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Using Expected Payoff to Decide on a Product Warranty
A practical application of expected payoff is the decision of whether to purchase a warranty for a product, like a washing machine. The outcome is uncertain because the owner does not know if the appliance will fail. The decision can be made by calculating and comparing the expected payoffs of the two choices: buying the warranty versus not buying it. This calculation would factor in the estimated probability of a breakdown and the potential cost of repairs against the known cost of the warranty.
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Introduction to Microeconomics Course
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CORE Econ
Ch.4 Strategic interactions and social dilemmas - The Economy 2.0 Microeconomics @ CORE Econ
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General Calculation of Expected Payoff
A company is deciding whether to launch a new product. The marketing department provides the following analysis:
- If the launch is successful, the company will earn a profit of $5 million.
- If the launch fails, the company will incur a loss of $2 million.
- Based on market research, there is a 40% probability of success and a 60% probability of failure.
Assuming the company makes decisions based on maximizing the weighted average of all possible outcomes, what is the most rational course of action?
Investment Decision Analysis
Farmer's Planting Decision
A company is deciding between two mutually exclusive projects, Project X and Project Y. An initial analysis reveals that Project X has a significantly higher probability of success than Project Y. Based solely on this information, a rational, risk-neutral decision-maker should choose Project X to maximize their expected payoff.
A venture capitalist is evaluating four different startup investment opportunities. Match each opportunity, described by its potential outcomes and their probabilities, with its correct expected payoff.
A software company is considering adding a new feature. Market analysis suggests a 30% chance the feature will be a major success, generating $100,000 in profit; a 50% chance it will be moderately successful, generating $20,000 in profit; and a 20% chance it will fail, resulting in a loss of $40,000. The expected payoff of developing this feature is $____. (Enter a whole number without commas or dollar signs).
Critique of a Decision-Making Process
A manager needs to make a rational decision between two different investment strategies, where the final profit for each strategy is uncertain. Arrange the following steps into the correct logical sequence they should follow to determine the best strategy by comparing the weighted average of all possible results.
A firm is deciding between two mutually exclusive projects. Project A has a 70% chance of earning $10 million and a 30% chance of losing $5 million. Project B has a 40% chance of earning $20 million and a 60% chance of losing $6 million. The firm initially determines that Project A is the better choice by comparing the weighted average of all possible outcomes. Which of the following independent changes to the scenario would reverse this decision, making Project B the more rational choice?
Critique of a Business Expansion Analysis
Learn After
Laptop Warranty Decision
You are considering a one-year extended warranty for a new appliance that costs $100. There is a 20% probability that the appliance will need a major repair during the year, which would cost $600. If it does not break, the repair cost is $0. Based solely on minimizing expected costs, what is the most financially rational decision?
Warranty Decision Break-Even Point
An individual purchases a one-year, $150 warranty for a new television. They estimate there is a 30% chance the television will require a repair that would cost $600 without the warranty. At the end of the year, the television has not needed any repairs. The individual concludes that buying the warranty was a poor financial decision because they 'wasted' $150. Which statement best evaluates this conclusion from a probabilistic decision-making perspective?
A person is considering whether to purchase a $75 extended warranty for a new electronic device. They have determined that if the device fails, the cost to repair it will be $400. To make a financially rational decision based on expected outcomes, what is the most critical piece of information they still need?
A consumer is buying a new tablet and is presented with two warranty options. The tablet has a 20% chance of needing a repair within the warranty period, which would cost $400.
- Plan A: A one-time fee of $90 that covers the full cost of any repair.
- Plan B: A one-time fee of $50, plus a $100 deductible that must be paid only if a repair is needed.
Based on a purely financial calculation of expected costs, which of the following is the most rational choice?
Multi-Failure Scenario Warranty Decision
A consumer is buying a new smartphone and is offered a one-year warranty for $150. Based on historical data, there is a 10% chance the phone will require a major repair during that year, which would cost $800. A calculation shows that the expected cost of repairs without the warranty is $80. Despite this, the consumer decides to purchase the $150 warranty. Which statement best evaluates this consumer's decision?
A consumer is deciding whether to buy a $50 one-year warranty for a new coffee machine. They estimate there is a 15% chance the machine will break, requiring a $200 repair. Based on these numbers, the expected cost of going without the warranty is $30 (0.15 * $200), which is less than the $50 warranty price, so they initially decide against it. Which of the following new pieces of information would be most likely to make purchasing the warranty the more financially sound decision?
A consumer is deciding whether to buy a $150 warranty for a new drone. They estimate a 40% probability of a crash that would require a $500 repair. The consumer reasons as follows: 'My expected loss from a crash is $200 (0.40 * $500), but my expected gain from not crashing is $300 (0.60 * $500). Since the expected gain is higher than the expected loss, I will not buy the warranty.' What is the primary error in this line of reasoning?