Exercise 2: Consumer's Choice - Intertemporal Substitution Ken has access to a perfect capital market with interest rate r€ (0, 1). Ken's preference over bundles (x, y) E R of money for consumption in period 1 (r) and money for consumption in period 2 (y) can be represented by the following utility function u(x, y) = x - y³. Ken has an endowment of E = (500, 3000), i.e. Ken's income in period 1 is m₁ = 500 and Ken's income in period 2 is m₂ = 3,000. Ken can use the endowment and transfer money between periods by saving or borrowing money in the capital market with interest rate r. 1. Suppose Ken chooses bundle (x*(F), y* (F)) at some fixed interest rate F. Given this choice, how would you determine whether Ken is saving or borrowing money in the first period? If Ken is indeed saving, how do you compute the amount s(F) that he saves in period 1 based on his consumption choice? If he is borrowing, how do we compute the amount that Ken borrows b(r)? 2. Ken can use his endowment (income in periods 1 and 2) and transfer money between periods by saving or borrowing money in the capital market with interest rate r. Determine Ken's budget constraint. Explain. 3. At which interest rate is it optimal for Ken to exactly consume his endowment? That is, find ↑ such that Ken's optimal consumption choice is (x* (f), y* (f)) = (500, 3000). 4. Based on your previous answers, determine the interest rates for which Ken would be a saver (rather than a borrower) without solving for Ken's demand. 5. Solve for Ken's optimal bundle (x*(r), y* (r)) as a function of the interest rate r. 6. For all interest rates such that Ken becomes a borrower, determine the amount Ken borrows, b(r), as a function of the interest rate, r. Is b(r) increasing or decreasing in r? 7. Explain how Ken's budget line looks without the assumption of a perfect capital market. That is, if the interest rate for borrowing money, TB, exceeds the interest rate for saving money, rs, with rв > rs. How does this affect his optimal choice?
Exercise 2: Consumer's Choice - Intertemporal Substitution Ken has access to a perfect capital market with interest rate r€ (0, 1). Ken's preference over bundles (x, y) E R of money for consumption in period 1 (r) and money for consumption in period 2 (y) can be represented by the following utility function u(x, y) = x - y³. Ken has an endowment of E = (500, 3000), i.e. Ken's income in period 1 is m₁ = 500 and Ken's income in period 2 is m₂ = 3,000. Ken can use the endowment and transfer money between periods by saving or borrowing money in the capital market with interest rate r. 1. Suppose Ken chooses bundle (x*(F), y* (F)) at some fixed interest rate F. Given this choice, how would you determine whether Ken is saving or borrowing money in the first period? If Ken is indeed saving, how do you compute the amount s(F) that he saves in period 1 based on his consumption choice? If he is borrowing, how do we compute the amount that Ken borrows b(r)? 2. Ken can use his endowment (income in periods 1 and 2) and transfer money between periods by saving or borrowing money in the capital market with interest rate r. Determine Ken's budget constraint. Explain. 3. At which interest rate is it optimal for Ken to exactly consume his endowment? That is, find ↑ such that Ken's optimal consumption choice is (x* (f), y* (f)) = (500, 3000). 4. Based on your previous answers, determine the interest rates for which Ken would be a saver (rather than a borrower) without solving for Ken's demand. 5. Solve for Ken's optimal bundle (x*(r), y* (r)) as a function of the interest rate r. 6. For all interest rates such that Ken becomes a borrower, determine the amount Ken borrows, b(r), as a function of the interest rate, r. Is b(r) increasing or decreasing in r? 7. Explain how Ken's budget line looks without the assumption of a perfect capital market. That is, if the interest rate for borrowing money, TB, exceeds the interest rate for saving money, rs, with rв > rs. How does this affect his optimal choice?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
How do I solve question number 2? Please help.
Transcribed Image Text:Exercise 2: Consumer's Choice - Intertemporal Substitution
Ken has access to a perfect capital market with interest rate 7 € (0,1). Ken's preference over bundles
(x, y) = R of money for consumption in period 1 (2) and money for consumption in period 2 (y) can be
represented by the following utility function
u(x, y) = x. y³.
Ken has an endowment of E = (500, 3000), i.e. Ken's income in period 1 is m₁ = 500 and Ken's income
in period 2 is m2 = 3,000. Ken can use the endowment and transfer money between periods by saving or
borrowing money in the capital market with interest rate r.
1. Suppose Ken chooses bundle (x*(F), y* (F)) at some fixed interest rate F. Given this choice, how would
you determine whether Ken is saving or borrowing money in the first period? If Ken is indeed saving,
how do you compute the amount s(F) that he saves in period 1 based on his consumption choice? If
he is borrowing, how do we compute the amount that Ken borrows b(r)?
2. Ken can use his endowment (income in periods 1 and 2) and transfer money between periods by saving
or borrowing money in the capital market with interest rate r. Determine Ken's budget constraint.
Explain.
3. At which interest rate is it optimal for Ken to exactly consume his endowment? That is, find such
that Ken's optimal consumption choice is (x*(î), y* (î)) = (500, 3000).
4. Based on your previous answers, determine the interest rates for which Ken would be a saver (rather
than a borrower) without solving for Ken's demand.
5. Solve for Ken's optimal bundle (x*(r), y* (r)) as a function of the interest rate r.
6. For all interest rates such that Ken becomes a borrower, determine the amount Ken borrows, b(r), as
a function of the interest rate, r. Is b(r) increasing or decreasing in r?
7. Explain how Ken's budget line looks without the assumption of a perfect capital market. That is, if
the interest rate for borrowing money, TB, exceeds the interest rate for saving money, rs, with TB > rs.
How does this affect his optimal choice?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education