12. (8%) Consider a scenario where there is a single train traveling from Taichung to Taipei, making a brief stop at Hsinchu. A passenger intending to cover the entire journey requires two tickets: one from Taichung to Hsinchu and another from Hsinchu to Taipei. Let the price of travel, denoted by p, represent the sum of these two ticket prices.
The number of passengers traveling from Taichung to Taipei is given by
q = 120 - 4p,
where q is the number of passengers. Consider the following two scenarios:
● Scenario I: there are two competing monopolists; one of them decides the ticket price from Taichung to Hsinchu, and the other one decides the ticket price from Hsinchu to Taipei.
● Scenario II: there is one monopolist, who decides both the ticket prices from Taichung to Hsinchu and from Hsinchu to Taipei.
Assume the operation cost is zero for monopolists in both scenarios. Which of the following statements is (are) correct?
(A) The consumers are strictly better in Scenario I comparing Scenario II.
(B) The consumers are strictly better in Scenario II comparing Scenario I.
(C) The price of travel is strictly lower in Scenario I comparing Scenario II.
(D) The price of travel is strictly lower in Scenario II comparing Scenario I.
(E) None of the above.