Paris has a utility function over berries (denoted by B) and chocolate (denoted by C) as follows: U(B, C) = 2ln(B) + 4ln(C) The price of berries and chocolate is PB and pc, respectively. Paris's income is m. 1. What preferences does this utility function represent? 2. Find the MRSBC as a function of B and C assuming B is on the x-axis. 3. Find the optimal bundle B and C as a function of income and prices using the tangency condition.
Paris has a utility function over berries (denoted by B) and chocolate (denoted by C) as follows: U(B, C) = 2ln(B) + 4ln(C) The price of berries and chocolate is PB and pc, respectively. Paris's income is m. 1. What preferences does this utility function represent? 2. Find the MRSBC as a function of B and C assuming B is on the x-axis. 3. Find the optimal bundle B and C as a function of income and prices using the tangency condition.
Chapter4: Utility Maximization And Choice
Section: Chapter Questions
Problem 4.13P
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![Paris has a utility function over berries (denoted by B) and chocolate (denoted by C) as
follows:
U(B, C) = 2ln(B) + 4ln(C)
The price of berries and chocolate is PB and pc, respectively. Paris's income is m.
1. What preferences does this utility function represent?
2. Find the MRSBC as a function of B and C assuming B is on the x-axis.
3. Find the optimal bundle B and C as a function of income and prices using the tangency
condition.
4. What is the fraction of total expenditure spent on berries and chocolate out of total income,
respectively?
5. Now suppose Paris has an income of $600. The price of a container of berries is $10 and the
price of a chocolate bar is $10. Find the numerical answers for the optimal bundle, by
plugging the numbers into the solution you found in Q3.3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0017105f-b55d-4e51-9144-7f95b6238702%2Fd8d8b4ee-09e0-4bd7-9c02-efcfb00091c9%2F6hmee7e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Paris has a utility function over berries (denoted by B) and chocolate (denoted by C) as
follows:
U(B, C) = 2ln(B) + 4ln(C)
The price of berries and chocolate is PB and pc, respectively. Paris's income is m.
1. What preferences does this utility function represent?
2. Find the MRSBC as a function of B and C assuming B is on the x-axis.
3. Find the optimal bundle B and C as a function of income and prices using the tangency
condition.
4. What is the fraction of total expenditure spent on berries and chocolate out of total income,
respectively?
5. Now suppose Paris has an income of $600. The price of a container of berries is $10 and the
price of a chocolate bar is $10. Find the numerical answers for the optimal bundle, by
plugging the numbers into the solution you found in Q3.3.
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