Question

A fashion designer wants to produce a new line of clothes. In the production of the clothes, expensive, medium-priced, or inexpensive materials can be used. The profit associated with each type of material depends upon economic conditions next year. Below you are given the payoff table.

​	States of Nature
​ Decisions	Economy Improves	Economy Stays the Same	Economy Gets Worse
Expensive	80,000	40,000	10,000
Medium	40,000	60,000	70,000
Inexpensive	10,000	30,000	60,000

-Which decision would you make using the Maximin criterion? What is the value associated with that decision?

-Complete a regret table. Which decision would you make using the Minimax criterion?

-List the values of the top row of your regret table with a space between each one.

-Which decision would you make using the Hurwicz criterion?   What is the value associated with that decision?

-Which decision would you make using the Equal Likelihood criterion? What is the value associated with that decision?

Answer 1

1.

The worst payoff for Expensive decison is 10,000

The worst payoff for Medium decison is 40,000

The worst payoff for Inexpensive decison is 10,000

The maximum of worst payoff is for Medium decision.

Using the Maximin criterion, we would make Medium decision. The value associated with that decision is 40,000.

2.

Regret for States of Nature = Best Payoff - Payoff Received

	Economy Improves	Economy Stays the Same	Economy Gets Worse
Expensive	80,000 - 80,000 = 0	60,000 - 40,000 = 20,000	70,000 - 10,000 = 60,000
Medium	80,000 - 40,000 = 40,000	60,000 - 60,000 = 0	70,000 - 70,000 = 0
Inexpensive	80,000 - 10,000 = 70,000	60,000 - 30,000 = 30,000	70,000 - 60,000 = 10,000

The maximum regret for Expensive decison is 60,000

The maximum regret for Medium decison is 40,000

The maximum regret for Inexpensive decison is 70,000

The minimum of maximum regret is for Medium decision.

Using the Minimax Regret criterion, we would make Medium decision. The value associated with that decision is 40,000.

The values of the top row of your regret table are

0 20,000 60,000

3.

Assuming coefficient of realism, = 0.5 .

Expected payoff = 0.5 * Best Payoff + (1 - 0.5) * Worst payoff = 0.5 * Best Payoff + 0.5 * Worst payoff

The expected payoff for Expensive decison is 0.5 * 80,000 + 0.5 * 10,000 = 45,000

The expected payoff for Medium decison is 0.5 * 70,000 + 0.5 * 40,000 = 55,000

The expected payoff for Inexpensive decison is 0.5 * 60,000 + 0.5 * 30,000 = 45,000

The maximum of expected payoff is for Medium decision.

Using the Hurwicz criterion, we would make Medium decision. The value associated with that decision is 55,000.

4.

The expected payoff for Expensive decison is (80,000 + 40,000 + 10,000) / 3 = 43333.33

The expected payoff for Medium decison is (40,000 + 60,000 + 70,000) / 3 = 56666.67

The expected payoff for Inexpensive decison is (10,000 + 30,000 + 60,000) / 3 = 33333.33

The maximum of expected payoff is for Medium decision.

Using the Equal Likelihood criterion, we would make Medium decision. The value associated with that decision is 56666.67.