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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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?
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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