Jim Sellers Is Thinking About Producing A New Type Of Electr ✓ Solved
Jim Sellers Is Thinking About Producing A New Type Of Electric Razor F
Jim Sellers is considering producing a new type of electric razor for men. The decision involves evaluating the potential market conditions and the value of conducting research studies such as surveys or pilot studies. The expected payoffs depend on whether the market is favorable or unfavorable, with associated probabilities and costs. This scenario requires constructing decision trees with probability assessments and payoffs, calculating expected monetary values (EMVs), and determining the optimal decision for Jim based on the analysis.
Sample Paper For Above instruction
Introduction
Decision-making under uncertainty is a vital aspect of strategic business planning. In the context of Jim Sellers contemplating launching a new electric razor, it’s essential to analyze the potential outcomes, incorporate the value of additional information through research, and evaluate the cost-benefit trade-offs. This paper presents a detailed decision analysis, including constructing decision trees, calculating revised probabilities, assessing the value of information, and deriving the best decision for Jim.
Step 1: Constructing the Decision Tree Without Research
Initially, we analyze the decision scenario without any research. Jim's choices are either to produce the razor immediately or to abstain. If he produces, the market conditions determine the outcome. The market is favorable with a probability of 0.5, yielding a return of $100,000, and unfavorable with a probability of 0.5, resulting in a loss of $60,000.
The decision tree structure:
- Decision to produce or not.
- If producing, chance outcomes:
- Favorable market (probability 0.5), payoff = $100,000.
- Unfavorable market (probability 0.5), payoff = -$60,000.
Expected monetary value (EMV) of producing without research:
\[ \text{EMV} = (0.5 \times 100,000) + (0.5 \times -60,000) = 50,000 - 30,000 = \$20,000 \]
Choosing not to produce yields zero payoff, so the optimal decision without research is to produce since the EMV is positive.
Step 2: Revising Probabilities Considering the Market Conditions
Jim’s initial belief is that the chance of a favorable market is 0.5, and unfavorable is 0.5. However, if Jim obtains additional information from research, these probabilities can be updated based on the test results using Bayesian inference. For this, we utilize likelihood ratios derived from the survey and pilot study data.
For the survey:
- Probability of a favorable survey result given favorable market: 0.7.
- Probability of a favorable survey result given unfavorable market: 0.2.
- Prior probability of favorable market: 0.5.
Bayesian update for probability of the market given a favorable survey:
\[
P(\text{Favorable market} | \text{Favorable survey}) = \frac{P(\text{Favorable survey} | \text{Favorable market}) \times P(\text{Favorable market})}{P(\text{Favorable survey})}
\]
where
\[
P(\text{Favorable survey}) = 0.7 \times 0.5 + 0.2 \times 0.5 = 0.35 + 0.10 = 0.45
\]
Thus,
\[
P(\text{Favorable market} | \text{Favorable survey}) = \frac{0.7 \times 0.5}{0.45} \approx 0.778
\]
and
\[
P(\text{Unfavorable market} | \text{Favorable survey}) = 1 - 0.778 = 0.222
\]
Similarly, for an unfavorable survey result:
- Probability of unfavorable survey given favorable market = 1 - 0.7 = 0.3.
- Probability of unfavorable survey given unfavorable market = 0.8.
- Prior similar as above, the total probability:
\[
P(\text{Unfavorable survey}) = 0.3 \times 0.5 + 0.8 \times 0.5 = 0.15 + 0.40 = 0.55
\]
Posterior probability of favorability given unfavorable survey:
\[
P(\text{Favorable market} | \text{Unfavorable survey}) = \frac{0.3 \times 0.5}{0.55} \approx 0.273
\]
and unfavorable market:
\[
P(\text{Unfavorable market} | \text{Unfavorable survey}) = 1 - 0.273 \approx 0.727
\]
Thus, the survey provides informative updates to the market probabilities, guiding the subsequent decisions.
Step 3: Constructing Decision Tree Including Research Options
Jim's options now include:
1. Conduct no research — decide based on initial probabilities.
2. Conduct a survey at a cost of $5,000, then decide whether to produce based on survey results.
3. Conduct a pilot study at $20,000, which is more accurate but costlier.
For the survey, after observing the result, Jim can choose to produce or not. The EMVs are calculated based on updated probabilities and payoffs.
For the pilot study, similar Bayesian updates are necessary, which involve more detailed likelihood ratios, but the core principles mirror the survey analysis, with higher accuracy.
The expected payoffs incorporate costs of research, potential payoffs from production, and the probability-adjusted market conditions.
Summarized Calculations of EMV with Survey:
- If the survey is favorable, the probability of a favorable market is approximately 0.778, leading to an expected payoff:
\[
EMV_{favorable} = (0.778 \times 100,000) + (0.222 \times -60,000) \approx 77,800 - 13,320 = \$64,480
\]
subtract the survey cost of \$5,000 for a net of:
\[
\$64,480 - \$5,000 = \$59,480
\]
- If the survey is unfavorable, the probability of a favorable market drops to 0.273, leading to an expected payoff:
\[
(0.273 \times 100,000) + (0.727 \times -60,000) \approx 27,300 - 43,620 = -\$16,320
\]
subtracting the survey cost yields:
\[
-16,320 - \$5,000 = -\$21,320
\]
Expected value after conducting the survey:
\[
EMV_{survey} = (0.45 \times 59,480) + (0.55 \times -21,320) \approx 26,766 - 11,727 = \$15,039
\]
Given this, Jim would proceed with production if the survey is favorable, but may avoid it if unfavorable, based on the calculated EMV.
The pilot study results, with higher accuracy, would lead to more precise decisions, but at higher costs.
Step 4: Computing EMVs and Deciding
The overall value of the options, considering the costs and the updated probabilities, guides Jim to select the path with the highest EMV. The calculations indicate:
- Producing without research yields an EMV of \$20,000.
- Performing the survey yields an EMV of approximately \$15,039 after considering costs.
- Conducting the pilot study might offer an even higher refined EMV due to increased accuracy but with greater expense, potentially increasing overall benefits if the market is favorable.
The decision analysis suggests that Jim should produce directly without research if he is risk-neutral solely based on expected value calculations, since the EMV exceeds the costs of the research. However, if Jim is risk-averse or prefers certainty, conducting the survey may provide valuable information. The pilot study, given its higher accuracy, could be justified if Jim places significant weight on the value of information and can absorb the cost.
Conclusion
The optimal decision balances the expected payoff and associated costs. Based on the analysis, Jim's best choice—without considering risk preferences—is to proceed with production directly, as the EMV is positive and exceeds the costs of research. The survey, while helpful in refining probabilities, presents a lower EMV, suggesting that immediate action might be more advantageous unless Jim highly values the reduced uncertainty. Incorporating more detailed Bayesian updates and considering the higher cost and potential benefit of the pilot study could further fine-tune this decision.
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