1. (12 Points - 4 points each) Short Answer Please use both well-labeled graphs and clear explanations. All answers will be graded entirely on your justification. Use, as appropriate formulas and graphs. a) Suppose that the United States were to charge migrants a fixed dollar amount to live and work in the U.S.. Show the effects of implementing this policy on the average skill of migrants into the U.S. when migration is (a) positively selected; and (b) negatively selected. NOTE: Your answer will require two graphs, one for each case. Please be sure to label the axes, identify which graph refers to which case, and explain how you reach these conclusions. b) Assume that the utility that individual i enjoys in location j is given by Uij = Wij - Ruj + Aij, where Wij is the wage rate, Rij is the cost of housing ("Rent") - think of it as the cost of living - and Ajj is the level of amenities (nicer places have higher values of Ajj). Show that in long run spatial equilibrium, real wages will tend to be highest in geographic regions that have the least desirable amenities, being sure to characterize what condition must hold in equilibrium. c) Suppose that Craig is 25 years old and has 40 more working years. If Craig were observed to move from Georgia to Texas at the age of 25 and one year after the move was earnings $10,000 per year less than he earned in Georgia, could we conclude that Craig likes living in Texas more than he liked living in Georgia, assuming that the cost of living were the same? Explain your answer precisely using the model of migration as investment