i) What is the marginal propensity to consume in period 1 out of first period income (@c₁/Əy₁) if the borrowing constraint is not binding? ii) What is the marginal propensity to consume in period 2 out of first period income (ac₂/dy₁) if the borrowing constraint is binding?
i) What is the marginal propensity to consume in period 1 out of first period income (@c₁/Əy₁) if the borrowing constraint is not binding? ii) What is the marginal propensity to consume in period 2 out of first period income (ac₂/dy₁) if the borrowing constraint is binding?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Hi,
Could you help me solve the question in the attachments?
![2. Consider the following household savings (or borrowing) problem:
max,{log(c₁) + Blog(c₂)}
subject to
C₁ = y₁ + b
C₂ = y2 (1+r)b
b ≤ b
-
where C1 and C2 denote consumption in periods 1 and 2, ß > 0 subjective discount factor, y₁
and Y2 income in periods 1 and 2, b borrowing (if it is positive) or savings (if its negative) and
r interest rate. The first two constraints are the periodic budget constraints. The last con-
straint represents a borrowing constraint: household is allowed to borrow or only up to 6 > 0.
i) What is the marginal propensity to consume in period 1 out of first period income (@c₁/Əy₁)
if the borrowing constraint is not binding?
ii) What is the marginal propensity to consume in period 2 out of first period income
(ac₂/dy₁) if the borrowing constraint is binding?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd767b79f-bceb-4e58-8cb7-4a9804b54e7b%2F93aea0d7-c174-4414-8a58-72061a1846e8%2Fj2tusj1_processed.png&w=3840&q=75)
Transcribed Image Text:2. Consider the following household savings (or borrowing) problem:
max,{log(c₁) + Blog(c₂)}
subject to
C₁ = y₁ + b
C₂ = y2 (1+r)b
b ≤ b
-
where C1 and C2 denote consumption in periods 1 and 2, ß > 0 subjective discount factor, y₁
and Y2 income in periods 1 and 2, b borrowing (if it is positive) or savings (if its negative) and
r interest rate. The first two constraints are the periodic budget constraints. The last con-
straint represents a borrowing constraint: household is allowed to borrow or only up to 6 > 0.
i) What is the marginal propensity to consume in period 1 out of first period income (@c₁/Əy₁)
if the borrowing constraint is not binding?
ii) What is the marginal propensity to consume in period 2 out of first period income
(ac₂/dy₁) if the borrowing constraint is binding?
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