Lecture Notes on Mathematics for
Economists: A refresher
(Draft for teaching only. Do not cite.)
Andrs Carvajal
University of Warwick
[email protected]
August, 2006
Contents
Preface
ix
1 Preliminary concepts
1.1 Some useful notation . . . . . . .
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 11
Total points: 10
1.
Consider the difference equation = 21 6 .
a.) (3) What is the backward solution of the equation, given an initial value 0 = 18 .
b.) (1) Is the
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 4
Total points: 17.
1. Consider the system of equations
+ 2 + = 5
3 2 = 12
a.) (7) Does the system implicitly define x and y as functions of z in the neighbourhood of
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 10
Total points: 6
1. (2) Prof. Shiell is considering buying an apartment building, which he will rent out to
university students. The estimated annual profit is $75,0
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 7
Total points: 8
1.
Consider the function () = + , where > 0 and 0. Does the function satisfy the
algebraic definition of quasi-concavity?
*
*
*
Some formulas
(1 (1 ,
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz I
Total points: 16
1. (5) Use Cramers rule to solve the following equation system for 2 . [No marks will be given
for the substitution method.]
51 + 92 = 14
71 32 = 4
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 6
Total points: 19.
1. Consider the problem of a consumer who must choose between two goods, necessities (n)
and luxuries (z), given a budget constraint. Her utility f
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 9 Answers
1. Minimizing f ( x, y) is equivalent to maximizing f (x, y) .
L (x 2 2y) 1 x 2 y 2
first-order conditions (Kuhn-Tucker) :
L x 2x 2x 0 and x 0
with complemen
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 2
Total points: 14
1. (5) Sketch the graph of the following set and indicate whether it is convex. Explain your
answer in terms of the definition of convex sets.
cfw_(
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 3
Total points: 7
1. Consider the equation x 2 xy 3 y 5 17 .
a.) (3) Show that the equation implicitly defines y as a function of x in the neighbourhood of
(x 5 , y 2)
University of Ottawa
ECO 3145 Mathematical Economics I
Fall 2015, Professor Shiell
Quiz 8
Total points: 6.
1.
Consider the manager of a chair factory who wishes to minimize the cost of production,
where the annual level of production is 35,000 chairs, i.e