Suppose in a region the unemployment rate for male is.10 and the unemployment ra
ID: 3271832 • Letter: S
Question
Suppose in a region the unemployment rate for male is.10 and the unemployment rate for female is .20. The unemployment rate of those with college degree is .05 and those without college degree is .25. Suppose half of the labor force is male and half is female.
(a) What is the unemployment in the region?
(b) Can you derive the unemployment rate for male college graduate from the information given. Why or why not?
(c) What additional information you will need to derive answers to (b) and (c). Do you think there is discrimination against female college graduate based on additional assumptions that (i) half of the college graduates are male and half are female; (ii) the unemployment rate for female college graduate is 6%? Explain your answer.
Explanation / Answer
a) The unemployment rate in the region is here computed as:
= ( Fraction of Males)*(Unemployment rate in Male ) + ( Fraction of Females)*(Unemployment rate in female )
= 0.5*0.1 + 0.5*0.2
= 0.05 + 0.1 = 0.15
Therefore the unemployment rate in the region is 0.15
b) No, we cannot derive the unemployment rate for male college graduate from the information given because we are not given the proportion of males/females who are college graduates.
c) Here the additional information we require is the proportion of males/females who are college graduates to derive the unemployment rate for male college graduates.
(i) Here we are given that half of the college graduates are males and half are female.
(ii) The unemployment rate for female college graduate is 6%.
Now let us assume that there are a total of 100 people in region then, clearly there would be 50 males and 50 females and 0.1*50 = 5 males would be unemployed and 0.2*50 = 10 females would be unemployed.
Now let there be X college graduate. Then X/2 would be male college graduates and X/2 would be female college graduates because of assumption 1 that half of the college graduates are male and half are female.
Also the unemployment rate for female college graduate is 6%, therefore out of the total X/2 female graduates, 0.06*(X/2) female graduates would be unemployed that is 0.03X would be unemployed.
Out of total X college graduates, unemployment rate in college graduates is 0.05 Therefore, 0.05X are unemployed, therefore as 0.03X are female unemployed graduates, rest 0.05X - 0.03X = 0.02 X would be male unemployed college graduates.
Therefore yes there is a clear discrimination according to the given data, as 6% of the female college graduates are unemployed but 0.02X/ (X/2) = 4% of the male college graduates are unemployed.