2A.2 Consider a closed linear monocentric city stretching from r = 0 to N(> 0). Land supply is L(r) = 1 at any r. In line with the theme of this segment (interurban economics), interpret the segment [0, N] as Canada itself rather than one particular city. with r = 0 being the west coast and r = N the east cost for example. Endowments are uniformly distributed across the coun- try (rather than only at r = 0 as in the usual monocentric city model), namely, w(r) = w anywhere in the country. The endowment w at r is split locally and evenly among n(r) res- idents at r with no commuting cost. However, transportation of the endowment to another location is prohibitively high. Suppose that the current population distribution is 110') = 1 for any r E [0, N] and that consumers can change their resi- dence at no cost. Preferences are identical and represented by u(s(r), z(r)) = 10380)) +103(Z(r))- 1. * Given 110') above, find equilibrium 20'), 30') and p(r). To find p(r), use the feasibility condition for land. 2. ** Are spatial arbitrage opportunities exhausted in item 1? Explain. 3. ** Based on your observation in item 2, do you expect to see any cities in equilibrium? Support your argument in connection with Starrett's theorem