Question

QUESTION 14 Use the table below to create a nonlinear model based on the table to answer the following question(s). The Atlas Movies Theater is planning to reprice their ticket rates to maximize revenues. They have three classes of tickets: Classic, Silver, and Gold. The table below provides information on the average ticket sales, revenue and price elasticity on demand. They have a total seating capacity of 300. The table also provides the price range within which they plan to reduce their ticket rates. Atlas Movie Theater Ticketing Ticket Class Current Rate Average Daily Sold Elasticity Price Range Classic Silver Gold 8.45 13.25 17.5 150 80 30 -1.3 -2.25 -1.1 6.5 11.5 15.5 7.5 12.5 16.5 Total Capacity 300 According to the nonlinear model, what is the new price for Silver tickets? O $12.06 O $7.40 $12.50 O $12.17

Answer 1

Answer:

$12.06

reason: As a range of price is given for the new consideration, it is easier to consider each option and select the one that yields maximum revenue.

Formula: Ed = (Change in quantity)/ (Change in price) * (original price/ original quantity)

a) new price = $12.06:
-2.25 =  (Change in quantity)/ -1.19 * (13.25/80) : So, (Change in quantity) = 16.17.
  New quantity = 80 + 16.17 = 96.17 seates are not divisible. So the nearest quantity = 96
Revenue would be: 96*12.06 = $1157.76

b) new price = $7.40: Although this price would create the maximum revenue because of high elasticity of demand of Silver class, this price is below the range under consideration. (range of new price = $11.50 - $12.50)
Also, the new quantity would be 339 which exceedss the theater capacity of 300
(-2.25 = (Change in quantity)/5.85 * (13.25/80). New quantity would be 159;
total seats would be: 159+180 = 339 (*) this option is not viable

c) new price = $12.50:
-2.25 = (Change in quantity)/ -0.75 * (13.25/ 80) So, (Change in quantity) = 10.19
New quantity = 80 + 10.19 = 90.19, nearest number = 90
Revenue would be: 90*12.50 = $1125.

d) new price = $12.17:
-2.25 = (Change in quantity)/ 1.08 * (13.25/80) So, (Change in quantity) = 14.67, nearest number = 15
New quantity would be 80 + 15 = 95
Revenue woud be 95 * 12.17 = $1156.15

Thus the highest revenue is from option (a) with the price $12.06.

Verification. The price of Silver tickets is highly elastic. It has the highest elasticity of the three types of tickets, too. So, it only makes sense to reduce the price of the tickets to the lowest possible price in order to earn maximum revenue because the property of elasitcity states that in the case of elastic demand, when price is decreased, the revenue increases.

Therefore, out of the three feasible options, $12.06 is the minimum price. It will fetch maximum revenue.

Again, the lowest in the range under consideration ($11.50) would have brought the maximum revenue.