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 Minimax Regret criterion?  a) new job. b) none of the answers provided is correct. c) weak economy. d) strong economy. e) current job

The **Minimax Regret criterion** helps in decision-making under uncertainty by choosing the option that minimizes the maximum regret. Here's how to apply the Minimax Regret criterion to this situation:

### Step 1: Construct the payoff table
The payoffs (net income) based on the economy and Hugh's decision are as follows:

| **Economy** | **Current Job** | **New Job** |
|-------------|-----------------|-------------|
| Strong      | $70,000          | $85,000     |
| Average     | $70,000          | $74,000     |
| Weak        | $70,000          | $63,000     |

### Step 2: Calculate the regret table
Regret is the difference between the best possible outcome for each state of the economy and the actual outcome. We compute it by finding the highest payoff for each economic condition and subtracting the payoffs in the table from this value.

1. **Strong economy:**
   - Best payoff = $85,000 (new job)
   - Regret for current job = $85,000 - $70,000 = $15,000
   - Regret for new job = $85,000 - $85,000 = $0

2. **Average economy:**
   - Best payoff = $74,000 (new job)
   - Regret for current job = $74,000 - $70,000 = $4,000
   - Regret for new job = $74,000 - $74,000 = $0

3. **Weak economy:**
   - Best payoff = $70,000 (current job)
   - Regret for current job = $70,000 - $70,000 = $0
   - Regret for new job = $70,000 - $63,000 = $7,000

Thus, the regret table is:

| **Economy** | **Current Job Regret** | **New Job Regret** |
|-------------|------------------------|--------------------|
| Strong      | $15,000                | $0                 |
| Average     | $4,000                 | $0                 |
| Weak        | $0                     | $7,000             |

### Step 3: Find the maximum regret for each option
- Maximum regret for current job = **$15,000**
- Maximum regret for new job = **$7,000**

### Step 4: Apply the Minimax Regret criterion
The Minimax Regret criterion suggests choosing the option with the smallest maximum regret. In this case:

- Current job has a maximum regret of $15,000.
- New job has a maximum regret of $7,000.

Since the **new job** has the smaller maximum regret, the optimal decision based on the Minimax Regret criterion is:

**(a) New Job**.

Would you like further details or explanations on this process?

Here are 5 related questions:
1. What are other decision-making criteria besides Minimax Regret?
2. How is the expected monetary value (EMV) calculated for this decision problem?
3. What is the difference between Minimax and Maximin decision criteria?
4. How does risk tolerance affect decision-making under uncertainty?
5. How would the decision change if the probabilities of the economic states changed?

**Tip:** The Minimax Regret criterion is particularly useful when you want to minimize the feeling of regret after making a decision in uncertain situations.

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 Minimax Regret criterion? a) new job. b) none of the answers provided is correct. c) weak economy. d) strong economy. e) current job.

Explore how to apply the Minimax Regret criterion to a job transition decision under economic uncertainty. Hugh must decide between keeping his current job or switching to a new one based on potential economic outcomes. The problem involves calculating regret and finding the optimal decision using the Minimax Regret formula. Suitable for undergraduate students studying decision theory.

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