Question

-Hula Products has reintroduced the hula hoop to the world and faces a growing demand for its product in two distinct markets: the United States and Europe. Demand in these markets is: PU=20−.1QUPU​=20−.1QU​ PE=10−.05QEPE​=10−.05QE​ where all quantities are expressed in thousands of units (i.e. QUQU​ = 50 means 50 thousand units). The company has an existing stock of 95 thousand hula hoops. How many should be sent to Europe?

-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: PS=200–2QSPS​=200–2QS​ Ebay Demand: PE=250–5QEPE​=250–5QE​ If your goal is to maximize total revenue, how many books will you sell on ebay?

-Assume Qx = 220 - 4Px + 3Po + 2.5Y. If Px = 150, Po =160, and Y = 120, what is the income elasticity?

Answer 1

(1) Since cost details are not provided, this is a revenue maximization problem.

QU + QE = 95

In US,

Total revenue (TRU) = PU x QU = 20QU - 0.1QU2 = 20 x (95 - QE) - 0.1 x (95 - QE)²

= 1,900 - 20QE - 0.1 x (9,025 - 190QE + QE²)

= 1,900 - 20QE - 902.5 + 19QE - 0.1QE²

= 997.5 - QE - 0.1QE²

In Europe,

Total revenue (TRE) = PE x QE = 10QE - 0.05QE²

Aggregate revenue (TR) = TRU + TRE = 997.5 - QE - 0.1QE² + 10QE - 0.05QE² = 997.5 + 9QE - 0.15QE²

Revenue is maximized when dTRdQE = 0.

dTR/dQE = 9 - 0.3QE = 0

0.3QE = 9

QE = 30 (thousand)

NOTE: As per Answering Policy, 1st question is answered.