Hugh is considering transitioning to a new job next year. He will either keep his current job which pays a net income of $70,000 or switch to a new job. If he changes jobs, his net income will vary depending on the state of the economy. He estimates that the economy will be Strong with 30% chance ( $85,000 net income), Average with 30% chance ($74,000 net income), or Weak with 40% chance ($63,000 net income. 

What is the optimal decision based on the Hurwicz approach with α=0.3. a) new job. b) current job. c) none of the answers provided is correct. d) weak economy. e) strong economy.


The **Hurwicz criterion** is a decision-making approach used under uncertainty that combines optimism and pessimism through a parameter, $ \alpha $, which reflects the decision maker's level of optimism. Here, $ \alpha = 0.3 $, which suggests that 30% weight is placed on the best possible outcome (optimism), and the remaining 70% weight ($ 1 - \alpha = 0.7 $) is placed on the worst possible outcome (pessimism).

Let's break it down step by step:

### 1. **Current Job:**
Hugh's current job pays a fixed net income of $70,000 regardless of the economy. Since the outcome is fixed, there's no need to apply the Hurwicz criterion:
\[
\text{Current job's value} = 70,000.
\]

### 2. **New Job:**
The new job's income depends on the state of the economy:

- **Strong economy** (best outcome): $85,000.
- **Weak economy** (worst outcome): $63,000.
- The probability of the economy being average or strong does not affect the calculation directly for the Hurwicz approach.

The **Hurwicz criterion** for the new job is calculated as:
\[
\text{Hurwicz value} = \alpha \times (\text{best outcome}) + (1 - \alpha) \times (\text{worst outcome}).
\]
Substituting the values:
\[
\text{Hurwicz value} = 0.3 \times 85,000 + 0.7 \times 63,000.
\]
\[
\text{Hurwicz value} = 25,500 + 44,100 = 69,600.
\]

### 3. **Comparison:**
- Current job's value: **$70,000**.
- New job's Hurwicz value: **$69,600**.

### Conclusion:
The **current job** has a higher value ($70,000) compared to the new job ($69,600) based on the Hurwicz criterion with $ \alpha = 0.3 $. Thus, the optimal decision is to keep the current job.

The correct answer is: **b) current job**.

Would you like further details on this method, or do you have any questions?

Here are 5 related questions to explore:
1. How does the Hurwicz criterion compare to the maximax or maximin approaches?
2. How would the decision change if $ \alpha $ was 0.5 instead of 0.3?
3. What if the probabilities of economic states were different (e.g., 50% weak, 25% strong)?
4. How would the expected value approach influence the decision?
5. Can the Hurwicz criterion be applied to other decision-making scenarios, like investments?

**Tip:** The Hurwicz criterion balances optimism and pessimism, so adjusting $ \alpha $ can reflect your personal attitude toward risk.

Hugh is considering transitioning to a new job next year. He will either keep his current job which pays a net income of $70,000 or switch to a new job. If he changes jobs, his net income will vary depending on the state of the economy. He estimates that the economy will be Strong with 30% chance ( $85,000 net income), Average with 30% chance ($74,000 net income), or Weak with 40% chance ($63,000 net income). What is the optimal decision based on the Hurwicz approach with α=0.3. a) new job. b) current job. c) none of the answers provided is correct. d) weak economy. e) strong economy.

Explore the application of the Hurwicz criterion to a job transition decision. Hugh must decide whether to keep his current job ($70,000 net income) or switch to a new job where his income depends on the economy. Learn how to calculate the Hurwicz value with α=0.3 to find the optimal decision. Suitable for Grades 11-12 and college-level decision theory courses.

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