Question

Question 7

Madeleine is the owner-manager of a small 200-seat theater for improv-comedy shows in downtown Chicago. The usual ticket price for the evening 90-minute show is $17, and this usually fills up about 65% of the capacity. You suggest experimenting with a discounted price of $13 for a while, and this improves attendance to about 85% of theater capacity.

Madeleine's marginal cost of each patron attending the show is zero.

Assuming demand is linear, and assuming all other demand related factors remained unchanged during the price experiment (and are expected to remain unchanged over the rest of the season), in order to maximize her profits from ticket sales, you could advise her that the optimal price is likely to be:

Group of answer choices

(a) Less than $10

(b) About $10, as this would fill the theater to full capacity

(c) Between $10 and $13

(d) Between $13 and $17

(e) Above $17

(f) There is not enough information from this one price experiment to determine optimal price; more experiments need to be run

Answer 1

Here,

At Price Level = $17, Capacity = 65%

At Price Level = $13, Capacity = 85%

The Graph is as below,

Here, Total Seats = 200,

At $17, Capacity Utilisation = 65%

So, Seats Filled = .65*200 = 130 seats

So Profit,

= 130*$17 = $2210

At $13, Capacity Utilisation = 85%

So, Seats Filled = .85*200 = 170 seats

So Profit,

= 170*$13 = $2210

At $10, Capacity Utilisation = 100%

So, Seats Filled = 1*200 = 200 seats

So Profit,

= 200*$10 = $2000

Now the Profit at 65% and 85% is same and higher than 100% capacity

Now if we Follow the chart and plot at $15, it would come to around 75%

At $15, Capacity Utilisation = 75%

So, Seats Filled = .75*200 = 150 seats

So Profit,

= 150*$15 = $2250

So the answer is choice d, between $13 and $17