Solutions to Problem Set 10
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
For Extra Practice - Not Collected or Graded
1. Linear-Quadratic Dynamic Prog
Solutions to Problem Set 4
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, October 8
The two welfare theorems of economics tell us that opti
Problem Set 3
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, October 1
Many famous results from microeconomic theory are now understood to
Problem Set 1
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Thursday, September 12
1. Prot Maximization
Consider a rm that produces output y with c
Problem Set 4
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, October 8
The two welfare theorems of economics tell us that optimal and equil
Solutions to Final Exam
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, December 17 at 12 noon
1. Dynamic Pricing by an Industry Leader
The
Solutions to Midterm Exam
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Thursday, October 31, 1:30 - 2:45pm
1. The Kuhn-Tucker Theorem
The problem is n
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
October 12, 2011
Problem Set 3 Solutions
4. Hotellings Lemma
(a) The Lagrangian for the rms problem is
L(y, k, l, ) = p
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
December 9, 2011
Problem Set 9 Solutions
1. Stochastic Linear-Quadratic Dynamic Programming
(a) Using the guess that th
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
December 3, 2011
Problem Set 8 Solutions
1. Human Capital Accumulation and Economic Growth
(a) The Bellman equation for
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
November 11, 2011
Problem Set 6 Solutions
1. Investment with Adjustment Costs
(a) The current-value Hamiltonian for thi
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
October 13, 2011
Midterm Exam - Solutions
1. Quasilinear Preferences
(a) There are a number of ways to dene the Lagrang
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
November 22, 2011
Problem Set 7 Solutions
1. Linear-Quadratic Dynamic Programming
(a) The Bellman equation for this pro
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
December 13, 2011
Final Exam - Solutions
1. Job Search
(a) The agents utility function has no explicit dependence on ti
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
October 24, 2011
Problem Set 4 Solutions
1. Optimal Lending
The lenders dynamic optimization problem can be stated form
EC720 - Problem Set 1 Solutions
Samson Alva
Department of Economics, Boston College
September 22, 2011
Exercise 2.1
1a. See notes.
1b. () Let x f 1 (B B ). Then there exists y f (x) B B , since x has
EC 720 - Math for Economists
Samson Alva
Department of Economics, Boston College
November 8, 2011
Problem Set 5 Solutions
1. Life Cycle Consumption and Saving in Discrete Time
(a) The Hamiltonian is
H
Problem Set 2
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, September 24
1. Utility Maximization - Second-Order Conditions
The following r
Final Exam
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, December 17 at 12 noon
This exam has two questions on ve pages; please check to m
Solutions to Problem Set 5
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, October 15
1. Optimal Lending
The lenders dynamic optimization pr
Solutions to Problem Set 3
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, October 1
Many famous results from microeconomic theory are now u
Solutions to Problem Set 2
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, September 24
1. Utility Maximization - Second-Order Conditions
Th
Solutions to Problem Set 1
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Thursday, September 12
1. Prot Maximization
Consider a rm that produces ou
Solutions to Problem Set 6
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, October 22
1. The Permanent Income Hypothesis
The consumer choose
Solutions to Problem Set 7
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, October 29
Consider an economy populated by a large number of ide
Solutions to Problem Set 11
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, December 3
Human Capital Accumulation and Economic Growth
In thi
Solutions to Problem Set 9
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, November 19
1. Natural Resource Depletion
A social planner choose
Solutions to Problem Set 8
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Due Tuesday, November 12
1. Life Cycle Saving
+1
The consumer chooses sequence
Solutions to Problem Set 12
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2013
Practice for Final - Not Collected or Graded
1. Stochastic Linear-Quadratic D
c) We need to introduce constraints that describe the evolution of stock variables over time:
e.g., larger ows of savings or investment today will lead to larger stocks of wealth or
capital tomorrow.