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 toC₁ = y₁ + bC₂ = y2 (1+r)bb ≤ b-where C1 and C2 denote consumption in periods 1 and 2, ß > 0 subjective discount factor, y₁and Y2 income in periods 1 and 2, b borrowing (if it is positive) or savings (if its negative) andr 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?

Answered: i) What is the marginal propensity to…

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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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?

Expert Solution

Step 1: Question (i)

i) Marginal Propensity to Consume in Period 1

To calculate the marginal propensity to consume in period 1 with respect to first period income, we're essentially calculating how much additional consumption in period 1 will result from an additional unit of income in period 1.

Given the constraint:

$c 1 equals y 1 plus b$

The derivative of $c 1$ with respect to $y 1$ is:

$partial differential c 1 space divided by space partial differential y 1 equals 1$

This result makes intuitive sense. If the borrowing constraint isn't binding and the household receives an additional unit of income in period 1, they would consume that additional unit in the same period. Thus, the marginal propensity to consume in period 1 out of first period income is 1 when the borrowing constraint is not binding.

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