Homework #8: Ricardian Neutrality
Professor Violante
Problem 1
Consider an economy that lasts for 2 periods t = 1, 2. The economy is populated by a
mass 1 of households, all equal, with preferences
U (c1 , c2 ) = ln (c1 ) + ln (c2 ) ,
where < 1 is the dis
MACROECONOMIC THEORY AND ANALYSIS
First Midterm, February 26th 2004
You have 1 hour and 15 minutes for this exam. Electronic calculators are allowed, but
neither books nor class-notes are permitted. Please, read through the whole exam before
starting. All
MACROECONOMIC THEORY AND ANALYSIS
First Midterm, February 26th 2008
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
ques
Homework #10: Search Model
Professor Violante
Problem 1
Consider the search model we studied in class, where the hazard rate from unemployment, i.e. the probability of nding an acceptable job and transiting from unemployment
into employment is = 1 G (w ),
Homework #9
Professor Violante
Problem 1: Optimal Taxation
Consider a two-period economy, where households have preferences
u (c1 , c2 ) = ln c1 + ln c2 .
Households receive an income endowment y in the rst period only, and decide optimally how
to allocat
Homework #7: Investment Theory
Professor Violante
Problem 1: Investment model with taxation
Consider an innitely lived rm that every period t chooses investment it . At each period t, the rm
produces with the stock of capital kt that inherited from the pa
SPECIAL REPORT
PENSIONS
April 9th 2011
Falling
short
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PENSIONS
Falling short
People in rich c
NBER WORKING PAPER SERIES
RESUSCITATING REAL BUSINESS CYCLES
Robert G. King
Sergio T. Rebelo
Working Paper 7534
http:/www.nber.org/papers/w7534
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
February 2000
Written for th
1
Asset Pricing: Bonds vs Stocks
In the data, historically, one dollar invested in the Dow-Jones yielded 6 times more than
one dollar invested in U.S. Treasury bonds. The return on stocks is roughly 6% and the
return on bonds roughly 1%. This dierence in
1
The PIH in the stochastic case
Recall the Euler equation under uncertainty
u0 (ct ) = (1 + r) E [u0 (ct+1 )] .
Lets now return to the two key assumptions of the PIH: 1) quadratic utility specication
u (c) = b1 (1/2) b2 c2 and 2) no intertemporal saving
Homework #6: Asset Pricing
Professor Violante
Problem 1: Risk Aversion
Consider a risk-averse individual with consumption c facing a bet that pays a random
amount z , with E (z ) = 0 and var (z ) = . Let be the premium that she would be willing to
pay to
Homework #11: Solow Growth Model
Professor Violante
Problem 1: Convergence
Lets use the Solow model for some quantitative macroeconomics. In the U.S. the poorest
state in 2010 was Mississippi with $35, 000 of income per capita and the richest state was
Ne
Advanced Macroeconomics and Finance
Homework #0: Measurement
Professor Violante
Problem 1: Wheat and Bread
An economy has two rms. Firm A produces wheat and rm B produces bread. In a given year,
A produces 50 bushels of wheat, sells 20 bushels to rm B at
Homework #12: Endogenous Growth Models
Professor Violante
Problem 2: Solow model with human capital
Consider an economy with Cobb-Douglas production technology which depends on physical capital
k (t) and human capital h (t)
y (t) = h (t) k (t)1
ih (t) + i
AMF - Homework #1: One Period Economy
Professor Violante
Problem 1: Tax on labor income
Consider an economy where the representative consumer has a utility function u (c, l) over consumption c and leisure l. Assume preferences satisfy the standard propert
Homework #2: Pareto Optimality
Professor Violante
Problem 1. Pareto Optimality in a Backyard Economy
Consider a static (one-period) economy inhabited by two households indexed by
i = 1, 2. Households can either work in a rm (h) or work in their backyard (
Homework #3: Consumption-Saving Decisions
Professor Violante
Question 1: Consumption Theory
Consider an individual living for two periods with preferences
U (c1 , c2 ) = u (c1 ) +
1
1
u (c2 ) , where u (c) = exp (c)
1+
The individual receives income cfw_y
Homework #4: Permanent Income Hypothesis
Professor Violante
Question 1: Consumption Theory with CRRA utility
Consider an individual with an innite horizon and CRRA preferences
X
c1+j
t
1
j =0
j
where 1 is the inverse of the intertemporal elasticity of sub
Homework #5: Consumption under uncertainty
Professor Violante
Question 1: Leisure under uncertainty
Agents live an innite number of periods. Their wage wt is uncertain. Uncertainty is
dened in terms of a random variable st S = cfw_s1 , s1 , ., sN , i.e.,
MACROECONOMIC THEORY AND ANALYSIS
First Midterm, March 6th 2003
You have 1 hour and 15 minutes for this exam. Electronic calculators are allowed, but
neither books nor class-notes are permitted. Please, read through the whole exam before
starting. All que
1
Consumption and saving under uncertainty
An economy with uncertainty: As in the deterministic case, we keep assuming that
agents live an innite number of periods. Their earnings are uncertain. Uncertainty is
dened in terms of a random variable st S = cf
1
The Permanent Income Hypothesis
We now study the standard theoretical framework used by macroeconomists to think
about consumption and saving behavior. Consider an agent with an innite planning
horizon who faces an innite sequence of earnings cfw_yt wh
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 past. The vast majority of important economic decisions are of this type:
the consumption decisi
1
Equilibrium Unemployment
The idea of modelling labor markets as frictional markets (i.e., markets which do
not clear) is due to Diamond, Mortensen and Pissarides. For this idea, they won
the Nobel Prize in Economics in 2011. The specic version of the m
1
Unemployment: Facts and Models
1.1
Facts
Denote the population of working age 16-65 at time t as Pt . This segment of the population can be divided into 3 groups. First, the group of all the individuals who hold a
job at time t , called employment, deno
1
Ricardian Neutrality of Fiscal Policy
We start our analysis of scal policy by stating a neutrality result for scal policy
which is due to David Ricardo (1817), and whose formal illustration is due to Robert
Barro (1974). The Ricardian proposition can be
1
Real Business Cycles
1.1
Motivation
Our empirical analysis of the U.S. time series has shown that there are movements in all
the aggregate variables of interest (output, consumption, investments, etc.) around the
trend. These uctuations in economic acti
1
Optimal Taxation
Until now, we have assumed that government policy is exogenously given, so the government had a very passive role. Its only concern was balancing the intertemporal
budget. In this section, we let the government be more proactive, and ch
1
Social Security
In the U.S. economy, and in the majority of developed countries, there is a Pay-As-YouGo (PAYG) social security system in place: all young workers alive in a given period pay
into a general fund administered by the Government (Trust Fund
1
Investment Theory
We now consider the problem of an innitely lived rm that in every period chooses
how much to invest, i.e., how much to add to its stock of productive capital. Note the
dierence with the way we modelled the rm so far: we are used to thi