Consider the model of Section 9.1 and Definition 9.1 where we defined economies of network for the airline industry. Assume that η1 = η2 = η3 = η, that is, there is an equal number of passengers on each route. Answer the following questions.

(a) Suppose that c(η) def = η for the cost function defined in (9.1). Find the condition on φ and η under which the total cost of operating a HS network is lower than the total cost of operating a FC network. Prove your answer.

(b) Answer the previous question assuming that c(η) def = √η.