MATH MODULE
10
Solutions to
Exercises
1. (a) dy/dx = 3, and d2y/dx2 = 0. This positively sloped straight line has no nite maxima or minima, since dy/dx > 0 everywhere.
(b) dy/dx = 2x + 20, and d2y/dx2
MATH MODULE
9
Solutions to
Exercises
1. Under option (a), you would owe Louie 1000(1.02)364 = $1,350,400.29, whereas
under option (b) you would owe him only 1000(1.1)52 = $142,042.93. The weekly rate
MATH MODULE
7
Solutions to
Exercises
1. Average price = 24 = 0.4(12) + 0.6x, where x is the average price of the remaining 60%
of the goods. Hence x = (24 4.80)/0.6 = 19.2/0.6 = $32/unit.
2. Average p
MATH MODULE
6
Solutions to
Exercises
1. Both methods, the = P /(mQ) point-slope technique and the = OF/AF segmentratio technique, should of course have given you the same results. The reason for
doing
MATH MODULE
5
Solutions to
Exercises
1. The following Table contains the Total Revenue, Average Revenue, and Marginal
Revenue equations and gives the value for each of the equations when Q = 10 tonnes
MATH MODULE
4
Solutions to
Exercises
1. (a) TR = P QD = $36/kg 24 kg = $864 in each period.
(b) (i) P = 6000 100QD
(ii) P = 6000 0.1QD
(iii) P = 6 0.0001QD
(iv) P = 6 0.1QD
(v) P = 60/2.2 1/[(2.2) 2]Q
MATH MODULE
3
Solutions to
Exercises
[Except for the answers to questions 7 and 8, the solutions below are not accompanied
by graphs. As an exercise, you may want to construct graphs for some of the c
MATH MODULE
2
Solutions to
Exercises
1. Equations (a), (d), and (e) all have the form y = 12 + 3x, and horizontal intercept
(4, 0). Equations (b), (c), and (f) all have the form y = 12 3x, and horizon
MATH MODULE
1
Solutions to
Exercises
1. You may wish to insert values for x, solve for y, and graph some of the following
equations. If any posed difculties, you should denitely graph them.
(a) y = f(
MATH MODULE
10
Calculus Results
for the
Non-Calculus Speaker
1. Discussion
1.1 THE BASICS
For some, Calculus (with a capital letter) has an aura of mystery, and can contribute to
math anxiety. Yet if
MATH MODULE
9
Growth Rates,
Interest Rates,
and Inflation:
The Economics of Time
1. Discussion
Time is at the core of economics. Economic activity occurs in time, takes time, and costs
time. A product
MATH MODULE
8
Some Special
Functions
and Formulas
1. Discussion
This module contains refresher notes on several mathematical topics with important
economic applications. Section 1.1 covers:
1. the use
MATH MODULE
7
Proportions, Weights,
and Percentages
1. Discussion
This Module deals with material which you likely rst encountered in elementary
school, but which still contains enough tricky aspects
MATH MODULE
6
Elasticities
1. Discussion
Elasticity measures play a number of important roles in economics. In the text you will
nd a wide range of applications of the elasticity concept in many forms
MATH MODULE
5
Total, Average, and
Marginal Functions
1. Discussion
A very important skill for economists is the ability to relate total, average, and marginal curves. Much of standard microeconomics i
MATH MODULE
4
Using Economic
Units
1. Discussion
[You will likely nd this Module to be either one of the most obvious wastes of time of
them all or one of the more useful ones. Skim it, and if everyth
MATH MODULE
3
Solving Linear
Equation Systems
1. Discussion
In Module 2, you reviewed the properties of linear equations and functions. One of the
principal uses of such functions is to describe an as
MATH MODULE
2
Linear Equations
1. Discussion
Linear functions or equations are used in economics in many contexts. They are used,
to give a few examples, to describe:
supply and demand functions;
bu
MATH MODULE
1
Functions, Graphs,
and the Coordinate
System
1. Discussion
This is the most abstract module of them all, but it is not particularly difcult. It is here
to provide a reminder of some of t
ECON 203 - Spring 2008
Quiz #3
Q1. If the government put a tax on good X and then lowered the income tax, how would that
be shown using a budget line model?
A) The budget line would shift parallel to
ECON 203, Spring 2008
Mid-Term Examination #2
You have 55 minutes to answer the questions on this examination. The Exam is out of a total of 30
points. You do not have the right to any aid or device o
ECON 203 Spring 2008
Quiz 1 February 1st 2008
1) Which of the following shifts the demand curve to the right.
a) Decrease in income of the individual.
b) Increase in the price of the complement of the
Econ 203, Fall 2006
Intermediate microeconomics
PRACTICE MATH TEST (50 minutes)
This test is two pages long. You can earn 50 marks in total, that is a mark per
minute. Use this to plan your time well.
University of Victoria, Economics 203, Spring 2008
Intermediate Microeconomics
Course Outline
Class: Tuesdays, Wednesdays and Fridays 1:30pm 2.30pm, DSB C118.
Instructor: Dr Daniel Rondeau, Office: BE
Econ 203
Mathematical Review
An important objective of Econ 203 is to initiate students to the formal modeling and analysis of
economic decisions. As such, basic algebra and calculus are used frequent
ECON 203
Spring 2007
FINAL EXAMINATION
Saturday April 14, 2007
You have 3 hours to answer the questions on this examination. The exam contains 24 questions on 6
pages for a total of 90 points. You do
Chapter 16: General Equilibrium Exchange Economy
Chapters 2+4: Demand in competitive markets
Central element demand: Consumers take prices as given
Question: How did we arrive at competitive markets
Chapter 13 Imperfect Competition
Chapters 1-12: No strategic interaction between agents
Consumers problem: prices are taken as given
Cost minimization problem: output and input prices are taken
as giv
Chapter 12: Monopoly
Question 1: Why is a hot dog and beer so expensive at sports and concert
venues?
Question 2: Why, as some say, is everyone on a plane paying a different
price?
Question 3: Why do