Problem 3: Well-Behaved Indifference Curves & Optimization [6 Points] Consider an Individual who buys Films (F) and Books (B) with the following utility function: U(F,B) = 2F¹/3B²/3 This individual also has the following incomes (m) and prices (pF and PB): m = $30, PF = $2,PB = $6 Given the above, the Marginal Utilities of each Films (MUF) and Books (MUB) are: 2 F¹3 ²3 B¹3 MUB= 23
Problem 3: Well-Behaved Indifference Curves & Optimization [6 Points] Consider an Individual who buys Films (F) and Books (B) with the following utility function: U(F,B) = 2F¹/3B²/3 This individual also has the following incomes (m) and prices (pF and PB): m = $30, PF = $2,PB = $6 Given the above, the Marginal Utilities of each Films (MUF) and Books (MUB) are: 2 F¹3 ²3 B¹3 MUB= 23
Chapter21: Demand: Consumer Choic
Section: Chapter Questions
Problem 1E
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![Problem 3: Well-Behaved Indifference Curves & Optimization [6 Points]
Consider an Individual who buys Films (F) and Books (B) with the following utility function:
U(F,B) = 2F¹/3B²/3
This individual also has the following incomes (m) and prices (pF and pB):
m = $30, PF = $2,PB = $6
Given the above, the Marginal Utilities of each Films (MUF) and Books (MUB) are:
2 F¹3
3 B¹3
1B²/3
3 F²/3
MUB= 25
MUF = 2;
9. Given the above Marginal Utilities and prices to form the optimality condition for utility
maximization. According to this optimality condition, what must be the ratio of Films to
Books in an optimal consumption bundle? Show your work.
10. Given your answer to Q9, what must be the household's optimal consumption of F & B
given their income (m)? Show your work.
11. Suppose that the price of Films changed from $2 to $4. What would need to happen to
the MRS according to the optimality condition in Q9 if the household wanted to keep
maximizing its utility?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fa42c6c-1d00-4b82-a0d1-311b978341d3%2F1fd1229e-44f4-412e-9f7e-4a5e61ff8f22%2F8bwcax_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3: Well-Behaved Indifference Curves & Optimization [6 Points]
Consider an Individual who buys Films (F) and Books (B) with the following utility function:
U(F,B) = 2F¹/3B²/3
This individual also has the following incomes (m) and prices (pF and pB):
m = $30, PF = $2,PB = $6
Given the above, the Marginal Utilities of each Films (MUF) and Books (MUB) are:
2 F¹3
3 B¹3
1B²/3
3 F²/3
MUB= 25
MUF = 2;
9. Given the above Marginal Utilities and prices to form the optimality condition for utility
maximization. According to this optimality condition, what must be the ratio of Films to
Books in an optimal consumption bundle? Show your work.
10. Given your answer to Q9, what must be the household's optimal consumption of F & B
given their income (m)? Show your work.
11. Suppose that the price of Films changed from $2 to $4. What would need to happen to
the MRS according to the optimality condition in Q9 if the household wanted to keep
maximizing its utility?
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