In the scenario where price is $200 yields 10,000 units and price $75 yields 20,000 units, at which price should the company set to maximize profits?

• A. $150
• B. $125
• C. $75
• D. $200

Answer: (D)

Profit depends on both price and how many units you can sell, and the goal is to maximize the difference between revenue and costs. If we denote unit cost as c, the profit at the higher price (selling 10,000 units) is 200 × 10,000 minus costs, i.e., 2,000,000 − 10,000c. At the lower price (selling 20,000 units) the profit is 75 × 20,000 minus costs, i.e., 1,500,000 − 20,000c. Compare the two: (2,000,000 − 10,000c) − (1,500,000 − 20,000c) = 500,000 + 10,000c, which is positive for any nonnegative cost per unit. Therefore the higher price yields higher profit, making the price of 200 the profit-maximizing choice. The other prices would produce lower profits under any realistic unit cost.