Question

1. (Using Excel) In the Stanford Stadium problem with 60000 seats and two prices (General Public vs. Student), suppose each General Public ticketholder also buys $20 in concessions resulting in a $10 contribution margin, and each Student ticketholder buys $10 in concessions resulting in a $5 contribution margin. What are the prices that maximize total contribution? Write out your formulation.

General Public: d_g (p _g) = (120000 - 3000 p _g )⁺

Student:   d_s (p_s) = (20000 -1250p_s) ⁺

Answer 1

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