Homework Help is Here – Start Your Trial Now!
Business
Economics
Aaron and his friends Britney, Carlos, Diana, Emily, Frank, Gwen, Hugo, Isabela, and Juliana have two choices for weekend activities. They can either go to the neighborhood park or get together in Aaron's hot tub. The park isn't much fun, which means that the benefits from being there are low on the friends' common utility scale. In fact, each of the friends receives a benefit equal to 6 "utils" from being at the park. This benefit doesn't depend on how many of the friends go to the park. Aaron's hot tub, on the other hand, can be fun, but the benefits of using it depend on how many of the friends are present. When the tub isn't too crowded, it's quite enjoyable. When lots of people show up, however, the tub is decidedly less pleasant. The relationship between benefit per person (measured in utils) and the number of people in the hot tub (denoted by T) is AB= 3+7 T-T², where AB denotes "average benefit." a) Using the above formula, compute AB for T = 1, 2, 3,...,10. Next compute total benefit from use of the hot tub for the above T' values as well as T = 0. Total benefit is just T times AB. Finally, compute marginal benefit (MB), which equals the change in total benefit from adding a person to the hot tub. To do so, adopt the following convention: define MB at T = T' to be the change in total benefit when T is increased from T' - 1 to T' (in other words, MB gives the change in total benefits from entry of the "last" person). Deviation from this convention will lead to inappropriate answers. For example, computation of MB using calculus will lead you astray, since we are dealing with a discrete problem rather than a continuous one.

Aaron and his friends Britney, Carlos, Diana, Emily, Frank, Gwen, Hugo, Isabela, and Juliana have two choices for weekend activities. They can either go to the neighborhood park or get together in Aaron's hot tub. The park isn't much fun, which means that the benefits from being there are low on the friends' common utility scale. In fact, each of the friends receives a benefit equal to 6 "utils" from being at the park. This benefit doesn't depend on how many of the friends go to the park. Aaron's hot tub, on the other hand, can be fun, but the benefits of using it depend on how many of the friends are present. When the tub isn't too crowded, it's quite enjoyable. When lots of people show up, however, the tub is decidedly less pleasant. The relationship between benefit per person (measured in utils) and the number of people in the hot tub (denoted by T) is AB= 3+7 T-T², where AB denotes "average benefit." a) Using the above formula, compute AB for T = 1, 2, 3,...,10. Next compute total benefit from use of the hot tub for the above T' values as well as T = 0. Total benefit is just T times AB. Finally, compute marginal benefit (MB), which equals the change in total benefit from adding a person to the hot tub. To do so, adopt the following convention: define MB at T = T' to be the change in total benefit when T is increased from T' - 1 to T' (in other words, MB gives the change in total benefits from entry of the "last" person). Deviation from this convention will lead to inappropriate answers. For example, computation of MB using calculus will lead you astray, since we are dealing with a discrete problem rather than a continuous one.

Principles of Economics 2e
Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter6: Consumer Choices
Section: Chapter Questions
Problem 1SCQ: Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can...
See similar textbooks
icon
Related questions
Question
100%
2. Aaron and his friends Britney, Carlos, Diana, Emily, Frank, Gwen, Hugo, Isabela, and Juliana have two choices for weekend activities. They can either go to the neighborhood park or get together in Aaron's hot tub. The park isn't much fun, which means that the benefits from being there are low on the friends' common utility scale. In fact, each of the friends receives a benefit equal to 6 "utils" from being at the park. This benefit doesn't depend on how many of the friends go to the park. Aaron's hot tub, on the other hand, can be fun, but the benefits of using it depend on how many of the friends are present. When the tub isn't too crowded, it's quite enjoyable. When lots of people show up, however, the tub is decidedly less pleasant. The relationship between benefit per person (measured in utils) and the number of people in the hot tub (denoted by T) is where AB denotes "average benefit." a) Using the above formula, compute AB for T = 1,2,3,...,10. Next compute total benefit from use of the hot tub for the above T' values as well as T = 0. Total benefit is just T times AB. Finally, compute marginal benefit (MB), which equals the change in total benefit from adding a person to the hot tub. To do so, adopt the following convention: define MB at T = T' to be the change in total benefit when T is increased from T' - 1 to T' (in other words, MB gives the change in total benefits from entry of the "last" person). Deviation from this convention will lead to inappropriate answers. For example, computation of MB using calculus will lead you astray, since we are dealing with a discrete problem rather than a continuous one. T 0 1 2 3 4 5 6 7 8 9 AB = 3 +7 T-T², 10 AB TB MB
Transcribed Image Text:2. Aaron and his friends Britney, Carlos, Diana, Emily, Frank, Gwen, Hugo, Isabela, and Juliana have two choices for weekend activities. They can either go to the neighborhood park or get together in Aaron's hot tub. The park isn't much fun, which means that the benefits from being there are low on the friends' common utility scale. In fact, each of the friends receives a benefit equal to 6 "utils" from being at the park. This benefit doesn't depend on how many of the friends go to the park. Aaron's hot tub, on the other hand, can be fun, but the benefits of using it depend on how many of the friends are present. When the tub isn't too crowded, it's quite enjoyable. When lots of people show up, however, the tub is decidedly less pleasant. The relationship between benefit per person (measured in utils) and the number of people in the hot tub (denoted by T) is where AB denotes "average benefit." a) Using the above formula, compute AB for T = 1,2,3,...,10. Next compute total benefit from use of the hot tub for the above T' values as well as T = 0. Total benefit is just T times AB. Finally, compute marginal benefit (MB), which equals the change in total benefit from adding a person to the hot tub. To do so, adopt the following convention: define MB at T = T' to be the change in total benefit when T is increased from T' - 1 to T' (in other words, MB gives the change in total benefits from entry of the "last" person). Deviation from this convention will lead to inappropriate answers. For example, computation of MB using calculus will lead you astray, since we are dealing with a discrete problem rather than a continuous one. T 0 1 2 3 4 5 6 7 8 9 AB = 3 +7 T-T², 10 AB TB MB
b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Equilibrium size_ c) Grand total benefits at equilibrium, Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size Grand total benefits at optimum Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana Optimal group (names): d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Grand total benefits for hot tub users Grand total benefits for golf players_ 8 10 14 20 27 30 31 Toll/subsidy in the park case 34 36 37 e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the golf case
Transcribed Image Text:b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Equilibrium size_ c) Grand total benefits at equilibrium, Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size Grand total benefits at optimum Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana Optimal group (names): d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Grand total benefits for hot tub users Grand total benefits for golf players_ 8 10 14 20 27 30 31 Toll/subsidy in the park case 34 36 37 e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the golf case
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

need assitance with D and E

b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Equilibrium size_ c) Grand total benefits at equilibrium, Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size Grand total benefits at optimum Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana Optimal group (names): d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Grand total benefits for hot tub users Grand total benefits for golf players_ 8 10 14 20 27 30 31 Toll/subsidy in the park case 34 36 37 e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the golf case
Transcribed Image Text:b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Equilibrium size_ c) Grand total benefits at equilibrium, Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size Grand total benefits at optimum Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana Optimal group (names): d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Grand total benefits for hot tub users Grand total benefits for golf players_ 8 10 14 20 27 30 31 Toll/subsidy in the park case 34 36 37 e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the golf case
Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

Answer parts D And E

b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. 니 Equilibrium size Grand total benefits at equilibrium 96 c) Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size 5 Ly value where Tis maximized 95 Grand total benefits at optimum. Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana 8 10 14 20 27 30 31 34 36 37
Transcribed Image Text:b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. 니 Equilibrium size Grand total benefits at equilibrium 96 c) Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size 5 Ly value where Tis maximized 95 Grand total benefits at optimum. Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana 8 10 14 20 27 30 31 34 36 37
d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Optimal group (names): Grand total benefits for hot tub users Grand total benefits for golf players e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the park case Toll/subsidy in the golf case
Transcribed Image Text:d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Optimal group (names): Grand total benefits for hot tub users Grand total benefits for golf players e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the park case Toll/subsidy in the golf case
Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

Answer parts d and e

Solution
Bartleby Expert
SEE SOLUTION
Follow-up Question

Answer parts D And E

b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. 니 Equilibrium size Grand total benefits at equilibrium 96 c) Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size 5 Ly value where Tis maximized 95 Grand total benefits at optimum. Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana 8 10 14 20 27 30 31 34 36 37
Transcribed Image Text:b) Recalling that the park yields 6 utils in benefits to each person, find the equilibrium size of the group using the hot tub. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. 니 Equilibrium size Grand total benefits at equilibrium 96 c) Find the optimal size of the hot tub group. Compute the grand total of benefits for all the friends, which is the sum of total benefits for the hot tub group and total benefits for those using the park. Optimal size 5 Ly value where Tis maximized 95 Grand total benefits at optimum. Now suppose that a new miniature golf course opens in the friends' town. While all the friends prefer playing golf to going to the park, some friends like golf more than others. The utils received from playing golf are as follows for the friends: Aaron Britney Carlos Diana Emily Frank Gwen Hugo Isabela Juliana 8 10 14 20 27 30 31 34 36 37
d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Optimal group (names): Grand total benefits for hot tub users Grand total benefits for golf players e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the park case Toll/subsidy in the golf case
Transcribed Image Text:d) Using the above information, identify the equilibrium group of hot tub users. Then identify the optimal group of hot tub users. Why do the groups differ? Compute the grand total of benefits for hot tub users and golf players in both situations. Equilibrium group (names): Optimal group (names): Grand total benefits for hot tub users Grand total benefits for golf players e) Find the toll charged (or subsidy paid) to achieve the optimal number of hot tub users in both the park case and the golf case. Toll/subsidy in the park case Toll/subsidy in the golf case
Solution
Bartleby Expert
SEE SOLUTION
Knowledge Booster
Arrow's Impossibility Theorem
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Principles of Economics 2e
Principles of Economics 2e
Economics
ISBN:
9781947172364
Author:
Steven A. Greenlaw; David Shapiro
Publisher:
OpenStax
Principles of Microeconomics
Principles of Microeconomics
Economics
ISBN:
9781305156050
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics, 7th Edition (MindTap Cou…
Principles of Economics, 7th Edition (MindTap Cou…
Economics
ISBN:
9781285165875
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Microeconomics (MindTap Course List)
Principles of Microeconomics (MindTap Course List)
Economics
ISBN:
9781305971493
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Microeconomic Theory
Microeconomic Theory
Economics
ISBN:
9781337517942
Author:
NICHOLSON
Publisher:
Cengage
SEE MORE TEXTBOOKS