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]),

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

Answer 1

In monopolist , second order price discrimination refers to charging different prices for different goods ie bul order etc are charged less than the individfual units of goods.

so as the quantity of rides increases the price reduces per ride .

eg : P = 5 – 0.25qO at qO = 1: P= 4.75 and at qO =2 : p\= 4.5 and so on.

total revenue would be P*qO+ P*qJ of the park since there are different quantities for both the cosnumers.

and cost is 100 ¢ since for every ticket issued the individual would take aride so the cost of operation would be added in the total cost.

TR from first type =5qO – 0.25qO² so MR =5 -0.5qO

TR from second type= 4qJ – 0.25qJ² so MR would be = 4 -0.5qJ

we are given that the additional cost for each side ( both operation and ticket is 1$) =$1 so this is the MC

also for monopoly equilibruim MR=MC

so 1= 5 -0.5qO so qO would be 8

similar;y for qJ the vaalue would be 1= 4 -0.5qJ which gives qJ as 6

so P fro type 1would be $3 ie $5-0.25*8

for type 2 would be $2.5

total revenue from type 1 consumers is $3*8* 500 =$12000

from type 2 =2.5*6 *500= $7500

profit of playland = total revenue - total cost

=  $12000 +7500 - 500(qJ) - 500(qO)

= $19500 - 500(6)-500(8)

=$12500