1. Two rival hotels (i = l, 2) located on a highway exit simultaneously post room prices to attract travelers with an inverse demand p = 410 (51 + S2), where Si is the number of rooms sold by hotel i. Let r. be i's total number of rooms. Moreover, assume that maintaining a room costs c = 10. a) (20) Determine the range of n and r2 under which (Nash) equilibrium prices are the most competitive, p1. = p2' = 10. Are all rooms sold out? b) (20) Determine the range of n and r2 under which all rooms are sold out in equilibrium i.e., 51" = n and 52' = r2. (Assume \"efcient rationing\" rule, as we did in class)