Question 2: Consider a model exactly like that in Question 1 - where the person receives income $48,326 - in period 1 and additional income $44,928 in period 2 except let's now suppose that the person faces a liquidity constraint. Specifically, she can still save at an interest rate of 4%, but if she borrows, then she must pay an interest rate of 8%. (a) If the person wants to save, the relevant interest rate is 4%. For what values of 8 is it optimal to save? [Hint: You already know the answer from Question 1.] (b) If the person wants to borrow, the relevant interest rate is 8%. (i) Suppose the interest rate is 8%, and solve for the optimal c₁ and c₂ as a function of 8. (ii) If the interest rate is 8%, for what values of 8 is it optimal to borrow? [Note: Please report your answer to 5 decimal points.] (c) Given the liquidity constraint, for what values of 8 is it optimal to neither borrow nor save? [Hint: Two conditions must hold: (i) 8 must be such that the person does NOT want to save at an interest rate of 4%, and (ii) & must be such that the person does NOT want to borrow at an interest rate of 8%.] (d) Draw three pictures that illustrate the three cases - when it's optimal to save, when it's optimal to borrow, and when it's optimal to neither borrow nor save. Each picture should depict (i) the budget constraint, (ii) some indifference curves, and (iii) the optimal c₁ and c2.
Question 2: Consider a model exactly like that in Question 1 - where the person receives income $48,326 - in period 1 and additional income $44,928 in period 2 except let's now suppose that the person faces a liquidity constraint. Specifically, she can still save at an interest rate of 4%, but if she borrows, then she must pay an interest rate of 8%. (a) If the person wants to save, the relevant interest rate is 4%. For what values of 8 is it optimal to save? [Hint: You already know the answer from Question 1.] (b) If the person wants to borrow, the relevant interest rate is 8%. (i) Suppose the interest rate is 8%, and solve for the optimal c₁ and c₂ as a function of 8. (ii) If the interest rate is 8%, for what values of 8 is it optimal to borrow? [Note: Please report your answer to 5 decimal points.] (c) Given the liquidity constraint, for what values of 8 is it optimal to neither borrow nor save? [Hint: Two conditions must hold: (i) 8 must be such that the person does NOT want to save at an interest rate of 4%, and (ii) & must be such that the person does NOT want to borrow at an interest rate of 8%.] (d) Draw three pictures that illustrate the three cases - when it's optimal to save, when it's optimal to borrow, and when it's optimal to neither borrow nor save. Each picture should depict (i) the budget constraint, (ii) some indifference curves, and (iii) the optimal c₁ and c2.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
![Question 2:
Consider a model exactly like that in Question 1
-
where the person receives income $48,326
-
in period 1 and additional income $44,928 in period 2 except let's now suppose that the person
faces a liquidity constraint. Specifically, she can still save at an interest rate of 4%, but if she
borrows, then she must pay an interest rate of 8%.
(a) If the person wants to save, the relevant interest rate is 4%. For what values of 8 is it optimal
to save? [Hint: You already know the answer from Question 1.]
(b) If the person wants to borrow, the relevant interest rate is 8%.
(i) Suppose the interest rate is 8%, and solve for the optimal c₁ and c₂
as a function of 8.
(ii) If the interest rate is 8%, for what values of 8 is it optimal to borrow?
[Note: Please report your answer to 5 decimal points.]
(c) Given the liquidity constraint, for what values of 8 is it optimal to neither borrow nor save?
[Hint: Two conditions must hold: (i) 8 must be such that the person does NOT want to save at an
interest rate of 4%, and (ii) & must be such that the person does NOT want to borrow at an interest
rate of 8%.]
(d) Draw three pictures that illustrate the three cases - when it's optimal to save, when it's
optimal to borrow, and when it's optimal to neither borrow nor save. Each picture should depict (i)
the budget constraint, (ii) some indifference curves, and (iii) the optimal c₁ and c2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8138ff39-b256-474a-bb09-d41fc9e0d28c%2Fa88ddc31-9316-46ef-9e63-06595295fca5%2Fjtj5hjj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2:
Consider a model exactly like that in Question 1
-
where the person receives income $48,326
-
in period 1 and additional income $44,928 in period 2 except let's now suppose that the person
faces a liquidity constraint. Specifically, she can still save at an interest rate of 4%, but if she
borrows, then she must pay an interest rate of 8%.
(a) If the person wants to save, the relevant interest rate is 4%. For what values of 8 is it optimal
to save? [Hint: You already know the answer from Question 1.]
(b) If the person wants to borrow, the relevant interest rate is 8%.
(i) Suppose the interest rate is 8%, and solve for the optimal c₁ and c₂
as a function of 8.
(ii) If the interest rate is 8%, for what values of 8 is it optimal to borrow?
[Note: Please report your answer to 5 decimal points.]
(c) Given the liquidity constraint, for what values of 8 is it optimal to neither borrow nor save?
[Hint: Two conditions must hold: (i) 8 must be such that the person does NOT want to save at an
interest rate of 4%, and (ii) & must be such that the person does NOT want to borrow at an interest
rate of 8%.]
(d) Draw three pictures that illustrate the three cases - when it's optimal to save, when it's
optimal to borrow, and when it's optimal to neither borrow nor save. Each picture should depict (i)
the budget constraint, (ii) some indifference curves, and (iii) the optimal c₁ and c2.
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