# General-equilibrium effects with labor complementarity. Consider an economy comprised of 100 cities. Each city initially contains 1

## Question:

General-equilibrium effects with labor complementarity. Consider an economy comprised of 100 cities. Each city initially contains 1 million each of high school dropouts, high school graduates, workers with some college, and college graduates. There is free mobility across cities, so that no matter what happens, wages for each category of worker are equalized across cities. Suppose that the equilibrium in the labor market works in such a way that the response of wages for high school dropouts to immigration flows is given by: (∆wHSD) / wHSD = -3(∆IHSD) / LHSD + (∆IHSG) / LHSG + (∆ISC) / LSC + (∆ISG) / LSG, where wHSD is the wage for high school dropouts and ∆ indicates a change; IHSD is the number of high school dropouts in the national immigrant pool, and LHSD is the number of high school dropouts in the existing national labor force, so (∆I HSD) / L HSD represents the proportional immigrant supply shock for high school dropouts.
Similarly, the other three terms measure the immigrant supply shock for high school graduates (HSG), workers with some college (SC), and for college graduates (CG), respectively. Suppose that the wage response of the other groups is symmetric, so that for high school graduates the response is given by (∆w HSD) / wHSD = -3 (∆IHSG) / LHSG + (∆IHSD) / LHSD + (∆ISC) / LSC + (∆ICG) / LCG, the response for workers with some college by (∆wSC) / wSC = -3(∆ISC) / LCG + (∆IHSD) / LHSD + (∆fHSG) / LHSG + (∆ICG) / LCG, and the response for college graduates by (∆wCG) / wCG = - 3(∆ICG) / LCG + (∆iHSD) / LHSD + (∆iHSG) / LHSG + (∆ISC) / LSC. In other words, for each category of worker, the "own effect" of that immigration is three times the size of, and opposite in sign to, the "cross effect."
(a) Suppose that 100,000 high school dropouts immigrate, landing in city number 12 (for example), thereby raising the number of high school dropouts in city 12 by 10%. What will be the effect on the wages of high school dropouts in city 12? In the rest of the country? Now, compare this with the effect of 100,000 new high school dropouts immigrating into every city at the same time. Can this contrast help explain the contrast between the findings of the local-impact studies and the national labor-market studies in Section 12.3?
(b) Now, suppose that 100,000 workers of each category immigrate to each city, adding 10% to the total labor force. What happens to all wages? Can a comparison of this result with the result of part (a) help explain the tension between the results of Borjas and Ottaviano and Peri in Section 12.3?
(c) Now, try a different thought experiment. Suppose that immigrants are distributed randomly across cities. For example, suppose that the country receives 10 million high school dropouts as immigrants (and no others) and that those 10 million are scattered across the 100 cities, with some cities receiving a few and some cities receiving a lot. Draw a scatterplot with the local immigration supply shock measured on the horizontal axis and the proportional change in the local high school dropout wage on the vertical axis, and where each dot in the scatterplot represents the value of those two variables for one of the 100 cities. Show what the scatterplot would look like, and explain how it could be misinterpreted as a demonstration that immigration has no effect on wages.
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