Question

War Games Inc., produces games that simulate historical battles. The market is small buy loyal and War Games is the largest manufacturer. The company is now thinking about introducing a new game in honor of the sixtieth anniversary of the outbreak of World War II.

Based on historical data regarding sales, War Games management forecast demand for this game to be P = 50-0.002 Q, where Q denotes unit sales per year and P denoted the price in dollars. The cost of manufacturing (based on royalty payments to the designer of the game and the cost of printing and distribution) is C = 140000 + 10 Q.

a) If the goal of War Games is to maximize profits, calculate the firm's optimal output, price, and profits?

b) if instead, the company's goal is to maximize sales revenues, what will the price, output, and profit be?

Answer 1

P = 50 - 0.002Q

C = 140,000 + 10Q

Marginal cost (MC) = dC/dQ = 10

(a) Profit is maximized when Marginal revenue (MR) equals MC.

Total revenue (TR) = P x Q = 50Q - 0.002Q²

MR = dTR/dQ = 50 - 0.004Q

Equating with MC,

50 - 0.004Q = 10

0.004Q = 40

Q = 10,000

P = 50 - (0.002 x 10,000) = 50 - 20 = 30

TR = P x Q = 30 x 10,000 = 300,000

TC = 140,000 + (10 x 10,000) = 140,000 + 100,000 = 240,000

Profit = TR - TC = 300,000 - 240,000 = 60,000

(b) Revenue is maximized when dTR/dQ = MR = 0.

50 - 0.004Q = 0

0.004Q = 50

Q = 12,500

P = 50 - (0.002 x 12,500) = 50 - 25 = 25

TR = 25 x 12,500 = 312,500

TC = 140,000 + (10 x 12,500) = 140,000 + 125,000 = 265,000

Profit = 312,500 - 265,000 = 47,500