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 two-part tariff scheme (the park may choose to ticket each ride, or they may choose to let people go on as many rides [at zero price per ride] as they want and only charge the gate fee for the access to the rides),

6. what would be the gate entry fee for guests 48” or taller ($ per guest)?

7. what would be the gate entry fee for guests under 48” ($ per guest)?

8. what would be the price per ride ($ per ride)?

9. what is Playland’s profit on an average day ($ per day)? Assume zero fixed cost.

Answer 1

6) Gate entry fee for guests 48" or taller-

Given eq. for 48" or taller is P=5-.25qO

Let qO=1 therefore, P=5-.25*1

P=4.75$

NOW, if park may choose to ticket each ride then P=4.75$

And, if they choose so many rides(at zero price per ride) then, P= 4.75*31=147.25$ (no. of total rides is given 31).

7) Gate entry fee for guests under 48"-

Given eq for under 48" is P=4-.25qO

let qO =1 then, P=4-.25*1=3.75$

Now, park may choose to ticket each ridethen P=3.75$

And,if they choose so many rides(at zero per ride)then,P=3.75*31=116.25$

8) Price per Ride-

Price per ride for 48"or taller is

P=5-.25*1

P= 4.75$

Price per ride for under 48" is

P=4-.25*1

P=3.75$

9) Playland's profit on an avg. day (assuming zero fixed cost)

no. of guests are 500

Price as per rides = 147.25 for 48" or taller

Therefore, 147.25*500=73625

Price per rides = 116.25 for under48"

Therefore,116.25*500= 58125

So, Total profit = 73625+58125= 131750