Consider a country which is divided into North and South. The utility to live in the North is () = 41 + 12 2² and the utility to live in the South is ₍) = 15 + 20 2², where n and s are the number of residents in each region (millions).

a) Currently, there are 4 million people living in the North and 7 million living in the South. Are these city sizes a stable equilibrium? Explain your answer.

b) If an oil Reserve is found in the South and the utility to live in this city is now given by () = 25 + 12 ² . What would happen to both regions? Explain your answer.