. S. A. (2) 紐西蘭 New Zealand 資料來源 : 我國行政院主計處薪資與生產力統計月報,2013 年 9 月, 表 35 (1) Average monthly hours. (2) Production and nonsupervisory employees. 22

23 Table: 主要國家製造業每月週日時薪中華民國日本韓國香港紐西蘭新加坡美國年別 R. O. C. Japan Korea, R. O. Hong New NT$ N.T.$ Yen 1000 Won Singapore U. S. A. Kong Zealand 新幣 (M) (M) (M) (M) Dollar(H) 港幣 (D) 紐幣 (H) 資料來源 : 我國行政院主計處薪資與生產力統計月報,2013 年 9 月, 表 34 (M) Month (D) Day (H) Hour. 23

24 Table: 主要國家製造業勞動生產力指數主要國家製造業勞動生產力指數 Base period: 2006 = 100 年別中華民國 R. ROC O. C. 日本 Japan (1) 韓國 Korea, R. O. (1) (3) 美國 U. S. A. (2)(3) 資料來源 : 我國行政院主計處薪資與生產力統計月報,2013 年 9 月, 表 36 (1) 基期 : 2010 = 100 (2) 基期 :2009 = 100. (3) 季平均 24

d y d = d 2 y d 2 = > 0 Figure45 :Price consumer curve not a Giffen good X & Y are substitutes From the demand curves. Figure46 Deman

d y d = d 2 y d 2 = > 0 Figure45 :Price consumer curve not a Giffen good X & Y are substitutes From the demand curves. Figure46 Deman Ch4. 個體經濟學一 M i c r o e c o n o m i c s (I) Comparative Statics and Demand EX: u(, y) = 2 + y, Ma,y 2 + y s. t. P + P y y = m FOC MRS y = P P y P + P y y = m MRS y = MU = 2 0.5 0.5 = P MU y 1 P y 1 0.5