Question

Your company receives 40 excess copies of a book. You plan to sell these books in two markets: directly in the store or sell them on ebay. Here are the two demand equations: Store Demand: P_S = 200 – 2Q Ebay Demand: P_E = 250 – 5Q If your goal is to maximize total revenue, how many books will you sell on ebay?

Answer 1

For Store:

PS = 200 - 2QS

Total revenue (TRS) = PS x QS = 200QS - 2QS²

For Ebay:

PE = 250 - 5QE

Total revenue (TRE) = PE x QE = 250QE - 5QE²

Aggregate revenue (TR) = TRS + TRE = (200QS - 2QS²) + (250QE - 5QE²)

TR = (200QS - 2QS²) + [250 x (40 - QS) - 5 x (40 - QS)²]

TR = (200QS - 2QS²) + [10,000 - 250QS - 5 x (1,600 - 80QS + QS²)]

TR = 200QS - 2QS² + 10,000 - 250QS - 8,000 + 400QS - 5QS²

TR = 350QS - 7QS² + 2,000

Aggregate revenue is maximized when dTR/dQS = 0.

dTR/dQS = 350 - 14QS = 0

14QS = 350

QS = 25

QE = 40 - QS = 40 - 25 = 15