Question

In: Statistics and Probability

A fashion designer wants to produce a new line of clothes. In the production of the...

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?

Solutions

Expert Solution

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.


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