3. (Ancillary Revenue) Stanford Stadium has been repaired so that it seats 60,00

Question

3. (Ancillary Revenue) Stanford Stadium has been repaired so that it seats 60,000 people. Now assume that, on average, each member of the general public will consume $20 worth of concessions, resulting in a $10 contribution margin, while each student only consumes $10, resulting in a $5 contribution margin. Assuming no cannibalization, what are the prices for students and the general public that maximize total contribution margin (including ticket revenue). Complete in Excel

Price-Response functions:

General Public: dg(pg)= (120,000-3,000pg)

Students: ds(ps)= (20,000-1,250ps)

where pg is the price charged to the general public and ps is the student price

Explanation / Answer

Marginal cost for general public, MCpg = $20

Marginal cost for students, MCps = $10

Demand of general public, dg = 120,000 - 3,000pg

pg = (120,000 - dg) / 3,000

Total revenue from general public, TRpg = pg x dg = (120,000dg - (dg)2) / 3,000

Marginal revenue from general public, MRpg = dTRpg / d(dg) = (120,000 - 2dg) / 3,000

Again,

Demand of students, ds = 20,000 - 1,250ps

ps = (20,000 - ds) / 1,250

Total revenue from students, TRpg = ps x ds = (20,000ds - (ds)2) / 1,250

Marginal revenue from students, MRps = dTRps / d(ds) = (20,000 - 2ds) / 1,250

Contribution margin is maximized when each group equates its MR with MC.

(i) MCpg = MRpg

20 = (120,000 - 2dg) / 3,000

60,000 = 120,000 - 2dg

dg = (120,000 - 60,000) / 2 = 30,000

pg = (120,000 - dg) / 3,000 = (120,000 - 30,000) / 3,000 = 90,000 / 3,000 = 30

(ii) MCps = MRds

10 = (20,000 - 2ds) / 1,250

12,500 = 20,000 - 2ds

ds = (20,000 - 12,500) / 2 = 3,750

ps = (20,000 - ds) / 1,250 = (20,000 - 3,750) / 1,250 = 16,250 / 1,250 = 13

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