3. (24 pts total] There are two cities in the region of vacationers, Santorini and Marmaris (see graph below), with attached shaped urban utility functions. (Please note that the chart below is to the scale, slopes of the Santorini and Marmaris urban utility curves are (+/-) $20/million and (+/-) $10/million, respectively. Santorini and Marmaris urban utility curves peak at utility levels of $210 and $150, respectively. Denote the population levels (in millions) in each city by "Ps" and "Pm", respectively). Each part of the question below is independent unless otherwise stated. 3 3 3 Give two examples (each) of stable and unstable equilibrium distribution of populations across two cities (no restrictions on population levels for this part of the question). Find the unstable equilibrium (where both cities are populated) that yields the highest utility for all residents. State the population and utility levels in each city. Find the stable equilibrium (where both cities are populated) that yields the highest utility for all residents. State the population and utility levels in each city. Now, assume Ps=10 and Pm=12 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. Now assume that Ps=10 and Pm=14 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. Assume that Ps= Pm=14 million. The major of the region is considering initiating an infrastructure project in Marmaris that will shift the urban utility curve for Marmaris by $35 upwards vertically (vertical shift at all population levels). How much should the major pay for the project, at most? 240 5 5 Marmaris Santorini Utility (in $) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 - Marmaris 30 40 50 60 70 80 90 100 110 120 130 140 150 140 130 120 110 100 90 80 70 Santorini 10 30 50 70 90 110 130 150 170 190 210 190 170 150 130 110 90 70 50 30 10 Population in millions 3. (24 pts total] There are two cities in the region of vacationers, Santorini and Marmaris (see graph below), with attached shaped urban utility functions. (Please note that the chart below is to the scale, slopes of the Santorini and Marmaris urban utility curves are (+/-) $20/million and (+/-) $10/million, respectively. Santorini and Marmaris urban utility curves peak at utility levels of $210 and $150, respectively. Denote the population levels (in millions) in each city by "Ps" and "Pm", respectively). Each part of the question below is independent unless otherwise stated. 3 3 3 Give two examples (each) of stable and unstable equilibrium distribution of populations across two cities (no restrictions on population levels for this part of the question). Find the unstable equilibrium (where both cities are populated) that yields the highest utility for all residents. State the population and utility levels in each city. Find the stable equilibrium (where both cities are populated) that yields the highest utility for all residents. State the population and utility levels in each city. Now, assume Ps=10 and Pm=12 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. Now assume that Ps=10 and Pm=14 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. Assume that Ps= Pm=14 million. The major of the region is considering initiating an infrastructure project in Marmaris that will shift the urban utility curve for Marmaris by $35 upwards vertically (vertical shift at all population levels). How much should the major pay for the project, at most? 240 5 5 Marmaris Santorini Utility (in $) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 - Marmaris 30 40 50 60 70 80 90 100 110 120 130 140 150 140 130 120 110 100 90 80 70 Santorini 10 30 50 70 90 110 130 150 170 190 210 190 170 150 130 110 90 70 50 30 10 Population in millions