Caroline is a consumer who enjoys candys. Her preferred are licorice candies (good x) and sour candies (goody y), as given by the utility function u (x, y) = xy. Today is Sunday and she is visiting a store where the per unit price of licorice candies is px = $1 and the per unit price of sour candies is py = $2. Today she is willing to spend $12 on candies. a) Using appropriate scale, draw Caroline's indifferences curves representing utility levels U = 6 and U = 12. Label these indifference curves as U6 and U₁2, respectively. b) Write the equation of Caroline's budget line and draw it on the same graph as in (a). c) Look at your graph, can Caroline afford any bundle of candies that gives her utility of U = 6? What about utility of U = 12? Explain.
Caroline is a consumer who enjoys candys. Her preferred are licorice candies (good x) and sour candies (goody y), as given by the utility function u (x, y) = xy. Today is Sunday and she is visiting a store where the per unit price of licorice candies is px = $1 and the per unit price of sour candies is py = $2. Today she is willing to spend $12 on candies. a) Using appropriate scale, draw Caroline's indifferences curves representing utility levels U = 6 and U = 12. Label these indifference curves as U6 and U₁2, respectively. b) Write the equation of Caroline's budget line and draw it on the same graph as in (a). c) Look at your graph, can Caroline afford any bundle of candies that gives her utility of U = 6? What about utility of U = 12? Explain.
Economics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter20: Consumer Choice And Elasticity
Section: Chapter Questions
Problem 4CQ
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Show full answers to part a) b) c) d) e) & f)
![Caroline is a consumer who enjoys candys. Her preferred are licorice
candies (good x) and sour candies (goody y), as given by the utility function u(x, y) =xy. Today
is Sunday and she is visiting a store where the per unit price of licorice candies is px = $1 and the
per unit price of sour candies is py= $2. Today she is willing to spend $12 on candies.
a) Using appropriate scale, draw Caroline's indifferences curves representing utility
levels U = 6 and U = 12. Label these indifference curves as U6 and U₁2, respectively.
b) Write the equation of Caroline's budget line and draw it on the same graph as in (a).
c) Look at your graph, can Caroline afford any bundle of candies that gives her utility of
U = 6? What about utility of U = 12? Explain.
d) If we want to model Caroline's optimal candy-choice problem as a utility maximization
problem (UMP):
What would be the objective function and the constraint of this problem?
Formally (with notation) write the statement of her optimal choice problem.
• Conceptually (in words), rewrite the statement of her optimal choice problem.
[Hint: Review notes/slides/exercise from D01 to see how we describe and write
optimization problems]
e) Mathematically, solve Caroline's UPM to find her optimal candy-bundle today.
f) What is level of utility Caroline gets from consuming her optimal bundle found in part
(e)?
●](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2Fddf7cb21-380f-4c1b-a0ca-b9ee330ccd35%2Fqliauq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Caroline is a consumer who enjoys candys. Her preferred are licorice
candies (good x) and sour candies (goody y), as given by the utility function u(x, y) =xy. Today
is Sunday and she is visiting a store where the per unit price of licorice candies is px = $1 and the
per unit price of sour candies is py= $2. Today she is willing to spend $12 on candies.
a) Using appropriate scale, draw Caroline's indifferences curves representing utility
levels U = 6 and U = 12. Label these indifference curves as U6 and U₁2, respectively.
b) Write the equation of Caroline's budget line and draw it on the same graph as in (a).
c) Look at your graph, can Caroline afford any bundle of candies that gives her utility of
U = 6? What about utility of U = 12? Explain.
d) If we want to model Caroline's optimal candy-choice problem as a utility maximization
problem (UMP):
What would be the objective function and the constraint of this problem?
Formally (with notation) write the statement of her optimal choice problem.
• Conceptually (in words), rewrite the statement of her optimal choice problem.
[Hint: Review notes/slides/exercise from D01 to see how we describe and write
optimization problems]
e) Mathematically, solve Caroline's UPM to find her optimal candy-bundle today.
f) What is level of utility Caroline gets from consuming her optimal bundle found in part
(e)?
●
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