The "bucket" diagram below models a split in population between three different areas. 1. City 1: Population N1 is represented by the distanoe to the righty along the average benefit curve am. It rises quickly and then falls gently while moving to the right. 1. City 2: Population N2 is represented by the distanoe to the left. along the average benefit curve AB; It rises quickly, then falls gently while moving to the left. 3. A rural area, with population NR, which is represented by anyr remaining population. They all receive ABR- This does not vary with the number of inhabitants. The entire population across the three areas is fixed at \"TOTAL, with N1 + N: + Na = NmuL No exact math is required here. In fact it is impossible. But answer as best you can. 02 Population in city 1 {N1} .3. ( Population in city 2 {NJ} 1. Imagine there is perfect mobility across sites. yet everyone starts by living in the rural area. In this case no one person will want to move to city 1. You may ignore city 2 for now and answer in the graph below a. Show the loss in benefits of a person who is the rst to move to city 1? Drawa line segment in the graph below and label it "la\" b. Show the minimum population city 1 needs to maintain in order for anyone to want to move to city 1. Draw a line segment in the graph below and label it "1b\" c. Say that minimum is reached through some historical accide nt. and migration forces take hold. In an equilibrium with free migration, between oountryside and city 1, what will be the population in city 1? Mark the point along the horizontal axis as "1:." d. Is there any benet to anyone in the population from city 1 existing at all? Population in city 1 {N1} 4,: { Population in city 2 [N 1}