Suppose Frank enjoys traveling and his utility is a function of the number of airplane trips he takes and the number of bus rides he takes. His utility function is given by U(b,p) = 3b0.4p0.8. A trip on a plane costs $400, a trip on the bus costs $50 and Frank has $3,000 to spend on travel. a. Draw Frank's budget line on a graph with bus trips on the vertical axis. b. Calculate AND INTERPRET the slope of Frank's budget line. c. Draw a representative indifference curve on your graph and provide a function that describes the slope of this indifference curve (i.e., find Frank's marginal rate of substitution). What is the INTERPRETATION of the marginal rate of substitution? d. What two conditions must be met in order for Frank to maximize his utility? e. What are the utility maximizing quantities of plane trips and bus trips før Frank?

Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter6: Consumer Choice And Demand
Section: Chapter Questions
Problem 2QFR
icon
Related questions
Question
1.
2.
Suppose Frank enjoys traveling and his utility is a function of the number of
airplane trips he takes and the number of bus rides he takes. His utility function
is given by U(b,p) = 3b0-4p0.8. A trip on a plane costs $400, a trip on the bus costs
$50 and Frank has $3,000 to spend on travel.
a. Draw Frank's budget line on a graph with bus trips on the vertical axis.
b. Calculate AND INTERPRET the slope of Frank's budget line.
c. Draw a representative indifference curve on your graph and provide a
function that describes the slope of this indifference curve (i.e., find Frank's
marginal rate of substitution). What is the INTERPRETATION of the marginal
rate of substitution?
d. What two conditions must be met in order for Frank to maximize his utility?
e. What are the utility maximizing quantities of plane trips and bus trips for
Frank?
Given income of $1000, Px = 25 and Py = 40, find (1) a function for the MRS and
(2) the utility maximizing consumption bundle for each of the following utility
functions. Hint: a graph may be very helpful for some of these.
a. U(X,Y)= 3X0.4Y0.6
b. U(X,Y) = 20X0.20.8
c. U(X,Y) = X0.2y0.3
d. U(X,Y)= 4*Min(X,2Y)
e. U(X,Y) = 2X + 6Y
f. U(X,Y) = 30X⁰.5+4Y
Transcribed Image Text:1. 2. Suppose Frank enjoys traveling and his utility is a function of the number of airplane trips he takes and the number of bus rides he takes. His utility function is given by U(b,p) = 3b0-4p0.8. A trip on a plane costs $400, a trip on the bus costs $50 and Frank has $3,000 to spend on travel. a. Draw Frank's budget line on a graph with bus trips on the vertical axis. b. Calculate AND INTERPRET the slope of Frank's budget line. c. Draw a representative indifference curve on your graph and provide a function that describes the slope of this indifference curve (i.e., find Frank's marginal rate of substitution). What is the INTERPRETATION of the marginal rate of substitution? d. What two conditions must be met in order for Frank to maximize his utility? e. What are the utility maximizing quantities of plane trips and bus trips for Frank? Given income of $1000, Px = 25 and Py = 40, find (1) a function for the MRS and (2) the utility maximizing consumption bundle for each of the following utility functions. Hint: a graph may be very helpful for some of these. a. U(X,Y)= 3X0.4Y0.6 b. U(X,Y) = 20X0.20.8 c. U(X,Y) = X0.2y0.3 d. U(X,Y)= 4*Min(X,2Y) e. U(X,Y) = 2X + 6Y f. U(X,Y) = 30X⁰.5+4Y
Expert Solution
steps

Step by step

Solved in 7 steps with 10 images

Blurred answer
Knowledge Booster
Budget Constraint
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
Microeconomics A Contemporary Intro
Microeconomics A Contemporary Intro
Economics
ISBN:
9781285635101
Author:
MCEACHERN
Publisher:
Cengage
Economics: Private and Public Choice (MindTap Cou…
Economics: Private and Public Choice (MindTap Cou…
Economics
ISBN:
9781305506725
Author:
James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:
Cengage Learning
Microeconomics: Private and Public Choice (MindTa…
Microeconomics: Private and Public Choice (MindTa…
Economics
ISBN:
9781305506893
Author:
James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:
Cengage Learning
Micro Economics For Today
Micro Economics For Today
Economics
ISBN:
9781337613064
Author:
Tucker, Irvin B.
Publisher:
Cengage,
Economics For Today
Economics For Today
Economics
ISBN:
9781337613040
Author:
Tucker
Publisher:
Cengage Learning
Microeconomics
Microeconomics
Economics
ISBN:
9781337617406
Author:
Roger A. Arnold
Publisher:
Cengage Learning