Let's go through the problem step by step, performing each calculation.

1. Maximax Criterion

• Expand: Max payoff = $350,000
• Maintain Status Quo: Max payoff = $200,000
• Sell Now: Max payoff = $100,000

Maximax Decision: Expand (since $350,000 is the highest maximum payoff).

2. Maximin Criterion

• Expand: Min payoff = $-\$30,000$
• Maintain Status Quo: Min payoff = $100,000
• Sell Now: Min payoff = $100,000

Maximin Decision: Maintain Status Quo (since $100,000 is the highest minimum payoff).

3. Minimax Regret Criterion

• First, calculate the maximum payoff in each state:

  • Good Conditions: Max payoff = $350,000 (from Expand)
  • Poor Conditions: Max payoff = $100,000 (common for Maintain Status Quo and Sell Now)

• Then, calculate the regret for each decision in both states:

  • Expand:
    • Regret (Good) = $350,000 - $350,000 = $0
    • Regret (Poor) = $100,000 - $-\$30,000$ = $130,000
  • Maintain Status Quo:
    • Regret (Good) = $350,000 - $200,000 = $150,000
    • Regret (Poor) = $100,000 - $100,000 = $0
  • Sell Now:
    • Regret (Good) = $350,000 - $100,000 = $250,000
    • Regret (Poor) = $100,000 - $100,000 = $0

• Maximum regrets:

  • Expand: Max regret = $130,000
  • Maintain Status Quo: Max regret = $150,000
  • Sell Now: Max regret = $250,000

Minimax Regret Decision: Expand (since $130,000 is the smallest maximum regret).

4. Expected Value Criterion

• Expand: $\text{Expected Value} = (0.7 \times 350,000) + (0.3 \times -30,000) = 245,000 - 9,000 = \$236,000$
• Maintain Status Quo: $\text{Expected Value} = (0.7 \times 200,000) + (0.3 \times 100,000) = 140,000 + 30,000 = \$170,000$
• Sell Now: $\text{Expected Value} = (0.7 \times 100,000) + (0.3 \times 100,000) = 70,000 + 30,000 = \$100,000$

Expected Value Decision: Expand (since $236,000 is the highest expected value).

Final Recommendations:

• Expand is the best decision according to the Maximax, Minimax Regret, and Expected Value criteria.
• Maintain Status Quo is preferred only under the Maximin criterion, which is more conservative and focuses on minimizing losses in the worst-case scenario.

Would you like more detailed explanations or have any questions about these calculations?

Related Questions:

1. How does risk preference impact these decision criteria?
2. Can the Minimax Regret criterion be applied in real-world investment decisions?
3. What happens if the probabilities change in the expected value calculation?
4. How does the concept of opportunity cost relate to the regret matrix?
5. What is the role of sensitivity analysis in decision-making under uncertainty?

Tip:

When using the Expected Value criterion, it's essential to consider the accuracy of the probabilities used, as they significantly affect the decision-making process.