Question

1. War Game, Inc. produces games that simulate historical battles. The market is small but loyal, and War Game is the largest manufacturer. It is thinking about introducing a new game in honor of the eightieth anniversary of the end of World War II. Based on historical data regarding sales, War Game management forecasts demand for this game to be P = 50 - 0.002Q, where Q denotes unit sales per year, and P denotes price in dollars. The cost of manufacturing (based on royalty payments to the designer of the game, and the costs of printing and distributing) is C = 140,000 + 10Q.

(a) If the goal of War Game is to maximize profit, calculate the optimal output and price.?

(b) If instead the company’s goal is to maximize sales revenue, what is its optimal price and quantity?

Answer 1

1.a) If the goal is to maximize profit then it will produce at the point where MR=MC. Profit maximizing price will be set at the point where profit-maximizing quantity lies on the demand curve.

The demand equation is given as,

P = 50 - 0.002Q

Multiplying both sides by Q we get,

PQ = Total revenue (TR) = 50Q - 0.002Q²

Or, MR = d(TR)/dQ = 50 - 0.004Q

And, Total cost, C = 140,000+10Q

Or, MC = d(C)/dQ = 10

Setting MR = MC we get,

50 - 0.004Q = 10

Or, 0.004Q = 40

Or, Q = 40/0.004 = 10,000

Now, from the demand equation we get, when Q = 10,000

P = 50 - (0.002*10,000) = 30

Therefore, optimal output is 10,000 units and price is $30 per unit.

B) If the company's goal is to maximize sales revenue, then d(TR)/dQ will be equal to 0. It means MR = 0.

Therefore, MR = 50 - 0.004Q = 0

Or, 0.004Q = 50

Or, Q = 12,500

Now from demand equation we get when Q = 12,500

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

Therefore, optimal quantity is 12,500 units and price is $25 per unit.