Homework 7
Graduate Macroeconomics. Viktor Tsyrennikov
Question 1. Exercise 9.3.
Assume u(c) = ln(c). Ignore part (c).
Question 2. Time is discrete. There is one perishable good at each
date. Uncertainty is fully summarized by a rst-order Markov process s
Homework 6. Solution Graduate Macroeconomics. Viktor Tsyrennikov
Question 1. Your task is to solve a model in which consumption growth
process resembles that in the data and compare the models predictions about
the equity premium with the data.
Model envi
Macroeconomic Theory I. Viktor Tsyrennikov
Homework 3
Question 1. Government needs to nance a stream of government purchases gt > 0, t. It can raise tax revenue Tt in any period t up to the total
income Yt > 1. Government seeks to minimize the welfare cos
Macroeconomic Theory I. Viktor Tsyrennikov
Homework 1
Question 1. An individual seeks to maximize his utility
t u (d t ),
U ( c) =
(0, 1),
t=0
where dt is a non-negative consumption level of a durable good in period t.
Durable goods are accumulated acco
Homework 1. Solution
Macroeconomic Theory I. Viktor Tsyrennikov
Question 1. An individual seeks to maximize his utility
U (c1 , c2 ) = ln(c1 ) + ln(c2 ),
(0, 1),
where c1 and c2 are non-negative consumption levels of a perishable good in
period 1 and 2 r
Macroeconomic Theory I. Viktor Tsyrennikov
Homework 1
Question 1. An individual seeks to maximize his utility
U (c1 , c2 ) = ln(c1 ) + ln(c2 ),
(0, 1),
where c1 and c2 are non-negative consumption levels of a perishable good in
period 1 and 2 respectivel
Midterm Exam 2
Viktor Tsyrennikov
Graduate Macroeconomics
October 28, 2011
The exam is designed to be nished in 80 minutes.
There are 2 problems, worth 50 and 50 points respectively.
Read carefully the whole problem before answering.
Show your work guesse
Midterm Exam 1
Viktor Tsyrennikov
Graduate Macroeconomics
September 23, 2011
The exam is designed to be nished in 75 minutes.
There are 2 problems, worth 40 and 60 points respectively.
Read carefully the whole problem before answering.
Show your work gues
Viktor Tsyrennikov
Graduate Macroeconomics
Complete Financial Markets
So far we have assumed that agents individuals or households can trade
only one asset. This asset was a credit bank account. It could also be thought
of as risk-free debt. In a determin
Mathematical Appendix
1
Real Analysis Preliminaries
First we need to build a mathematical apparatus. This section serves the
purpose by providing a collection of denitions from Real Analysis and examples demonstrating their application.1
1.1
Metric spaces
Viktor Tsyrennikov
Graduate Macroeconomics
Dynamic Programming
In the notes on the recursive formulation of the saving problem we showed
that the sequence problem (SP)
t u(ct ) s.t. at+1 = Rt+1 (at + y ct ), at+1
max
cfw_ct ,at+1
Bt+1 , t, (SP)
t=0
and
Viktor Tsyrennikov
Graduate Macroeconomics
Savings Problem
In this part we study the building block of macroeconomics the savings
problem. Our subject is an economic agent a household or an individual.
It receives variable income and decides how much to s
1
Endogenous Labor Supply
Before we assumed that an agent works full time every period and receives
an exogenous income yt . We now let an agent choose how much to work.
Income is proportional to the number of hours spent at work lt and the wage
in period