# 3240 Week 12 Exercise

Example 1:
YM=40135; YF=28001
YF/YM= 0.70
ln( / )  ln  ln  ln 28001  ln 40135 10.24 10.60  0.36  ln(0.70) F M F M Y Y Y Y
Suppose
lnYM = 9.2+0.1SM
lnYF=9.4+0,07SF
And the averages of the schoolings are SM=14 and SF=12
lnYM – lnYF= 9.2+0.1SM – 9.4 – 0.07SF
= 9.2-9.4 + 0.1SM-0.07SF+0.1SF-0.1SF
=9.2-9.4+0.1(SM-SF)+(0.1-0.07)SF
= 0.1*2+ [9.2-9.4+0.03*12]
=0.2 + 0.16
Note that ln(YF/YM) = ln(0.7) = -0.36
0.2 is the explained differential (because of the difference of the schooling) and 0.16 is the
unexplained differential
44% (16/36) are the unexplained.
The unexplained female earnings ratio is
ln(YM/YF) = -0.16 = (YM/YF) = exp(-0.16) = 0.85
Page 2 of 4
Example 2:
Example 2:
lnW
lnWMM = 0.40 + 0.07ED= 0.40 + 0.07EDMM + 0.06Exp+ 0.06ExpMM + 0.05Mar+ 0.05MarMM + 0.01Children+ 0.01ChildrenMM
lnW
lnWFF = 0.01+ 0.10ED= 0.01+ 0.10EDFF + 0.04Exp+ 0.04ExpFF — 0.02Mar0.02MarFF — 0.05Children0.05ChildrenFF
W=Wage
W=Wage
ED=Years of education (average 14 for M and 15 for F)
ED=Years of education (average 14 for M and 15 for F)
Exp=Years of labor market experiences (aveage 10 for M and 7 f
Exp=Years of labor market experiences (aveage 10 for M and 7 for F)or F)
Mar=Married (50% for both M and F)
Mar=Married (50% for both M and F)
Children=children presence (60% for both married M and F)
Children=children presence (60% for both married M and F)
1) Interpret the equations:
For M:
1 unit increase in ED, 7% increase in W etc.
Marriage: increase in W by 5%
Children: increase in W by 1%
For F:
Marriage decreases W by 2%, Children decreases W by 5%, etc.
2) Mean Wages:
E(lnW
E(lnWMM) = 0.40 + 0.07(14) + 0.06(10) + 0.05(0.5) + 0.01(0.6) = 2.01) = 0.40 + 0.07(14) + 0.06(10) + 0.05(0.5) + 0.01(0.6) = 2.01
E(lnWE(lnWFF) = 0.01+ 0.10(15) + 0.04(7) ) = 0.01+ 0.10(15) + 0.04(7) — 0.02(0.5) 0.02(0.5) — 0.05(0.6) = 1.750.05(0.6) = 1.75
3) Wage ratio between F and M
E(lnWF)/E(lnWM) = 1.75/2.01= 0.87
4) Average male wage if male has the same wage structure with female.
E(lnWE(lnWMM) = 0.01+ 0.10(14) + 0.04(10) ) = 0.01+ 0.10(14) + 0.04(10) — 0.02(0.5) 0.02(0.5) — 0.05(0.6) = 1.770.05(0.6) = 1.77
5) Average female wage if female has the same wage structure with male.
E(lnWE(lnWFF) = 0.4) = 0.40 + 0.07(15) + 0.06(7) + 0.05(0.5) + 0.01(0.6) = 1.900 + 0.07(15) + 0.06(7) + 0.05(0.5) + 0.01(0.6) = 1.90
Page 3 of 4
Exercises:
Exercises: Ch 12 Ch 12
Review Questions: #1, 2, Problems #1, 2, 3, 4
Review Questions: #1, 2, Problems #1, 2, 3, 4
Ch 12 #1
Ch 12 #1–2 (modified)2 (modified)
Ym = 5,000 + 100*Pm Ym = 5,000 + 100*Pm
Yf = 4,000 + 80*PfYf = 4,000 + 80*Pf
Where Ym=income for male dominated jobs,
Where Ym=income for male dominated jobs, Yf=income for female dominated jobs, Pm=job Yf=income for female dominated jobs, Pm=job evaluation points for male dominated jobs, etc.evaluation points for male dominated jobs, etc.
1) When Pf=200, Yf?  Yf=4000+80*200= 20000
2) Pay equity when Pf=200
Ym-Yf= 1000 + 20P = 1000+20*200= 5000
Y
25000
2000020000
50005000
40004000
200 P
 Higher pay for higher evaluation points for both M and F (slopes are positive)
 Male receives higher return for additional evaluations (male is steeper sloped)
 Male receives higher base pay
 Equity award: anyone, man or woman, who works in a female-dominated occupation should earn a wage based on the pay scale (with its rates per year of experience, educational degree, etc.) of the male-dominated occupation
= 5000 for this case.
3) If average of Pm=300 and Pf=200, compute Y.
Ym= 5000 + 100*300= 35000
Yf=4000+80+200 = 20000
4) Oaxaca Decomposition:
Ym = 5,000 + 100*Pm Ym = 5,000 + 100*Pm
Yf = 4,000 + 80*PfYf = 4,000 + 80*Pf
Ym-Yf = 5000+100Pm-4000-80Pf = 1000 + 100Pm – 80Pf + 100Pf-100Pf
Page 4 of 4
= 1000 + 100(Pm-Pf) + (100-80)Pf
Male-female discrimination = 1000+ 20*200= 5000
Non-discriminatory factor = 100*100 = 10000.
Note that Note that YmYm–Yf= 35000Yf= 35000–20000=1500020000=15000
Ch 12 #3 (Modified)
Ch 12 #3 (Modified)
Demand for M: MRP
Demand for M: MRPMM = W= WM M (1 (1 –– ddMM) and for women is: MRP) and for women is: MRPFF = W= WF F (1 + d(1 + dFF))..
Where d=discriminat
Where d=discrimination coefficiention coefficient
If no discrimination: MRP
If no discrimination: MRPMM=W=WMM, and MRP, and MRPFF=W=WFF
WWMM WWFF
WWMM**
WWFF**
LLMM LLFF
Profit function:
Π = P*Q – WF(1 + dF)LF – WM(1 – dM)LM
1) Profit maximizing demand for labor:
FOCLF= -WF(1+dF)
FOCLM= -WM(1-dM)
Demand for labor:
MPLM=WM(1-dM), MPLF=WF(1+dF)
With discrimination, employer hires more male and less female
2) If df=dm=0.1
MRP = WF(1+0.1) = WM(1-0.1)  1.1WF=0.9WM  WF/WM = 0.9/1.1 = 0.82

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