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2. [30 pts] There are two cities in the state of California (CA), LA and SF (see graph below), with attached shaped urban utility functions. [Please note that the chart below is to the scale, slopes of the LA and SF utility curves are (+/-) 12/million and (+/-) 20/million, respectively.]. Each part of the question below is independent from each other unless otherwise stated. [Need exact answers using the slopes, not rounded-up integer answers] 180 160 LA SF 140 120 Utility 100 80 60 40 20 O 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 LA 32 44 56 68 80 92 104 116 128 140 128 116 104 92 80 68 56 44 32 20 8 SF 50 70 90 110 130 150 170 150 130 110 90 70 50 30 10 Population in millions a. If CA has current total population of 18 million, and is equally split between LA and SF, would that be an equilibrium? Explain why or why not. If an equilibrium, determine whether stable ora. If CA has current total population of 18 million, and is equally split between LA and SF, would that be an equilibrium? Explain why or why not. If an equilibrium, determine whether stable or unstable. If not an equilibrium (and everyone is free to move, i.e. no costs of moving}, what would the population levels be in equilibrium, in each city? Determine whether this is a stable or unstable population distribution. b. If you were a benevolent urban planner working for CA, and were asked to calculate the optimum (highest utility) stable equilibrium distribution of population across SF and LA, how would you distribute the total population of IBM across the two cities? Eye-balling is acceptable if you explain very clearly. [Conjecture on stability (which side of the urban curves to look for) carefully before you start calculating, review C55 appendix Slides] Additional guestions [independent from parts above, i.e. no total population restrictions]: c. How many equilibria distribution of populations (across SF and LA) can you find where the utility levels are 100 in both in SF and LA? What are the population levels in each of your equilibria? d. How many of the equilibria you found are stable vs unstable? Explain