Question 1

Eleven consumers are trying to decide whether to connect to a new communications network.Consumer 1 is of type 1,consumer 2 is of type 2,consumer 3 is of type 3,and so on.Where k is the number of consumers connected to the network (including oneself),a consumer of type n has a willingness to pay to belong to this network equal to k times n.What is the highest price at which 11 consumers could all connect to the network and either make a profit or at least break even?

A) $12
B) $10
C) $1
D) $0
E) $11

$11

Accepted Answer

The willingness to pay for a consumer of type n when all 11 consumers are connected is 11n. The highest price at which all consumers could connect without losing money is when the consumer with the lowest willingness to pay (type 1) breaks even. For consumer 1, the willingness to pay is 11*1 = 11. Therefore, the highest price at which all 11 consumers could connect and at least break even is $11.

Question 2

Eleven consumers are trying to decide whether to connect to a new communications network.Consumer 1 is of type 1,consumer 2 is of type 2,consumer 3 is of type 3,and so on.Where k is the number of consumers connected to the network (including oneself),a consumer of type n has a willingness to pay to belong to this network equal to k times n.What is the highest price at which 11 consumers could all connect to the network and either make a profit or at least break even?

A) $12
B) $10
C) $1
D) $0
E) $11

$11

Accepted Answer

For 9 consumers to connect and at least break even, the price must be equal to or less than the willingness to pay of the consumer with the lowest willingness to pay among the 9. This would be consumer 9, as the willingness to pay increases with the consumer type number. The willingness to pay for consumer 9 when 9 consumers are connected is 9 times 9, which equals 81. However, the question asks for the highest price at which 9 consumers could connect, not the willingness to pay of the 9th consumer. To find this price, we need to consider the consumer with the lowest willingness to pay who would still choose to connect, which would actually be consumer 1 when 9 consumers are connected. Consumer 1's willingness to pay would be 1 times 9 = 9. However, my explanation mistakenly focused on the wrong aspect of the problem, leading to an incorrect conclusion. The correct approach is to find the consumer with the highest type among those who are willing to connect and use their willingness to pay to determine the maximum price. For 9 consumers, the 9th consumer's willingness to pay sets the maximum price they are all willing to pay or break even on, which is 9 times 9 = 81. However, to find the highest price at which exactly 9 consumers could connect, we need to consider the marginal consumer, who is the 9th consumer in this case. The correct calculation involves finding the price at which the consumer with the lowest willingness to pay among the 9 (which would actually be the 9th consumer, not the 1st, in terms of willingness to pay, but the calculation involves ensuring all 9 are willing to pay the price) is willing to pay. The error in the initial explanation was in the interpretation of how to apply the willingness to pay to determine the maximum price. The correct answer involves calculating the willingness to pay of the marginal consumer willing to join the network at a given price, ensuring that this price allows for 9 consumers to connect without any of them incurring a loss. This involves a more nuanced understanding of the economic principles at play, including the concept of marginal utility and the role of the marginal consumer in determining market outcomes.

Question 3

If the demand function for the DoorKnobs operating system is related to perceived market share s and actual market share x by the equation p = 512s(1 - x),then in the long run,the highest price at which DoorKnobs could sustain a market share of 4/5 is

A) $96.
B) $256.
C) $113.78.
D) $128.
E) $81.92.

$81.92.

Accepted Answer

$81.92.&#10;

Question 4

If the demand function for the DoorKnobs operating system is related to perceived market share s and actual market share x by the equation p = 512s(1 - x),then in the long run,the highest price at which DoorKnobs could sustain a market share of 4/5 is

A) $96.
B) $256.
C) $113.78.
D) $128.
E) $81.92.

$81.92.

Accepted Answer

The answer of If the demand function for the DoorKnobs...

Question 5

If the demand function for the DoorKnobs operating system is related to perceived market share s and actual market share x by the equation p = 512s(1 - x),then in the long run,the highest price at which DoorKnobs could sustain a market share of 4/5 is

A) $96.
B) $256.
C) $113.78.
D) $128.
E) $81.92.

$81.92.

Accepted Answer

In the long run, equilibrium is achieved where the actual market share x is equal to the perceived market share s (i.e., x = s). Thus, we have:

p = 512s(1 - s)

To find the highest price at which DoorKnobs could sustain a market share of 3/4 (i.e., s = 0.75), we need to find the maximum value of p that satisfies the above equation.

Taking the derivative of p with respect to s, we get:

dp/ds = 512(1 - 2s)

Setting dp/ds = 0 to find the maximum, we get:

1 - 2s = 0
s = 1/2

This means that the maximum value of p occurs when s = 1/2. Substituting s = 1/2 into the demand function, we get:

p = 512(1/2)(1 - 1/2) = 256

Therefore, the highest price at which DoorKnobs could sustain a market share of 3/4 is $256. The correct answer is (D).

Question 6

Eleven consumers are trying to decide whether to connect to a new communications network.Consumer 1 is of type 1,consumer 2 is of type 2,consumer 3 is of type 3,and so on.Where k is the number of consumers connected to the network (including oneself),a consumer of type n has a willingness to pay to belong to this network equal to k times n.What is the highest price at which 11 consumers could all connect to the network and either make a profit or at least break even?

A) $12
B) $10
C) $1
D) $0
E) $11

$11

Accepted Answer

The answer of Eleven consumers are trying to decide whether...

Question 7

If the demand function for the DoorKnobs operating system is related to perceived market share s and actual market share x by the equation p = 512s(1 - x),then in the long run,the highest price at which DoorKnobs could sustain a market share of 4/5 is

A) $96.
B) $256.
C) $113.78.
D) $128.
E) $81.92.

$81.92.

Accepted Answer

The answer of If the demand function for the DoorKnobs...

Question 8

Professor Kremepuff's new,user-friendly textbook has just been published.This book will be used in classes for two years,after which it will be replaced by a new edition.The publisher charges a price of p₁ in the first year and p₂ in the second year.After the first year,bookstores buy back used copies for p₂/2 and resell them to students in the second year for p₂.(Students are indifferent between new and used copies. )The cost to a student of owning the book during the first year is therefore p₁ - p₂/2.In the first year of publication,the number of students willing to pay $v to own a copy of the book for a year is 50,000 -500v.The number of students taking the course in the first year who are willing to pay $w to keep the book for reference rather than sell it at the end of the year is 50,000 - 2,500w.The number of persons who are taking the course in the second year and are willing to pay at least $p for a copy of the book is 30,000 - 500p.If the publisher sets a price of p₁ in the first year and p₂ $\lt$ =p₁ in the second year,then the total number of copies of the book that the publisher sells over the two years will be

A) 100,000 - 500(p₁ -p₂/2).
B) 80,000 - 500(p₁ -p₂/2).
C) 100,000 - 500p₁- 500p₂.
D) 100,000 - 1,500p₂.
E) 80,000 - 750p₂.

Accepted Answer

The answer of Professor Kremepuff's new,user-friendly textbook has just been...

Question 9

Eleven consumers are trying to decide whether to connect to a new communications network.Consumer 1 is of type 1,consumer 2 is of type 2,consumer 3 is of type 3,and so on.Where k is the number of consumers connected to the network (including oneself),a consumer of type n has a willingness to pay to belong to this network equal to k times n.What is the highest price at which 11 consumers could all connect to the network and either make a profit or at least break even?

A) $12
B) $10
C) $1
D) $0
E) $11

$11

Accepted Answer

The answer of Eleven consumers are trying to decide whether...

Question 10

Professor Kremepuff's new,user-friendly textbook has just been published.This book will be used in classes for two years,after which it will be replaced by a new edition.The publisher charges a price of p₁ in the first year and p₂ in the second year.After the first year,bookstores buy back used copies for p₂/2 and resell them to students in the second year for p₂.(Students are indifferent between new and used copies. )The cost to a student of owning the book during the first year is therefore p₁ - p₂/2.In the first year of publication,the number of students willing to pay $v to own a copy of the book for a year is 60,000 -1,000v.The number of students taking the course in the first year who are willing to pay $w to keep the book for reference rather than sell it at the end of the year is 60,000 -5,000w.The number of persons who are taking the course in the second year and are willing to pay at least $p for a copy of the book is 45,000 - 1,000p.If the publisher sets a price of p₁ in the first year and p₂ $\lt$ =p₁ in the second year,then the total number of copies of the book that the publisher sells over the two years will be

A) 120,000 - 3,000p₂.
B) 120,000 -1,000(p₁ - p₂/2).
C) 120,000 F- 1,000p₁ - 1,000p₂.
D) 105,000-1,000(p₁ -p₂/2).
E) 105,000 - 1,500p₂.

Accepted Answer

The answer of Professor Kremepuff's new,user-friendly textbook has just been...

Question 11

Professor Kremepuff's new,user-friendly textbook has just been published.This book will be used in classes for two years,after which it will be replaced by a new edition.The publisher charges a price of p₁ in the first year and p₂ in the second year.After the first year,bookstores buy back used copies for p₂/2 and resell them to students in the second year for p₂.(Students are indifferent between new and used copies. )The cost to a student of owning the book during the first year is therefore p₁ - p₂/2.In the first year of publication,the number of students willing to pay $v to own a copy of the book for a year is 50,000 - 1,500v.The number of students taking the course in the first year who are willing to pay $w to keep the book for reference rather than sell it at the end of the year is 50,000 - 7,500w.The number of persons who are taking the course in the second year and are willing to pay at least $p for a copy of the book is 45,000 - 1,500p.If the publisher sets a price of p₁ in the first year and p₂ $\lt$ = p₁ in the second year,then the total number of copies of the book that the publisher sells over the two years will be

A) 100,000-1,500p₁ -1,500p₂.
B) 100,000 -1,500(p₁ -p₂/2).
C) 95,000 -1,500(p₁ -p₂/2).
D) 100,000 - 4,500p₂.
E) 95,000- 2,250p₂.

Accepted Answer

The answer of Professor Kremepuff's new,user-friendly textbook has just been...

Question 12

If the demand function for the DoorKnobs operating system is related to perceived market share s and actual market share x by the equation p = 512s(1 - x),then in the long run,the highest price at which DoorKnobs could sustain a market share of 4/5 is

A) $96.
B) $256.
C) $113.78.
D) $128.
E) $81.92.

$81.92.

Accepted Answer

The answer of If the demand function for the DoorKnobs...

Question 13

Professor Kremepuff's new,user-friendly textbook has just been published.This book will be used in classes for two years,after which it will be replaced by a new edition.The publisher charges a price of p₁ in the first year and p₂ in the second year.After the first year,bookstores buy back used copies for p₂/2 and resell them to students in the second year for p₂.(Students are indifferent between new and used copies. )The cost to a student of owning the book during the first year is therefore p₁ - p₂/2.In the first year of publication,the number of students willing to pay $v to own a copy of the book for a year is 50,000 -500v.The number of students taking the course in the first year who are willing to pay $w to keep the book for reference rather than sell it at the end of the year is 50,000 - 2,500w.The number of persons who are taking the course in the second year and are willing to pay at least $p for a copy of the book is 30,000 - 500p.If the publisher sets a price of p₁ in the first year and p₂ $\lt$ =p₁ in the second year,then the total number of copies of the book that the publisher sells over the two years will be

A) 100,000 - 500(p₁ -p₂/2).
B) 80,000 - 500(p₁ -p₂/2).
C) 100,000 - 500p₁- 500p₂.
D) 100,000 - 1,500p₂.
E) 80,000 - 750p₂.

Accepted Answer

The answer of Professor Kremepuff's new,user-friendly textbook has just been...

Question 14

Professor Kremepuff's new,user-friendly textbook has just been published.This book will be used in classes for two years,after which it will be replaced by a new edition.The publisher charges a price of p₁ in the first year and p₂ in the second year.After the first year,bookstores buy back used copies for p₂/2 and resell them to students in the second year for p₂.(Students are indifferent between new and used copies. )The cost to a student of owning the book during the first year is therefore p₁ - p₂/2.In the first year of publication,the number of students willing to pay $v to own a copy of the book for a year is 50,000 - 1,500v.The number of students taking the course in the first year who are willing to pay $w to keep the book for reference rather than sell it at the end of the year is 50,000 - 7,500w.The number of persons who are taking the course in the second year and are willing to pay at least $p for a copy of the book is 45,000 - 1,500p.If the publisher sets a price of p₁ in the first year and p₂ $\lt$ = p₁ in the second year,then the total number of copies of the book that the publisher sells over the two years will be

A) 100,000-1,500p₁ -1,500p₂.
B) 100,000 -1,500(p₁ -p₂/2).
C) 95,000 -1,500(p₁ -p₂/2).
D) 100,000 - 4,500p₂.
E) 95,000- 2,250p₂.

Accepted Answer

The answer of Professor Kremepuff's new,user-friendly textbook has just been...

Question 15

Eleven consumers are trying to decide whether to connect to a new communications network.Consumer 1 is of type 1,consumer 2 is of type 2,consumer 3 is of type 3,and so on.Where k is the number of consumers connected to the network (including oneself),a consumer of type n has a willingness to pay to belong to this network equal to k times n.What is the highest price at which 11 consumers could all connect to the network and either make a profit or at least break even?

A) $12
B) $10
C) $1
D) $0
E) $11

$11

Accepted Answer

The answer of Eleven consumers are trying to decide whether...

Deck 36: B: Information Technology