Texas Central, a company undertaking the development of a new high-speed passenger rail service between Houston and Dallas, is examining two different kinds of service options. One service option is to provide amenities such as a pantry car with a cafeteria and port outlets for notebook computers, and another service option is to not provide these amenities. Providing amenities might increase ridership because of the additional convenience and comfort. However, the provision of amenities will also cost money to the rail provider, which will then be transferred to passengers as an increased fare. This might in turn reduce ridership. Transportation analysts have developed the following demand function for the number of passengers who will use the service as a function of a generalized cost measure D and whether or not amenities are provided: V = 6200 40D + 600 * A, where V is the number of passengers who would use the high-speed rail service per day, D is a generalized cost of travel for passengers, and A is a variable which takes the value of 1 if amenities are included as part of the service and zero otherwise. The generalized cost for passengers includes both travel time costs as well as actual fare costs: D = (27)* B + C, where T is the one-way travel time in minutes (T = 75 minutes), C is the fare cost in $, and B is a conversion factor equal to $0.5 per minute (i.e., individuals value one hour of time at $30). D is in effective dollars. a) Consider the case when amenities are not provided (A = 0). What fare should be charged per passenger if the objective is to maximize revenue? What is the corresponding ridership V? b) Next, consider the case when amenities are provided (A = 1). What fare should be charged per passenger if the objective is to maximize revenue? What is the corresponding ridership V? Texas Central, a company undertaking the development of a new high-speed passenger rail service between Houston and Dallas, is examining two different kinds of service options. One service option is to provide amenities such as a pantry car with a cafeteria and port outlets for notebook computers, and another service option is to not provide these amenities. Providing amenities might increase ridership because of the additional convenience and comfort. However, the provision of amenities will also cost money to the rail provider, which will then be transferred to passengers as an increased fare. This might in turn reduce ridership. Transportation analysts have developed the following demand function for the number of passengers who will use the service as a function of a generalized cost measure D and whether or not amenities are provided: V = 6200 40D + 600 * A, where V is the number of passengers who would use the high-speed rail service per day, D is a generalized cost of travel for passengers, and A is a variable which takes the value of 1 if amenities are included as part of the service and zero otherwise. The generalized cost for passengers includes both travel time costs as well as actual fare costs: D = (27)* B + C, where T is the one-way travel time in minutes (T = 75 minutes), C is the fare cost in $, and B is a conversion factor equal to $0.5 per minute (i.e., individuals value one hour of time at $30). D is in effective dollars. a) Consider the case when amenities are not provided (A = 0). What fare should be charged per passenger if the objective is to maximize revenue? What is the corresponding ridership V? b) Next, consider the case when amenities are provided (A = 1). What fare should be charged per passenger if the objective is to maximize revenue? What is the corresponding ridership V
