Consider a consumer, Jennie, who only consumes tea (t) and cookies (c). Jennie's utility func- tion is U(t, c) = min{5t, c}. The min function gives you the smaller of the two arguments.¹ For example, the min{1,3} = 1 since 1 is less than 3. She has $10 to spend, the price of a cup of tea is normalized to $1, and the price per cookie is $2. Assume she can buy tea and cookies in fractions. a. Graph the set of the tea and cookie pairs that yield the utility level of 5 with tea on the x-axis and cookies on the y-axis. Now graph an indifference curve associated with the level of utility equal to 7. b. Given the market prices that Jennie faces and her income, how much tea and how many cookies will Jennie choose to consume? Show her optimal choice graphically with cookies on the x-avis and tea on the y-avis [Note: You cannot use the standard Lagrangian technique
Consider a consumer, Jennie, who only consumes tea (t) and cookies (c). Jennie's utility func- tion is U(t, c) = min{5t, c}. The min function gives you the smaller of the two arguments.¹ For example, the min{1,3} = 1 since 1 is less than 3. She has $10 to spend, the price of a cup of tea is normalized to $1, and the price per cookie is $2. Assume she can buy tea and cookies in fractions. a. Graph the set of the tea and cookie pairs that yield the utility level of 5 with tea on the x-axis and cookies on the y-axis. Now graph an indifference curve associated with the level of utility equal to 7. b. Given the market prices that Jennie faces and her income, how much tea and how many cookies will Jennie choose to consume? Show her optimal choice graphically with cookies on the x-avis and tea on the y-avis [Note: You cannot use the standard Lagrangian technique
Chapter21: Demand: Consumer Choic
Section: Chapter Questions
Problem 1E
Related questions
Question
![2 COOKIES AND TEA
Consider a consumer, Jennie, who only consumes tea (t) and cookies (c). Jennie's utility func-
tion is U(t, c) = min{5t, c}. The min function gives you the smaller of the two arguments.¹ For
example, the min{1,3} = 1 since 1 is less than 3. She has $10 to spend, the price of a cup of
tea is normalized to $1, and the price per cookie is $2. Assume she can buy tea and cookies in
fractions.
a. Graph the set of the tea and cookie pairs that yield the utility level of 5 with tea on the x-axis
and cookies on the y-axis. Now graph an indifference curve associated with the level of utility
equal to 7.
b. Given the market prices that Jennie faces and her income, how much tea and how many
cookies will Jennie choose to consume? Show her optimal choice graphically with cookies on
the x-axis and tea on the y-axis. [Note: You cannot use the standard Lagrangian technique
here because the slope of the indifference curve is not defined at the kink. Try working with
the graph of the indifference curve and the budget constraint to gain some intuition with
regard to the optimal bundle. Then, try to formalize this intuition with math. ]
c. It turns out that Jennie is a math tutor in an after school program for youths. One of her
students wants to get Jennie a small gift. She has a choice between a $2 gift certificate for tea
or $2 in cash. What would be Jennie's consumption under each option? Which option would
Jennie prefer? Show this on the same figure.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf5b15e2-e6d6-41f9-adf4-8004644211b0%2F0af0166f-aa52-49ab-93d9-cc7715e10a55%2Fly9w5ip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2 COOKIES AND TEA
Consider a consumer, Jennie, who only consumes tea (t) and cookies (c). Jennie's utility func-
tion is U(t, c) = min{5t, c}. The min function gives you the smaller of the two arguments.¹ For
example, the min{1,3} = 1 since 1 is less than 3. She has $10 to spend, the price of a cup of
tea is normalized to $1, and the price per cookie is $2. Assume she can buy tea and cookies in
fractions.
a. Graph the set of the tea and cookie pairs that yield the utility level of 5 with tea on the x-axis
and cookies on the y-axis. Now graph an indifference curve associated with the level of utility
equal to 7.
b. Given the market prices that Jennie faces and her income, how much tea and how many
cookies will Jennie choose to consume? Show her optimal choice graphically with cookies on
the x-axis and tea on the y-axis. [Note: You cannot use the standard Lagrangian technique
here because the slope of the indifference curve is not defined at the kink. Try working with
the graph of the indifference curve and the budget constraint to gain some intuition with
regard to the optimal bundle. Then, try to formalize this intuition with math. ]
c. It turns out that Jennie is a math tutor in an after school program for youths. One of her
students wants to get Jennie a small gift. She has a choice between a $2 gift certificate for tea
or $2 in cash. What would be Jennie's consumption under each option? Which option would
Jennie prefer? Show this on the same figure.
Expert Solution
Step 1
Given utility function
U=min{5t,c)
t--- cup of tea
c--- cup of cookies
Price of tea=1
Price of cookies=2
Income level=10
Step by step
Solved in 3 steps with 5 images
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