Econ 431: Mathematical Economics
Assignment 6
From Chapter 20, exercise 20.2 questions 2, 3, 4
Summer 2007
Kevin Wainwright
2 The Hamiltonian is H = 6y + y + u (linear in u). Thus to maximize H, we have u = 2 (if is positive) and u = 0 (if is negative) Fr
Econ 431: Mathematical Economics
Assignment 5 ANSWER KEY
Summer 2007
Kevin Wainwright
Denition 1 The particular integral (solution) yp is ANY solution that completes equation ?. In the case of the linear, automomous, rst-order dierential equation, this wi
Econ 431: Bang-Bang Optimal Control Example
Example 1 Find the optimal control that will
M ax
R2
V =
0
subject to
(2y 3u) dt
y0 = y + u
y(0) = 4 y(2)
f ree
and
u(t) U = [0, 2]
Since the problem is characterized by linearity in u and a closed control set,
ECON 431
Linear, First-Order Dierential Equations
1
Autonomous Equations
Definition 1 The general form of a linear, automomous, first-order dierential equation is
dy
+ ay = b
dt
(1)
where a, b are known constants
1.1
Homogeneous solution
Definition 2 The
Econ 431: Mathematical Economics
Summer 2007
Assignment 1
Kevin Wainwright
Instructions:The following assignment is a review of material from the second half of ECON 331. These
questions focus on chapters 8 to 13 of the textbook.
1. Consider the following