a. There are 2 cities C1 and C2. Everyone in both the cities has same concave, increasing utility function. There's only 1 good, with the social planner. How should s/he allocate it?
b. Now assume that initially the endowment resides in C1 (but with the planner himself) and a transfer of 1 unit from C1 to C2 results in a loss of fraction 'v'. How should s/he allocate now?
My analysis: If I assume a Rawlsian welfare function I'll get a different result than I'll get from maximising sum of utilities which would be different from weighted sum of utilities.
The only other thing I can think of is he may want the allocation to be fair i.e no one envies each other and locations are pareto optimal. No envy just means everyone gets the same allocation.
How do I go about this?