Answer sketches for the 3rd set of questions
8. 2
With all of these, keep in mind that we are talking about inequality among those with jobs.
(a) Indexing the minimum wage to inflation would prop up the wages of less skilled workers, thus reducing wage inequality
(b) Welfare benefits are most attractive to those with poor labor market opportunities. If welfare benefits are reduced, some leave the welfare program and join the labor force, but they will likely earn very low wages. Wage inequality would increase.
[(c) This would increase the demand for less-skilled workers, reducing wage inequality.]
(d) If illegal aliens are less skilled, then increased border enforcement would reduce the supply of low skill-labor, raise its wage, and thus reduce wage inequality.
9.1
PV(Pennsylvania)=20,000 + 20,000/(1.1) + 20,000/(1.21) = 54,710.74
PV(Illinois)= 22,000 + 22,000/(1.1) + 22,000/(1.21) = 60,181.82
The person would move from PA to IL as long as the moving costs are less than 5,471.08
9.2
a) Neolandia has a more compressed income distribution (the intercept is greater and the slope is smaller) than the U.S. The immigrant flow is “positively selected”. Try to graph it. To find the cut-off skill level, equate the two functions (that’s where the lines cross), and solve for s:
700+0.5s=670+s, or
30=0.5s, or
60=s.
60 is the skill level of the person just on the edge; all other movers have more skills (61, 62,…,100). The average skill level among the immigrants from Neolandia is 80.
b) The migration costs ($10) reduces the attractiveness of the U.S. The U.S. intercept is reduced to 660. The cutoff is where
700+0.5s=660+s, or
40=0.5s
80=s.
The immigrant flow is still positively selected, but it’s smaller. The average skill level is 90.
c) If costs are very high for skilled workers, then there may be no migration from Neolandia.
9.7
We are told the immigrant flow from that country is “negatively selected”. That means those with the least skills want to immigrate. Restricting the entry to those at the very top of the skill distribution means that no one will immigrate (because those at the top of the skill distribution would still not want to).
10.4
(a) The average wage for men is wM=500+100*14= 1,900. The average wage for women is wF=300+75*12=1,200. So the differential is 700.
(b) I’ll start the answer in general terms, and plug the numbers in later.
We can write the male-female differential, wM-wF in this way:
wM- wW= aM - aW -bW*SW+ bM*SM.
wM- wW= aM - aW + bM*SW -bW*SW + bM*SM – bM*SW, (adding and subtracting bM*SW), or
wM- wW= aM - aW + (bM-bW)*SW + bM*(SM – SW).
With the numbers given, we have
wM- wW = (500-300)+(100-75)*12 + 100*(14-12).
The second part of this differential is due to skill differences: 100*(14-12)=200.
The first part is due to discrimination: (500-300)+(100-75)*12 =500. So 5/7 of the total wage differential is due to discrimination.
Keep in mind the premise of the question, though. For the purpose of this example, schooling is the only variable that matters, and it is measured correctly.
10.6
Again, I’ll start the answer in general form, and plug the numbers in later.
Wages are wW=aW + bW*SW for white workers, and wH=aH + bH*SH for Hispanic workers.
Just as in the previous question, the difference can be written as
wW- wH= aW - aH -bH*SH + bW*SW.
wW- wH= aW - aH + bW*SH -bH*SH + bW*SW - bW*SH, using the usual trick of adding and subtracting bW*SH.
wW- wH= aW - aH + (bW-bH)*SH + bW*(SW - SH).
The last part of this differential is due to differences in schooling; the first part is due to discrimination.
In fact, our problem is a bit easier because bW=bH, in both years, so the middle part disappears.
In 1970, the total difference is .15 + .07*(12-9)=.36
So .15/.36 is the share of the difference that is due to discrimination.
In 1980, the total difference is X + .07*(13-11)=.24
X must be 0.10, and the share due to discrimination is .10/.24
There was a decrease in discrimination in the sense that the gap diminished between white and Hispanic workers with the same level of education. But the gap in average education levels diminished, too (2 instead of 3 years). As a result, the fraction of the difference that was accounted for by discrimination (or skills) stayed the same (.10/.24 = .15/.36).
13.2 (a), (b) [Think about it, then see you notes from April 24.]
(c) Solve for w. It equals $18. The worker would not accept a wage offer of $15.
(d) Solve for w again. The asking wage has fallen to $12, so a wage offer of $15 would be accepted.