1. A worker with an annual discount rate of 5% currently resides in Tucson and is
considering whether to remain there or move to Phoenix. There are three work
periods remaining in the life cycle. Ifthe worker stays in Tucson, she will earn
$40,000 per year in each ofthe three periods. If she moves to Phoenix she will earn
$42,000 per year in each ofthe three periods. What is the highest (present-value)
migration cost she will be willing to incur and still make the move?
2. Looking at the data, suppose that we see that immigrants who have just arrived in
the US one year ago earn 15% less than their native equivalents (same age,
education, etc), while immigrants that arrived 20 years ago earn 5% more than their
US equivalents. How might assimilation explain this phenomenon? How might
selection/composition bias instead explain this phenomenon?
3. In the US, the wage-skills relationship in the labor market before government
intervention is wus=100+0.4s, where s is the number of “efficiency units of skill” and
w is the weekly wage. In Canada, the wage-skills relationship is WC 2 250 + 0.2s.
a. Draw the wage-skills relationships for the 2 countries on a graph. Will
immigration from Canada to the US be positively or negatively selected?
Where will the skill cutoff be between immigrants and non-immigrants in
Canada (i.e. what value of s)?
b. Now suppose the US creates a welfare program that imposes a weekly wage
floor of $280 (i.e. it provides a subsidy for any worker that earns less than
$280 per week that brings them up to that level). Draw the wage-skills
relationship for the US and Canada on a graph. What happens to migration
from Canada to the US? Who will migrate? What are the new cutoffs?
4. Consider the case of “extremity’ selection, where both the most skilled and the least
skilled from a source country choose to migrate.
a. In the Roy Model, what must the graph ofthe return to skill on the two
countries look like to generate this scenario? Draw an example.
b. How can we explain this type of selection? Give two different explanations.
c. Looking at immigrants from Mexico to the US, Chiquiar and Hanson find
evidence for the opposite kind ofselection- “intermediate” selection, where
only workers from the middle ofthe skill distribution migrate. How do they
explain this finding in the context ofthe Roy Model?
5. Phil has two periods ofwork remaining prior to retirement. Assume that Phil
maximizes the present value of his expected lifetime earnings and his discount rate
is 10 percent. He is currently employed in a firm that pays him the value of his
marginal product, $62,000 per period. There is one other firm that Phil could
potentially work for. There is an 80 percent chance of Phil being a good match for
the other firm and a 20 percent chance of him being a bad match. If he is a good
match, his VMP at the new firm will be $65,000 per period. If he is a bad match, his
VMP at the new firm will be $40,000 per period.
a. Suppose it takes a full period to discover whether Phil is a good or bad match
with the new firm. Thus, when the firm is making Phil’s initial offer, the
managers do not know what his productivity will be, though they do know
the distribution ofpossible outcomes described above. What wage will the
firm offer in this initial period?
b. After the value of the match is determined, Phil will then be offered a wage
equal to the realized value of his marginal product in the firm. When offered
that wage, Phil is free to (a) accept or (b) return to his original firm and his
original wage. He can do this immediately, so that if he gets a low wage offer
from the new firm, he can go back to his original firm and earn his original
wage in the second period (*Note – this is different than the example I gave
in class*). What should Phil do?