Suppose a person has allocated a monthly budget of 200 and they like to consume coffee (C) and bagels (B). The price of a cup of coffee (pC) is 2, while the price of a bagel (p³) is 1. Their preferences for coffee and are shown by the following utility function: U(C,B) = (C)². (B). A. Before you make your calculation, set up the constrained utility maximization problem. Also, write one sentence that gives the intuition behind your set-up. FYI: The words "set up" means writing the constrained optimization problem that you will solve (the objective function and the constraint). B. How many cups of coffee and how many bagels should the person purchase per month? [You can use either the substitution method or the Lagrangian method to solve this problem.] FYI: This utility function is not a Cobb-Douglas function. So, carefully apply the rules of differentiation as learned in Calculus (Math Review). C. Suppose there is a promotion so that the price of bagels falls to 0.50. How many cups of coffee and how many bagels should the person then purchase per month? FYI: Rewrite your constraint and then solve the new problem. D. Given your answers to B and C, can you draw a demand curve of bagels? If the answer is yes, then please draw the demand curve. FYI: To draw a demand curve we need to hold all factors that affect demand constant (such as income, preferences, and prices of related goods). Then we change the price of the particular good (like bagels) and see how the quantity demanded (of bagels) changes. Then we plot the two (price, quantity)- combinations.
Suppose a person has allocated a monthly budget of 200 and they like to consume coffee (C) and bagels (B). The price of a cup of coffee (pC) is 2, while the price of a bagel (p³) is 1. Their preferences for coffee and are shown by the following utility function: U(C,B) = (C)². (B). A. Before you make your calculation, set up the constrained utility maximization problem. Also, write one sentence that gives the intuition behind your set-up. FYI: The words "set up" means writing the constrained optimization problem that you will solve (the objective function and the constraint). B. How many cups of coffee and how many bagels should the person purchase per month? [You can use either the substitution method or the Lagrangian method to solve this problem.] FYI: This utility function is not a Cobb-Douglas function. So, carefully apply the rules of differentiation as learned in Calculus (Math Review). C. Suppose there is a promotion so that the price of bagels falls to 0.50. How many cups of coffee and how many bagels should the person then purchase per month? FYI: Rewrite your constraint and then solve the new problem. D. Given your answers to B and C, can you draw a demand curve of bagels? If the answer is yes, then please draw the demand curve. FYI: To draw a demand curve we need to hold all factors that affect demand constant (such as income, preferences, and prices of related goods). Then we change the price of the particular good (like bagels) and see how the quantity demanded (of bagels) changes. Then we plot the two (price, quantity)- combinations.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Suppose a person has allocated a monthly budget of 200 and they like to consume coffee (C)
and bagels (B). The price of a cup of coffee (p) is 2, while the price of a bagel (p³) is 1. Their
preferences for coffee and are shown by the following utility function: U(C,B) = (C)². (B).
A. Before you make your calculation, set up the constrained utility maximization problem.
Also, write one sentence that gives the intuition behind your set-up.
FYI: The words "set up" means
writing the constrained optimization
problem that you will solve (the
objective function and the
constraint).
B. How many cups of coffee and how many bagels should the person purchase per month?
[You can use either the substitution method or the Lagrangian method to solve this problem.]
FYI: This utility function is not a
Cobb-Douglas function. So, carefully
apply the rules of differentiation as
learned in Calculus (Math Review).
C. Suppose there is a promotion so that the price of bagels falls to 0.50. How many cups of
coffee and how many bagels should the person then purchase per month?
FYI: Rewrite your constraint and
then solve the new problem.
D. Given your answers to B and C, can you draw a demand curve of bagels? If the answer is
yes, then please draw the demand curve.
FYI: To draw a demand curve we need to
hold all factors that affect demand constant
(such as income, preferences, and prices of
related goods).
Then we change the price of the particular
good (like bagels) and see how the quantity
demanded (of bagels) changes.
Then we plot the two (price, quantity)-
combinations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04c291c3-b5f3-44f9-94d9-068de8214981%2F0b39c683-0ad0-4c90-882d-790ec762de15%2Fqw6fjtl_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a person has allocated a monthly budget of 200 and they like to consume coffee (C)
and bagels (B). The price of a cup of coffee (p) is 2, while the price of a bagel (p³) is 1. Their
preferences for coffee and are shown by the following utility function: U(C,B) = (C)². (B).
A. Before you make your calculation, set up the constrained utility maximization problem.
Also, write one sentence that gives the intuition behind your set-up.
FYI: The words "set up" means
writing the constrained optimization
problem that you will solve (the
objective function and the
constraint).
B. How many cups of coffee and how many bagels should the person purchase per month?
[You can use either the substitution method or the Lagrangian method to solve this problem.]
FYI: This utility function is not a
Cobb-Douglas function. So, carefully
apply the rules of differentiation as
learned in Calculus (Math Review).
C. Suppose there is a promotion so that the price of bagels falls to 0.50. How many cups of
coffee and how many bagels should the person then purchase per month?
FYI: Rewrite your constraint and
then solve the new problem.
D. Given your answers to B and C, can you draw a demand curve of bagels? If the answer is
yes, then please draw the demand curve.
FYI: To draw a demand curve we need to
hold all factors that affect demand constant
(such as income, preferences, and prices of
related goods).
Then we change the price of the particular
good (like bagels) and see how the quantity
demanded (of bagels) changes.
Then we plot the two (price, quantity)-
combinations.
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