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Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company’s profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price: a) Does either player in this game have a dominant strategy? b) Does your answer to part (a) help you figure out what the other player should do? What is the Nash equilibrium? Is there only one? c) Big Brew threatens Little Kona by saying, “If you enter, we’re going to set a low price, so you had better stay out.” Do you think Little Kona should believe the threat? Why or why not?

Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 5EQ: 5. A coffee merchant sells three blends of coffee. A bag of the house blend contains 300 grams of...

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Little Kona is a small coffee company that is considering entering a market dominated by Big Brew. Each company’s profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price:

a) Does either player in this game have a dominant strategy?

b) Does your answer to part (a) help you figure out what the other player should do? What is the Nash equilibrium? Is there only one?

c) Big Brew threatens Little Kona by saying, “If you enter, we’re going to set a low price, so you had better stay out.” Do you think Little Kona should believe the threat? Why or why not?

Big Brew
High Price
Low Price
Brew makes
Brew makes
$3 million
$1 million
Enter
Kona makes
Kona loses
Little
$2 million
$1 million
Kona
Brew makes
Brew makes
$7 million
$2 million
Don't
Enter
Kona makes
Kona makes
zero
zero

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5. A coffee merchant sells three blends of coffee. A bag of the house blend contains 300 grams of Colombian beans and 200 grams of French roast beans. A bag of the special blend contains 200 grams of Colombian beans, 200 grams of Kenyan beans, and 100 grams of French roast beans. A bag of the gourmet blend contains 100 grams of Colombian beans, 200 grams of Kenyan beans, and 200 grams of French roast beans. The merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 25 kilograms of French roast beans. If he wishes to use up all of the beans, how many bags of each type of blend can be made?

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