Sheila decides to take a trip to Peru for her 60th birthday. She looks forward to the guided tours (T) and the food (F). She is allocating $2,000 to spend on guided tours and food. Sheila's preferences over these two goods T and F is represented by the utility function: U(FT)=√ √F+T Denote prices for tours and food as pr and pF, respectively, and take them to be pt = $100 and pF = $20. a. Carefully draw at least two indifference curves to get a sense of Sheila's preferences. Are Sheila's preferences "well-behaved"? [Note: Go ahead and put T on the y-axis and F on the x-axis so that your pictures are consistent with mine.] b. Derive an expression for Sheila's marginal rate of substitution. What is the MRS in words? What does her MRS approach as F-0? How about when F→∞o? How do you interpret these findings, in words? c. In the above analysis, you found that Sheila's MRS does not depend on T. Please show what it means for the MRS to be independent of T either in a new graph in the space below or in the graph of indifference curves that you provided in part (a). d. Suppose that Sheila receives a larger than expected tax return and decides to increase her budget for her trip from $2,000 to $2,500. Based on your analysis in part (c), should we expect Sheila to consume more tours? How about more food? [Note: you need not set up a Lagrangian or take any new derivatives to answer this question.] e. Derive explicit expressions for Sheila's demand for food and tours as functions of prices and income using the Lagrangian. This should verify that Sheila's consumption of food does not depend on income but her demand for tours does. Then plug in the given numeric values of prices and income to find Sheila's final chosen bundle.
Sheila decides to take a trip to Peru for her 60th birthday. She looks forward to the guided tours (T) and the food (F). She is allocating $2,000 to spend on guided tours and food. Sheila's preferences over these two goods T and F is represented by the utility function: U(FT)=√ √F+T Denote prices for tours and food as pr and pF, respectively, and take them to be pt = $100 and pF = $20. a. Carefully draw at least two indifference curves to get a sense of Sheila's preferences. Are Sheila's preferences "well-behaved"? [Note: Go ahead and put T on the y-axis and F on the x-axis so that your pictures are consistent with mine.] b. Derive an expression for Sheila's marginal rate of substitution. What is the MRS in words? What does her MRS approach as F-0? How about when F→∞o? How do you interpret these findings, in words? c. In the above analysis, you found that Sheila's MRS does not depend on T. Please show what it means for the MRS to be independent of T either in a new graph in the space below or in the graph of indifference curves that you provided in part (a). d. Suppose that Sheila receives a larger than expected tax return and decides to increase her budget for her trip from $2,000 to $2,500. Based on your analysis in part (c), should we expect Sheila to consume more tours? How about more food? [Note: you need not set up a Lagrangian or take any new derivatives to answer this question.] e. Derive explicit expressions for Sheila's demand for food and tours as functions of prices and income using the Lagrangian. This should verify that Sheila's consumption of food does not depend on income but her demand for tours does. Then plug in the given numeric values of prices and income to find Sheila's final chosen bundle.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.15P
Related questions
Question
![Sheila decides to take a trip to Peru for her 60th birthday. She looks forward to the guided
tours (T) and the food (F). She is allocating $2,000 to spend on guided tours and food. Sheila's
preferences over these two goods T and F is represented by the utility function:
U(F, T) = = √F+T
Denote prices for tours and food as på and pf, respectively, and take them to be pt = $100
and PF = $20.
a. Carefully draw at least two indifference curves to get a sense of Sheila's preferences. Are
Sheila's preferences "well-behaved"? [Note: Go ahead and put T on the y-axis and F on the
x-axis so that your pictures are consistent with mine.]
b. Derive an expression for Sheila's marginal rate of substitution. What is the MRS in words?
What does her MRS approach as F→ 0? How about when F→→∞o? How do you interpret these
findings, in words?
c. In the above analysis, you found that Sheila's MRS does not depend on T. Please show what
it means for the MRS to be independent of T either in a new graph in the space below or in
the graph of indifference curves that you provided in part (a).
d. Suppose that Sheila receives a larger than expected tax return and decides to increase
her budget for her trip from $2,000 to $2,500. Based on your analysis in part (c), should we
expect Sheila to consume more tours? How about more food? [Note: you need not set up a
Lagrangian or take any new derivatives to answer this question.]
e. Derive explicit expressions for Sheila's demand for food and tours as functions of prices
and income using the Lagrangian. This should verify that Sheila's consumption of food do
not depend on income but her demand for tours does. Then plug in the given numeric values
of prices and income to find Sheila's final chosen bundle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ed2ec0-4677-49f1-9f5f-8dd9046cd7b7%2F9df3fe72-1cc8-491a-8c1e-77da38cdddf5%2Fuwwypxf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Sheila decides to take a trip to Peru for her 60th birthday. She looks forward to the guided
tours (T) and the food (F). She is allocating $2,000 to spend on guided tours and food. Sheila's
preferences over these two goods T and F is represented by the utility function:
U(F, T) = = √F+T
Denote prices for tours and food as på and pf, respectively, and take them to be pt = $100
and PF = $20.
a. Carefully draw at least two indifference curves to get a sense of Sheila's preferences. Are
Sheila's preferences "well-behaved"? [Note: Go ahead and put T on the y-axis and F on the
x-axis so that your pictures are consistent with mine.]
b. Derive an expression for Sheila's marginal rate of substitution. What is the MRS in words?
What does her MRS approach as F→ 0? How about when F→→∞o? How do you interpret these
findings, in words?
c. In the above analysis, you found that Sheila's MRS does not depend on T. Please show what
it means for the MRS to be independent of T either in a new graph in the space below or in
the graph of indifference curves that you provided in part (a).
d. Suppose that Sheila receives a larger than expected tax return and decides to increase
her budget for her trip from $2,000 to $2,500. Based on your analysis in part (c), should we
expect Sheila to consume more tours? How about more food? [Note: you need not set up a
Lagrangian or take any new derivatives to answer this question.]
e. Derive explicit expressions for Sheila's demand for food and tours as functions of prices
and income using the Lagrangian. This should verify that Sheila's consumption of food do
not depend on income but her demand for tours does. Then plug in the given numeric values
of prices and income to find Sheila's final chosen bundle.
Expert Solution
Step 1
Utility function and ICs:
The utility function determines all those consumption bundles that provide the same level of utility to the consumer.
And the ICs are the graphical representation of the utility function for each level of utility
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