Question

In: Economics

Sierra Mountain Bike, Inc., is a producer and wholesaler of rugged bicycles designed for mountain touring....

Sierra Mountain Bike, Inc., is a producer and wholesaler of rugged bicycles designed for mountain touring. The company is considering an upgrade to its current line by making high-grade chrome alloy frames standard. Of course, the market response to this upgrade in product quality depends on the competitor’s reaction, if any. The company’s comptroller projects the following annual profits (payoffs) following resolution of the upgrade decision:
States of Nature
Sierra’s No
Decision Competitor          Competitor

Alternatives Upgrade Upgrade
Upgrade $1,000,000 $1,500,000
Do not upgrade    800,000 2,000,000

Determine the decision alternative that Sierra would choose given a maximin criterion? Explain your choice of answer .
Calculate the opportunity loss or regret matrix for the Competitor Upgrade.
Calculate the opportunity loss or regret matrix for the No Competitor Upgrade.
Which decision alternative would Sierra choose given a minimax regret criterion?

Solutions

Expert Solution

Pay-Off Table
States of nature

No Competitor Upgrade

S1

Competitor Upgrade

S2

Alternatives
A1 1000000 1500000
A2 800000 2000000

# Maximin Criterion-----

* The course of action that maximizes the minimum possible pay- off is selected .

At first , minimum value of each row is selected

Out of these maximum value out of selected row minima is the decision criterion.

Maximin Criterion
States of nature S1 S2 Row Minima
Alternatives
A1 1000000 1500000 1000000
A2 800000 2000000 800000

Out of row minima, column maxima ( maximum vale out of minima) is 800000, which belongs to A2.

So, As per Maximin criterion, decision alternative is do not upgrade

# Opportunity loss / Regret Matrix--------

* The regret table is formulated below by substracting all the elements of each column fro highest value for that column

* After that, using Minimax Regret Criterion, Minimum of these maximum regrets , corresponding to decision alternative should be selected.

Opportunity loss/ Regret Matrix
States of nature S1 S2 Maximum Regret
Alternatives
A1

0

(1000000--1000000)

500000

(2000000--1500000)

500000
A2

200000

(1000000--800000)

0

(2000000--2000000)

200000

Minimum of maximum regret is 200000 in A2.

so, Decision criterion under Minimax Regret is not to upgrade.


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