urban economics

\f2. [28 pts total] There are two cities in the region of Musicians, Jazzgir and Raptir (see graph below), with attached shaped urban utility functions (the chart below is to the scale). Denote the population levels (in millions) in each city by "P," and "PR", respectively. The slope of the Jazzgir urban utility curve is asymmetric around its peak, and (+) $37.5/million for P, 4 million. The slope of the Raptir urban utility curve is symmetric around its peak , and is (+/-) $10/million. Each part of the question below is independent from other parts unless otherwise stated. 1) Give two examples (each) of stable and unstable equilibrium distribution of populations across two cities (no restrictions on population levels). ii) Analyze the two intersection points between the two urban utility curves and determine whether each point is an equilibrium or not, and determine if stable or not. If there are 10 million residents in the region, what would be utility maximizing stable allocation of 10 million people across both cities? iv ) If there are 20 million residents in the region, what would be utility maximizing stable allocation of 20 million people across both cities? V) Assume PJ=5 and PR=6 million. Is this an equilibrium? If so, of what type? If not, find where it would converge to if everyone is free to move at no cost. vi) Assume PJ=8 and PR=8 million. Is this an equilibrium? If so, of what type? If not, find where it would converge to if everyone is free to move at no cost. vil) Assume the region population is 16, such that at PJ=2, and PR=14 million. How costly should moving across the cities be for this allocation to be an equilibrium? vili) The major of the region is considering constructing hyperloop which would make it free to move across the cities for everyone. How much should the major pay for the project, at most