Question

Playland at Pacific National Exhibition is an amusement park offering 31 different rides (including 4 rollercoasters and 1 water ride). The guests who are 48” or taller can go on any ride they want and so they get more value from visiting the park; let us say their individual demand is given by P = 5 – 0.25qO, where P is the price per ride ($ per ride) and qO is the number of the rides (per day) (the subscript O stands for “One Day;” that’s how the park calls its passes for the guests who are 48” or taller). The guests who are under 48” are not allowed on certain rides so they get less value from visiting the park; let us say their individual demand is given by P = 4 – 0.25qJ, where P is the price per ride ($ per ride) and qJ is the number of the rides (per day) (the subscript J stands for “Jr. One Day;” that’s how the park calls its passes for the guests under 48”). Assume it costs the park flat ¢25 per guest to operate a single ride, and it costs the park flat ¢75 to issue a single ticket to a ride. Assume there are 500 guests 48” or taller and 500 guests under 48” on an average day. We can consider Playland a monopolist in Vancouver.

If Playland employed a second-degree price discrimination scheme (single ride tickets are issued, each rider receives a book of tickets [qO or qJ]),

10. what would be the size qO of a package for guests 48” or taller (number of rides with a One Day admission)?

11. what would be the price TO of a package for guests 48” or taller ($ for a One Day admission)?

12. what would be the size qJ of a package for guests under 48” (number of rides with a Jr. One Day admission)?

13. what would be the price TJ of a package for guests under 48” ($ for a Jr. One Day admission)? 14. what is Playland’s profit on an average day ($ per day)? Assume zero fixed cost.

Answer 1