Using the Roy model, explain when migration between countries I, E would lead to an increase in human capital in both countries.

Consider the Roy model where log earnings for individual i in the immigration and emigration country are given by Yj; = j + bjS1i + bj2S2i, where j = E,I denote the emigration and immigration country respectively, i is an index for individual i and S and Sare cognitive and manual skills, with prices b;1, b;2 in country j. Assume that S and S are standard normally distributed with zero covariance. Finally, ; = lnR; where R, is the rental rate of human capital in country j. 1. Suppose the moving cost k is zero, and the skill prices for cognitive and manual skills are the same, but differ across country, i.e. bel bE2 = c and b = b12 = b where E = Mexico and I = the US. = (a) Suppose c> b, what does the Roy model predict about the selection of immigrants from Mexico to the US? Provide the economic intuition. (b) Assume c> b and the mean income in the US is higher than the mean income in Mexico. If the mean income in Mexico increases, what would happen to the average quality of Mexican immigrants in the US and why? Draw a diagram. Hint: Y = +Y. Also, explain what would happen if the mean income in Mexico increases a lot so that E > EMI. (c) Suppose 'in addition to the increase in the mean income of Mexico (and assuming still < ), there is now a subsidy for migrants to move from Mexico to the US. Compare to the case without the subsidy and the increase in E, what would happen to the average quality of Mexican immigrants in the US and why? Draw diagrams.