Labor Economics 5th Edition by George Borjas

Exercise 9

A country has two regions, the North and the South, which are identical in all respects except the hourly wage and the number of workers. The demand for labor in each region is:
w N = $20 -.5 E N and w S = $20 -.5 E S ,
where E N and E S are millions of workers. Currently there are 6 million workers in the North and 18 million workers in the South.
(a) What is the wage in each region
(b) If there were no shocks to the economy, migration over time will result in an equalization of wages and employment. What would be the long-run wage and employment level in each region
(c) Return to the original set-up where there are 6 million workers in the North and 18 million workers in the South. As a policy maker, you decide not only to allow 2 million immigrants of working age to enter your country, but you have the authority to resettle the immigrants wherever you want. How should you distribute immigrants across the regions to maximize the country's immigration surplus Besides maximizing the immigration surplus in the short-run, in what other ways does your distribution of immigrants help the economy