As the buyer for your business, you can choose to buy an extended warranty for each new computer for $200 each. During this period, each computer will experience either a minor ($100) or major ($500) repair bill. Repairs for each computer under warranty are reduced by 50% to $50 or $250. Assume the computer company wants to make as much money as possible, and you wish to spend as little as possible. What is your optimal strategy?
A) Never buy the warranty.
B) Always buy the warranty.
C) Buy the warranty for less than half of the computers.
D) Buy the warranty for more than half of the computers.

Question

Quizplus · Accepted Answer

If we never buy the warranty (option A), we will have to pay the full repair cost whenever a computer needs a repair. If we always buy the warranty (option B), we will pay the same amount of money for the warranty as we would for the average repair cost, which comes out as a break-even strategy, but it wouldn't be optimal for the business to spend that much money.

If we buy the warranty for all computers, we would pay $200 per computer for a total of $20,000 and have to pay only $50 or $250 in the event of a repair, which would be reduced by 50%. Given that half of the repairs will cost $100, and the other half will cost $500, the expected cost of repairs per computer would be $300. Thus, buying the warranty for all computers would not be the most optimal choice.

If we never bought the warranty, we would expect to pay an average of $300 per computer for repairs. However, since half of the repairs will cost only $100, buying the warranty for all computers would not provide us with any savings, and is not the best option.

By buying the warranty for less than half of the computers, we can minimize our cost. Since the expected cost of repairs per computer is the same as the cost of the warranty ($200), if we buy the warranty for only half of the computers, our expected repair costs would be $150 per computer. This gives our business a chance to reduce costs while still having a financial safety net in case of repairs.

As the Buyer for Your Business, You Can Choose to Buy