Question

A symphony orchestra is preparing to stage a short concert series. The first program in the series consists of music by Berlioz and Tchaikovsky, while the second program comprises music by Bartok and Stravinsky. The potential audience for the series can be thought of as divided into four,equal-sized groups. Members of the first group, whose tastes tend to the romantic, would be willing to pay up to $40 for a ticket to the first concert and up to $20 for a ticket to the second concert.Members of the second group, whose tastes tend more to the neo-classical, have the opposite preference: they would pay up to $20 for a ticket to the first concert and up to $40 for a ticket to the second concert. Members of the third group, confirmed Tchaikovsky lovers, would pay as much as$45 for a ticket to the first concert, but only $5 for a ticket to the second concert. Finally, members of the fourth group, who pride themselves on their sophisticated taste, would pay as much as $45 for a ticket to the second concert, but only $5 for a ticket to the first concert. This information is summarized in Table 2

While answering these questions, please clearly state your assumptions (if any) and your justification for those assumptions.

1. What is the best price to charge for each concert if you are not offering a single ticket for the concert series?
2. What is the best price to charge for the concert series if you are not offering tickets for each concert separately?
3. Now suppose you offer a single ticket for the concert series in addition to offering tickets for each concert separately. What prices will you charge for the series and each concert?
4. Now consider the case titled "Multiproduct Pricing"? What is the best price to sell each product individually? Can the company do better by bundling?

PATRON TYPE	BERLIOZ/TCHAIKOVSKY	BARTOK/STRAVINSKY
ROMANTIC	40	20
NEO-CLASSICAL	20	40
TCHAIKOVSKY	45	5
SOPHISTICATE	5	45

Answer 1

Assuming marginal costs for a ticket are 0 (Since all the seats and theatre are fixed cost)
Let the number of people in each of the 4 equal sized groups be n

a) The best price to charge for the first concert i.e. with the maximum profit will be 40 and 2 groups will attend i.e. romantic and tchaikovsky for a total profit of 40*2n = 80n from first concert(If we price it at 20, 3 groups will attend but profit will only be 60n)

Similarly the best price to charge for the second concert will be 40 and 2 groups i.e. Neoclassical land sophisticate will attend it for a total profit of 80n.

Therefore the total profit will be 80n+80n=160n

b) To get the best price for the concert series, we note that the first 2 groups romantic and neo-classical value the concert series ticket at 60 (60+40) and the other 2 at 50$

Now if we price it at 60$, we'll have 2 groups buying the concert series ticket for a total profit of 120n.

However, if we price the concert series ticket at 50$, all 4 groups willl buy the concert series ticket and the total profit will be 50*4n= 200n$

c) Now, if we were to have a concert series ticket and also the concert ticket for each of the 2 concerts seperately, we can maximize profit by having the bundle of 60$ while also pricing each of the individual tickets at 45$

With this, the first 2 groups will buy the concert series ticket at 60$ and the other 2 groups will buy individual concert ticket of one of the concerts for 45$ (Tchaikovsky group for first concert and sophisticate group for 2nd concert)

This allows to get the maximum out of the consumer's willingness to pay.

The total profit willl then be 60*2n from series ticket and 45n+45n from individual series tickets for a total profit of 210n

Thus the profit is maximized by bundling and also having a seperate individual ticket.

Hope it helps. Do ask for any clarifications if required.