Homework 4: Theory of Dynamic Programming
Mohammad Hossein Rahmati
October 17, 2015
1. SLP
1
Exercise 5.3 (correction k = argmaxk0 [f (k) k])
2. (A Tree-Cutting Problem) SLP Exercise 5.5
3. Show that the Bellman Equation of problem 6 in Homework 2 is Cont

In the name of GOD
Fiscal Policy
a. Taxes
content
Introduction
Output tax
Non-distortionary/Lump-Sum taxes
Distortionary/Proportional taxes
Laffer curve
Labor tax
Non-distortionary/Lump-Sum taxes
Distortionary/Proportional taxes
Laffer curve
Intr

In the name of GOD
Fiscal Policy
b. Social security
Dr. Seyed Ali Madanizade
Prepared by: M. Azizirad
2
content
Overlapping generation models
Optimizer agents
Social planner
Funded pension systems
Pay-as-you-go/unfunded systems
3
Overlapping generati

Homework 7: Recursive Competitive Equilibrium
Mohammad Hossein Rahmati
October 17, 2015
1. Consider a neoclassical growth model with logarithmic felicity function, Cobb-Douglas pro l) = Ak l1 , full depreciation of the capital stock in one period (the
duc

Homework 5: Dynamic Programming & Speed of Convergence
Mohammad Hossein Rahmati
October 17, 2015
1. (Adjustment cost model) Consider the following discrete-time dynamic programming problem in sequence formulation;
max
cfw_xt+1 t=0
X
t [h(xt ) a(xt+1 xt )

Homework 6: Sequential Competitive Equilibrium
Mohammad Hossein Rahmati
October 17, 2015
1. Consider a two-consumer, two-period exchange economy with date-0 trading. Type-1 consumers are endowed with 2 units of the consumption good in period 0 and 0 units

In the name of GOD
Fiscal Policy
c. Public debt
Dr. Seyed Ali Madanizade
Prepared by: M. Azizirad
2
content
Ricardian equivalence
Optimal taxation
3
Ricardian equivalence
Government: Two-period model:
=
+
=
1+
+
1+
=
+
1+
4
Ricardian equivalence
Gove

Homework 8: Stochastic Optimization Problem
Mohammad Hossein Rahmati
October 17, 2015
1. Do Exercise 8.10 Early resolution of uncertainty, from Ljungquist, Sarget, 2nd ed.
2. Do Exercise 13.4 The term structure and consumption, from Ljungquist, Sarget, 2n

Homework 3: Application of Dynamic Programming
Mohammad Hossein Rahmati
October 17, 2015
1. A consumer
P t seeks to maximize her lifetime utility of consumption and leisure, which is given
by:
t=0 u(ct , lt ), where ct is consumption in period t and lt is

Homework 2: Dynamic Optimization
Mohammad Hossein Rahmati
October 17, 2015
1. Consider the one time period problem we solved in the class. Lets change the production
function to zf (n). Here z is called total factor productivity. Find the first order cond