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?

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?

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Concept explainers

Revealed Preferences and Budget Constraint Analysis

Revealed means “Let Out,” and Preference means “Choice”; Choice Reveals Preference.

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

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Step 1: Define consumer theory

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Step 2: Draw the budget line

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Step 3: Figure out the slope of the budget line

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Step 4: Draw the indifference curve and interpret the MRS

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Step 5: Examine the conditions for utility maximization

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Step 6: Calculate the utility maximizing quantities

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