Solutions to Problem Set 2 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, September 24 1. Utility Maximization - Second-Order Conditions The following result specializes Theorem 19.8 from Simon and Blumes book to prov
Solutions to Problem Set 11 EC720.01 - Math for Economists Boston College, Department of Economics Due Tuesday, December 8 Human Capital Accumulation and Economic Growth In this version of the Uzawa-Lucas model, the representative consumer or social plann
Solutions to Problem Set 10 EC720.01 - Math for Economists Boston College, Department of Economics Due Tuesday, November 24 1. Linear-Quadratic Dynamic Programming The problem is to choose sequences cfw_zt and cfw_yt to maximize the objective function t
Solutions to Problem Set 9 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, November 12 1. Natural Resource Depletion A social planner chooses continuously dierentiable functions c(t) and s(t) for t [0, ) to maximize et
Solutions to Problem Set 8 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, November 5 1. Life Cycle Saving
+1 The consumer chooses sequences cfw_ct T=0 and cfw_kt T=1 to maximize t t T 1 ct 1 1
Peter Ireland Fall 2009
Solutions to Problem Set 7 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 29 Consider an economy populated by a large number of identical consumers, each of whom takes s0 as given, and chooses sequences cfw_ct
The Necessity of the Transversality Condition at
Innity: A (Very) Special Case
Peter Ireland
EC720.01 - Math for Economists
Boston College, Department of Economics
Fall 2010
Consider a discrete-time, innite horizon model that characterizes the optimal con
Solutions to Problem Set 5 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 15 1. Optimal Lending The lenders dynamic optimization problem can be stated formally as:
cL ,cL ,sL 01
Peter Ireland Fall 2009
max ln(
Solutions to Problem Set 4 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 8 The two welfare theorems of economics tell us that optimal and equilibrium resource allocations coincide but only under certain condi
Problem Set 1 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, September 17 1. Prot Maximization Consider a rm that produces output y with capital k and labor l according to the technology described by k a lb y, (1) whe
Dynamic Programming
Peter Ireland EC720.01 - Math for Economists Boston College, Department of Economics Fall 2009
We have now studied two ways of solving dynamic optimization problems, one based on the Kuhn-Tucker theorem and the other based on the maxim
The Maximum Principle
Peter Ireland EC720.01 - Math for Economists Boston College, Department of Economics Fall 2009
Here, we will explore the connections between two ways of solving dynamic optimization problems, that is, problems that involve optimizati
The Kuhn-Tucker and Envelope Theorems
Peter Ireland EC720.01 - Math for Economists Boston College, Department of Economics Fall 2009
The Kuhn-Tucker and Envelope theorems can be used to characterize the solution to a wide range of constrained optimization
Solutions to Problem Set 12 EC720.01 - Math for Economists Boston College, Department of Economics Not Collected or Graded 1. Stochastic Linear-Quadratic Dynamic Programming The problem is to choose contingency plans for a ow variable zt for all t = 0, 1,
Final Exam
Economics 720: Mathematics for Economists Fall 1999
This exam has three questions on three pages; before you begin, please check to make sure that your copy has all three questions and all three pages. Each question has ve parts. Each part of e
Syllabus
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2010
Tuesdays and Thursdays, 1:30 - 2:45 pm
Carney Hall, Room 305
Course Description
Economics studies the ecient allocation of scarce resources.
It follows
Saving Under Uncertainty
Peter Ireland
EC720.01 - Math for Economists
Boston College, Department of Economics
Fall 2010
This last example presents a dynamic, stochastic optimization problem that is simple
enough to allow a relatively straightforward appli
Dynamic Programming
Peter Ireland
EC720.01 - Math for Economists
Boston College, Department of Economics
Fall 2010
We have now studied two ways of solving dynamic optimization problems, one based
on the Kuhn-Tucker theorem and the other based on the maxim
The Kuhn-Tucker and Envelope Theorems
Peter Ireland
EC720.01 - Math for Economists
Boston College, Department of Economics
Fall 2010
The Kuhn-Tucker and envelope theorems can be used to characterize the solution to a
wide range of constrained optimization
Solutions to Final Exam
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2010
Due Tuesday, December 14, 2010 at 11:00am
1. Growth and Pollution, Part I
The social planners problem is
(Akz )1 1
max
z
1
B
(Akz ) subj
Final Exam
EC720.01 - Math for Economists
Boston College, Department of Economics
Peter Ireland
Fall 2010
Due Tuesday, December 14, 2010 at 11:00am
This exam has three questions on ve pages; before you begin, please check to make sure
your copy has all th
Problem Set 6 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 22 1. The Permanent Income Hypothesis The permanent income hypothesis describes how a forward-looking consumer optimally saves or borrows to smooth
Problem Set 5 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 15 This problem set asks you to solve a series of dynamic problems that characterize the optimal lending and borrowing behavior of individual consum
Problem Set 4 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 8 The two welfare theorems of economics tell us that optimal and equilibrium resource allocations coincide but only under certain conditions. Someti
LECTURE NOTES ON ECONOMIC DYNAMICS
Peter N. Ireland Department of Economics Boston College irelandp@bc.edu http:/www2.bc.edu/~irelandp/ec720.html
Copyright (c) 2008 by Peter N. Ireland. Redistribution is permitted for educational and research purposes,
Final Exam EC720.01 - Math for Economists Boston College, Department of Economics Sunday, December 20, 2009 This exam has two questions on four pages; before you begin, please check to make sure your copy has all two questions and all four pages. The rst
Solutions to Problem Set 6 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 22 1. The Permanent Income Hypothesis The consumer chooses c0 , c1 , and s to maximize the utility function ln(c0 ) + ln(c1 ) subject t
Solutions to Problem Set 3 EC720.01 - Math for Economists Boston College, Department of Economics Due Thursday, October 1 Many famous results from microeconomic theory are now understood to be special cases of the envelope theorem. This problem set will a
Saving Under Uncertainty
Peter Ireland EC720.01 - Math for Economists Boston College, Department of Economics Fall 2009
This last example presents a dynamic, stochastic optimization problem that is simple enough to allow a relatively straightforward appli