Problem Set #5
8 October 2013
Instructor: David Laibson
Economics 2010c
Problem 1: Solve the Merton Consumption problem assuming that
() = ln()
Do not set = 1 as we did in class. Instead, solve the problem from scratch
assuming () = ln() When you guess th
Economics 2010c: Lecture 8
Brownian Motion and Continuous Time
Dynamic Programming
David Laibson
10/1/2013
Outline: Continuous Time Dynamic Programming
1. Continuous time random walks: Wiener Process
2. Itos Lemma
3. Continuous time Bellman Equation
1
Bro
Economics 2010c: Lecture 3
The Classical Consumption Model
David Laibson
9/12/2013
Outline:
1. Consumption: Basic model and the early theories
2. Linearization of the Euler Equation
3. Empirical tests without precautionary savings eects
1
Application: Con
Problem Set #1
Due: 10 September 2013
Instructor: David Laibson
Economics 2010c
Problem 1 (Growth Model): Recall the growth model that we discussed
in class. We expressed the sequence problem as
(0 ) =
sup
f+1 g1
=0
subject to the constraint
1
X
=0
ln( +
2010c - Solution Set 2
Fall 2012
This solution set is based on the previous work of Filipe Campante, Fabi` Gumbau, Jason Hwang,
a
Yves Nosbusch, Neel Rao, Jenny Tang, and particularly Davide Cantoni and Giacomo Ponzetto.
Questions should be addressed to B
Economics 2010c: Lecture 7
Asset Pricing
David Laibson
September 26, 2013
Outline:
1. Equity premium puzzle
2. Calibration of risk aversion
3. Resolutions of the equity premium puzzle
1
Equity premium puzzle (Mehra and Prescott)
To derive an asset pricing
Problem Set #2
Due in class on Tuesday (9/17)
Instructor: David Laibson
Economics 2010c
Problem 1 (Eat-the-Pie Problem): Consider the following sequence
problem:
1
X
max
( )
1
f g=0
=0
subject to the constraints:
+1 = ( )
0
given.
0 0
Im now going to as
2010c - Solution Set 2
Fall 2013
This solution set is based on the previous work of Filipe Campante, Fabi` Gumbau, Jason Hwang,
a
Yves Nosbusch, Neel Rao, Jenny Tang, and particularly Davide Cantoni and Giacomo Ponzetto.
Questions should be addressed to B
2010c - Solution Set 5
Fall 2013
This solution set is based on the previous work of Filipe Campante, Fabi` Gumbau, Jason Hwang,
a
Yves Nosbusch, Oleg Itskhoki, Neel Rao, Jenny Tang, and particularly Davide Cantoni and Giacomo Ponzetto. Questions should be
Final Problem Set
10/11/2013
Due: 10/22/2013
Instructor: David Laibson
Economics 2010c
Problem 1: Recall the stopping problem from Lecture 10. The lecture notes
show that the optimal threshold rule is
=
+
p
2
2
+
22
Show that 0 Show that the following l
2010c - Solution Set 4
Fall 2013
This solution set is based on the previous work of Filipe Campante, Jason Hwang, Neel Rao,
Jenny Tang, and particularly Giacomo Ponzetto. Questions should be addressed to Ben Hebert
([email protected]).
1
Three-Perio
Problem Set #4
1 October 2013
Instructor: David Laibson
Economics 2010c
Problem 1: Three period hyperbolic discounting model.
Consider a person who lives for three periods, = 1 2 3. To simplify
exposition, Ill refer to three selves of this individual. The
Problem Set #3
24 September 2013
Instructor: David Laibson
Economics 2010c
Problem 1 (A simple consumption problem). Consider the following
sequence problem: Find () such that
(0 ) = sup
1
X
f g1 =0
=0
ln( )
subject to 2 [0 ] +1 = ( ) with 0 given.
Bellm
2010c - Solution Set 1
Fall 2013
This solution set is based on the previous work of Filipe Campante, Fabi` Gumbau, Jason Hwang,
a
Yves Nosbusch, Gustavo Suarez, Neel Rao, Jenny Tang, and particularly Giacomo Ponzetto.
Questions should be addressed to Ben
2010c - Solution Set 6
Fall 2013
This solution set is based on the previous work of Filipe Campante, Fabi` Gumbau, Oleg Itskhoki,
a
Neel Rao, Jenny Tang, and particularly Giacomo Ponzetto. Questions should be addressed to Ben
Hebert ([email protected]
2010c Section 1
Jenny Tang and Ben Hebert
September 7, 2013
1
Logistics
Section times: (usually) Thursdays, 6:00-7:30pm in M-15 & Fridays, 2-3:30pm in M-17
Oce hours: Monday 12:30-2:00pm at Littauer Basement and Friday 10-11:30am, in Baker
Library 220b. T
2010c Section 6
Ben Hebert and Jenny Tang
10/8/2013
1
Outline
General talk about continuous time
q Model (with depreciation)
(Optional) Irreversible Investment
(Optional) Adjustment Costs
2
q Model (with depreciation)
Setup: A rm facing traditional co
2010c Section 3
Ben Hebert and Jenny Tang
September 17, 2013
1
Outline
A Note on the IES and RRA
Precautionary Savings Model
Finite Horizon Dynamic Programming
Finite Horizon Examples
2
The Intertemporal Elasticity of Substitution and the
Relative Ris
2010c Section 2
Jenny Tang and Ben Hebert
September 10, 2013
1
Outline
The Contraction Mapping Theorem
Comment on Blackwells Theorem and Boundedness
Problem Set 1 (see solutions)
Euler Equation
Life Cycle Hypothesis
Certainty Equivalence Model
Exam
2010c Section 4
Ben Hebert and Jenny Tang
September 25, 2013
1
Outline
Hyperbolic Discounting
Hyperbolic Euler Equation
Asset Pricing
Examples
2
Hyperbolic Discounting
Note: This part isnt required material. Use it for reference later.
In continuous t