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 = 2 > 0 everywhere. Setting dy/dx = 0, this function
h
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
is much more of a bargain!
2. We need to solve the equa
MATH MODULE
8
Solutions to
Exercises
1. (a) 1/36; (b) 36; (c) a/2; (d) 1/144; (e) 243a5; (f) 81a5; (g) 4; (h) 1/2; (i) 2; (j) 1; (k) 8;
(l) 1.682; (m) 3.106.
2. (a) [The pairs of numbers in each case have the log value rst, followed by the ln
value.] (i)
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 = $32/unit.
2. Average price = 24 = 0.6(12) + 0.4x, where x is the average pric
MATH MODULE
6
Solutions to
Exercises
1. Both methods, the = P /(mQ) point-slope technique and the = OF/AF segmentratio technique, should of course have given you the same results. The reason for
doing them both ways is to convince yourself of that fact, a
MATH MODULE
5
Solutions to
Exercises
1. The following Table contains the Total Revenue, Average Revenue, and Marginal
Revenue equations and gives the value for each of the equations when Q = 10 tonnes:
CASE
a
Total Revenue
TR =P Q ($)
($)
30Q Q2 = 200
2
A
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]QD = 27.2727 0.2066 QD
(c) This one is in the trick ques
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 cases in
questions 1-3, and particularly for questions 5
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 horizontal intercept
(4, 0). Equation (g) has the form y = 12
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(x) = 20/x is a nonlinear function of x whose domain is
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 we stand back from it a bit, calculus (in the two-varia
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 production process, such as the conversion of inputs of iron o
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 of exponents or powers;
2. logarithms and exponential
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 that it is one of the principal
sources of slips and ca
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, the most
important of which are listed below in this
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 involves comparisons at the margin, for
the purpose of m
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 everything in it is obvious, then
move straight on to the next
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 aspect of economic reality, for example the quantity of a
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;
budget constraints and isocost lines;
indifference curve
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 the characteristics of mathematical functions and how
we
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 the right because of the tax on X and then
rotate count
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 other than pens, pencils, a ruler and an eraser.
Good lu
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 good.
c) Increase in the price of the substitute of th
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. With 30 marks you pass the math test,
but in other to
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 frequently (there is a reason
why there is a math pre-requisite
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 not have the right to any aid or device other than pens
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?
The Market is a Value Pump it moves goods from indiv
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 given
Competitive firms problem: choose output independent
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 you have to stay over on a Saturday night to qualify fo