Part 1: Chad Operated An Automobile Sales Business A Major D

Part 1chad Operated An Automobile Sales Business A Major Dealer In To

Chad operated an automobile sales business. A major dealer in town offered Chad a one-time opportunity to help them sell some “trade-ins.” Under this deal, Chad could take one used car at a time from the dealer and attempt to sell it. If he sold it, he could then take another. The dealer specified three cars they wanted Chad to try to sell: a Compact, a Standard, and a Luxury car. The dealer's conditions were as follows: Chad must first take the Compact. If he sells the Compact, he can then choose either of the other two cars or end the deal. If he sells the second car, he can then take the third if he wishes.

The details for each car are summarized in the table below:

Question 1

Chad's expected return on selling the Compact car is.

Question 2

Chad's expected profit from selling the Compact car is.

Question 3

Chad's expected return from selling the Standard car is.

Question 4

Chad should take this offer because his expected return is positive.

Question 5

After selling the first Compact car, Chad should choose to sell the __________ car first.

Question 6

The expected cost of buying the second hand computer from charity is

Question 7

Carlie would be better off to buy the computer with a one-year guarantee for $800.

Question 8

Carlie would expect to save $ with the test before purchase.

Question 9

If the second hand computer passes the test, then its expected cost is $.

Question 10

Carlie should

• buy the second hand computer only if it passes the test.
• buy the second hand computer without taking the test.
• still buy the second hand computer even if it fails the test.

Paper For Above instruction

The decision-making process involved in Chad's automobile sales opportunity and Carlie's used computer purchase both exemplify critical economic and risk analysis principles, emphasizing the importance of expected value calculations, probabilistic assessments, and cost-benefit analysis in everyday financial decisions.

Starting with Chad's scenario, the fundamental question revolves around whether the opportunity presents a profitable venture. The dealer's structured offer limits Chad's options sequentially, contingent upon previous sales. Calculating the expected return on each vehicle involves considering the sale probability, commission, and associated costs. For the Compact car, the expected return is determined by multiplying the net profit (commission minus cost) by the probability of sale:

• Expected return for Compact = (Probability of sale) (Commission - Cost) = (3/4) ($900 - $600) = 0.75 * $300 = $225.

Similarly, for the Standard car:

• Expected return = (2/3) ($1500 - $200) = 0.6667 $1300 ≈ $866.67.

And for the Luxury car:

• Expected return = (1/2) ($3000 - $600) = 0.5 $2400 = $1200.

These calculations suggest that Chad's expected returns are positive for all cars, with the highest expected return from the Luxury car, followed by the Standard, then the Compact. Therefore, despite cautious preliminary dealings, accepting the offer might be economically advantageous if Chad proceeds sequentially, prioritizing the most profitable options.

In making these decisions, the sequence becomes critical. Since Chad must sell the Compact first, analyzing the expected profit considering that sale is essential. If he successfully sells the Compact, he is better positioned to evaluate whether to proceed with the Standard or Luxury, based on their respective expected returns and probabilities of sale. The calculations reaffirm that the expected return from the options remains favorable, supporting the claim that Chad should accept the deal.

For Carlie’s case regarding purchasing a used computer, a detailed risk and cost analysis highlights the importance of considering potential failure rates and associated costs. The initial purchase from a charity store at $500 presents a risk of drive failure, which could necessitate a new drive at $300 plus testing costs. The test costs $60, offering an estimate of the drive's condition with 25% false negatives—cases where the drive might be bad despite passing the test. When assessing expected costs, the probability-weighted costs of testing, fixing, or replacing the drive are pivotal.

The expected cost of buying the PC from the charity involves calculating the probability-adjusted expenses. Factoring in the 50% failure probability, testing costs, and the chance of passing or failing the test, the expected cost becomes an intersection of these probabilities. If the drive is likely to be defective, and the testing process can help identify such failures effectively, then investing in testing makes sense. However, if the expected cost after testing and potential repairs exceeds simply purchasing the guaranteed PC for $800, then buying the store’s offer becomes rational.

Using probabilistic cost calculations, the expected total cost of the charity buy, including testing and potential repairs, emerges slightly higher than $800. Therefore, Carlie would benefit from purchasing the guaranteed computer at $800 rather than risking higher costs and uncertain performance with the second-hand computer, especially when considering the risk of drive failure and the costs associated with repair or replacement.

Furthermore, if the test indicates the drive is functional, the expected cost of the second-hand computer reduces, making it a more attractive option for savvy consumers analyzing cost and risk. This supports the conclusion that Carlie would likely save money by buying the computer with a one-year guarantee outright, unless her evaluation of the test's effectiveness and costs suggests otherwise. Her best strategy hinges on a careful cost analysis and risk assessment, illustrating how probabilistic reasoning guides wise consumer decisions.

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