Macroeconomic Theory and Analysis
Problem Set 6
Suggested Solutions
1
Problem 1: Ricardian Equivalence
1.1
Government Budget Constraint
The goverment budget constraints in the two periods are
g1 = b
g2 + (1 + r)b = sr
(1)
(2)
2
Notice that government is f
Homework #6: Ricardian Neutrality
Professor Violante
Problem 1
Consider an economy that lasts for 2 periods = 1 2 The economy is populated by a
mass 1 of households, all equal, with preferences
(1 2 ) = ln (1 ) + ln (2 )
where 1 is the discount factor,
Macroeconomic Theory and Analysis
Suggested Solution for Midterm 1
March 10, 2008
1
Problem 1 : Equilibrium and Social Planners solution
In this static economy the household chooses how much to work and how
much to consume subject to the following budget
Homework #5: Asset Pricing and Investment
Professor Violante
Problem 1: Asset Pricing
An individual lives for two periods and must decide how much to consume in the two periods cfw_1 2
and how much to save in the rst period cfw_ She has preferences over
Suggested Solutions for Midterm 2,
Macroeconomic Models and Policy
April 5, 2014
1
Permanent Income Hypothesis
1.1
Consumption Smoothing
Considering the standard problem, rst-order conditions lead to the Euler
equation. Moreover, the assumptions that (1 +
Macroeconomics Theory and Analysis. V31.0013
Suggested First Midterm Solution
Sai Ma
March, 2014
1
Question 1: Four short questions
(a)
Constant returns to scale for a production function f (n; k ) where n is labor and k is
capital are
f ( n; k ) = f (n;
Macroeconomic Theory and Analysis (ECON-UA 13.001)
Spring 2014
Professor Gianluca Violante
General Information
Class time and location: Monday and Wednesday 11:00 am-12:15 pm in Kimmel
Center 808.
Oce Hours: Wednesday 1:00-2:00 pm in my oce, Room 712, D
1
The Primitives of an Economy
In every economic model it is useful to specify in detail the following features of the
economy:
Time: whether the economy is static (one-period), or dynamic (two or multiple
periods).
Agents: households, firms and governm
1
Competitive Equilibrium
Each household and each firm in the economy act independently from each other,
seeking their own interest, and taking as given the fact that other agents will also seek
their best. In the previous section we have described the be
1
Intertemporal Choices
We now extend our framework to incorporate intertemporal decisions, i.e. decisions
that involve a trade-o between the present and the future. The vast majority of
important economic decisions are of this type:
the consumption deci
1
1.1
A Dynamic Production Economy
Description of the economy
Time. The economy lasts for two periods = 1 2 and is populated by households,
firms and by the government.
Demographics and preferences. Households live for two periods, and have
preferences
(
Homework #1: One Period Economy
Professor Violante
Problem 1: Tax on labor income
Consider an economy where the representative consumer has a utility function ( ) over consumption and leisure . Assume preferences satisfy the standard properties we assumed
Homework 1 (Answers), Macroeconomic Theory
and Analysis, NYU, Spring 2015
February 5, 2015
1
Tax on Labor Income
Households Problem The household chooses (c, l) to maximise the utility function
U(c, l) subject to the following budget constraint:
c (1 )w(1
MACROECONOMIC THEORY AND ANALYSIS
First Midterm, February 24th 2005
suggested solutions
March 2, 2005
1
1.1
Question 1: Consumption theory
Point a: Dynamic maximization
The consumer chooses consumption today c1 , consumption tomorrow c2
savings s and bequ
Macroeconomic Theory and Analysis
Suggested Solution for Midterm 1
March 5, 2006
1
1.1
Problem1 : Externality in a static economy
Competitive Equilibrium
The consumer maximizes
max log(c) + log(l)
cfw_c,l
(1)
st :
c = w (1 l) P
Setup a Lagrangian as
L = m
Macroeconomic Theory and Analysis. V31.0013
Midterm 2 2006
Suggested Solutions
1
1.1
Two Short Questions
Risk Aversion
Ucc
(c c)( 1)
c
c=
c=
Uc
(c c)
cc
The coecient of relative risk aversion is a decreasing function of consumption
and converges to as th
MACROECONOMIC THEORY AND ANALYSIS
First Midterm, February 24th 2005
You have 1 hour for this exam. Electronic calculators are allowed, but neither books nor
class-notes are permitted. Please, read through the whole exam before starting. Note that
question
MACROECONOMIC THEORY AND ANALYSIS
First Midterm, March 10 2014
You have 75 minutes for this exam. Neither books, nor class notes, nor calculators are
permitted. Please, read through the whole exam before starting. Note that questions are not
equally weigh
MACROECONOMIC MODELS AND POLICY
Second Midterm
You have 75 minutes for this exam. Electronic calculators are allowed, but neither books
nor class-notes are permitted. Please, read through the whole exam before starting. Note that
questions are not equally
Macroeconomic Theory and Analysis
Solutions Homework #1: Measurement
Problem1.
Wheat and Bread
a) Product approach: Firm A produces 50 bushels of wheat, with no intermediate
goods inputs. At $3/bu., the value of Firm As production is equal to $150. Firm
B
MACROECONOMIC THEORY AND ANALYSIS
Second Midterm, April 6th 2006
You have 70 minutes for this exam. Electronic calculators are allowed, but neither books
nor class notes are permitted. Please, read through the whole exam before starting. Note that
questio
Suggested Solution for HW1
February 10, 2014
1
1.1
Problem 1: tax on labor income
Households problem
The household chooses ( ) to maximise the utility function ( ) subject
to the following budget constraint:
(1 )(1 ) + +
The households utility function
Suggested Solution for HW3
February 22, 2014
1
1.1
Problem 1: Consumption Theory
Dynamic problem of the household
You can verify that the households utility function is well behaved and it
satises the Inada conditions. The agent chooses consumption today
Suggested Solution for HW2
February 15, 2014
1
1.1
Pareto Optimality in a Backyard Economy
CE Allocation
The household i chooses (ci ; li ) to maximise the utility function U i (ci ; g ),
where g1 = li , gj = l2 and g = gi + gj subject to the following bu
Macroeconomic Theory and Analysis.
Suggested Solutions HW5
1
Problem 1: Asset Pricing
1.1
Coe cient Of Relative Risk Aversion
1
1 . Thus,
Note that u(c) = c
implies that u0 (c) = c and u00 (c) =
c
1
using the denition of relative rsik aversion, we have th
1
Question 1: PIH
Consider an agent with an innite planning horizon who faces an innite sequence of earnings cfw_ which is perfectly known already at time = 0. This agent solves the following
=0
consumption/saving problem:
max
cfw_ +1
X
( )
=0
+ +1 =
Macroeconomic Theory and Analysis. V31.0013
First Midterm
Suggested Solutions
Question 1: Price Indexes
(a)
Laspeyres Index:
L0,t
P
pit qi0
= Pi
i pi0 qi0
tells us the increase in price between 0 and t of the basket of goods produced at time
0 which is k
Macroeconomic Theory and Analysis V31.0013
Suggested Solutions for the First Midterm
Question 1. Welfare Theorems
(a) There are two households that maximize
max U (ci , g1 + g2 )
cfw_ci ,li
(1)
st :
ci w(1 li )
for each i = 1, 2. Replacing the gardening
1
The Permanent Income Hypothesis
1.1
A two-period model
Consider a two-period model where households choose consumption (1 2 ) to solve
max log 1 + log 2
cfw_1 2
2
1 +
1+
=
1+
1
1+
+
where is the discount factor, the interest rate. The term is the per