Question

2. Consider a problem where a monopolistic airline chooses between a fully-connected (FC) network and a hub-and-spoke (HS) network for its operations. There are three cities in the airline's network, denoted by A, B, and H, respectively Note that there are 3 pairs of cities (equivalently 3 markets, including AH, HB, and AB markets) in the network. Under the FC network, the airline provides nonstop flight services for these 3 pairs of cities. Under the HS network, while the airline provides nonstop services for the AH and HB pairs of cities, there is no direct flight between A and B. The passengers traveling from A to B must transfer at H (hub airport). The inverse demand function on each pair of cities (each market) is given by p = 500-T, where p is the price per passenger and T is the number of passengers in each market The airline's cost on a nonstop route segment is given by C-10000 100T, where is the number passengers on a route. Note that there are three nonstop routes under the FC network (AH, HB, and AB), while there are only two nonstop routes under the HS network (AH and HB) (a) Letting q denote the number of passengers in each market, write down the expres- sion for total profit under the FC network. Note that since the airline provides nonstop flight services for all route segments, the market size equals the number of passengers on each route, so that T-T (b) Derive the first-order condition for q and compute the optimal value for q under the FC network. (c) Compute the airline's profit under the FC network by substituting the optimal q to the profit expression (d) Now consider the HS network. Letting g denote the number of passengers in each of the AH and HB markets and Q denote the number of passengers in the AB market (i.e., Qis the number of connecting passengers), write down the total- profit expression under the HC network. Note that T-g holds for AH and HB