ECO 3145 Mathematical Economics I
Lecture 1
Homework Problems
Answers
2
2
1. b.) f ( x 1 , x 2 , x 3 ) = x 1 + 2 x 2 + 3x 3 + 4 x 1 x 2 6 x 1 x 3 + 8x 2 x 3
2
df = [2 x 1 + 4 x 2 6x 3 ]dx 1 + [4 x 2 + 4 x 1 + 8x 3 ]dx 2 + [6 x 3 6 x 1 + 8x 2 ]dx 3
df x1 =
Maximization with Equality Constraint: The Lagrange
Multiplier
1. The CakeEating Problem
1.1. Problem Statement
An economy begins in period 0 with an oil reserve of size x0 . The problem faced by the central
planner is how to exploit this oil reserve ove
Differential Equations
1. The Most Fundamental Differential Equation in Economics
1.1. The Problem
An individual has a wealth x0 at time 0. She puts the money in a saving account, and her balance
rises through time due to the accrued interest. Let rt deno
The Kuhn Tucker Theorem
Maximization under Inequality Constraints
1. Utility Maximization under Budget and Rationing Constraints
Consider an individual who consumes two goods, called good 1 and good 2. Her preferences are
represented by the following util
Assignment 2
ECO 3145 B
Answer
Exercise
1
Find the stationary values of the following functions, and determine whether
they give maxima, minima, or points of inection. Our answer will be based on
sucient conditions.
a) y = 2x + 3/x
This function is dened
Assignment 3: (5 % of the nal grade)
ECO 3145 B
Due date: Tuesday, December 6 at 4:30 pm
Exercise
1
Recall that, the determinant of a 1 1 matrix is the single number in the
matrix.
For any n 2, the determinant of the n n matrix A is
A =
n
X
(1)i+j aij 
APDF MERGER DEMO
Answers Pamphlet for
MATHEMATICS FOR
ECONOMISTS
Carl P Simon
.
Lawrence Blume
W.W. Norton and Company, Inc.
Table of Contents
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 1
Chapter 2
Economic Policy Using Applied General
Equilibrium Models: An Overview
Abstract In the research presented throughout this book, a general equilibrium
model serves to assess how the economy as a whole will react to any exogenous
change. This chapt
ECO 3145 Mathematical Economics I
Lecture 1
Homework Problems
1. For the following two functions, derive the total differential, the partial differential with
respect to x1, and the second differential. Put the latter in matrix form.
2
a.) f ( x 1 , x 2 )
ECO 3145 Mathematical Economics I
Lecture 0
Review of Matrix Algebra
Chiang1, ch. 4.1 4.6, 5.1 5.5

linear equation system:
Ax
d , where A is an n n matrix of coefficients, x
x1
xn

inverse matrix: A 1A

determinant: A Solve using Laplace expansion.2

University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2014
Prof. Leslie Shiell
Rm. 9021, Faculty of Social Sciences
5625800 ext. 1693
[email protected]
Office hours:
Tues 10:00 11:30
Wed 2 :30 4:00
or by appointment
Course description:
This
ECO3145A Mathematical Economics I
Professor: N. V. Quyen
Assignment 4
Due date: 8 June 2016
1. Find the dimensions of the box with largest volume if the total surface area is 64 cm 2 . Observe
that if x, y, z are the dimensions of the box, then its volume