4. Suppose that a worker's skills can be summarized by the number of efficiency units she owns and the distribution of efficiency units in the population such that worker 1 has one efficiency unit, worker 2 has 2 efficiency units, and so on. There are 100 workers in the population of the country of Vin. In deciding whether to move to the U.S., Vinians compare their weekly earnings in Vin (wv) and their potential earnings in the U.S. (ws). The relationship between wages and skills are
wv = 700 + 0.5e
ws = 670 + e
where e gives the number of efficiency units.
(a) Assuming no migration costs, what is the immigration rate of Vinians (i.e., the fraction of the total population that moves to the U.S.)?
(b) What is the average number of efficiency units among immigrants?
(c) Is the immigrant flow positively or negatively selected?
(d) Suppose that it costs $10 to migrate from Vin. Do any of your answers to (a)-(c) change?
(a) We solve for e by setting wv = ws
700 + 0.5e = 670 + e
Or e - 0.5e = 700 - 670
Or 0.5e = 30
Therefore, e = 30/0.5 = 60
Therefore, the ...
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