3.2 Equilibrium and Break-even
Equilibrium in the goods and labour markets
1. Goods Market Equilibrium
Goods market equilibrium occurs when the quantity supplied
(Qs ) by producers
(Qd ) by consumers
Chapter 9
9.2 Matrices
Suppose that a firm produces three types of good, G1, G2 and G3, which it sells to
two customers, C1 and C2. The monthly sales for these goods are given in Table.
Monthly sales
9.3 Solution of equations: Elimination Methods
Gaussian Elimination
In its simplest form, Gaussian elimination is a technique for solving a system of n
linear equations in n unknowns by systematically
9.4 Determinants
Definition
A square matrix is a matrix in which the number of rows and columns are equal.
Definition
a b
A=
The number ad - bc is called the determinant of a square matrix
and is
c
9.5 Matrix inversion
For simplicity we concentrate on 2 x 2 and 3 x 3 matrices, although the ideas and
techniques apply more generally to n x n matrices of any size.
Definition
1 0
is called the unit
Section 4.1
MULTIPLE CHOICE
1. Find the simple interest on a $400 investment made for 5 years at an interest rate of 7%/year. What is
the accumulated amount?
a. The simple interest is $140,
the accumu
Section 4.2
MULTIPLE CHOICE
1. Find the amount of an ordinary annuity of 10 yearly payments of $1,800 that earn interest at 10% per
year, compounded annually.
a.
b.
c.
d.
$4,668.74
$28,687.36
$87,798.
Section 4.3
MULTIPLE CHOICE
1. Find the periodic payment R required to amortize a loan of P dollars over t years with interest earned
at the rate of r%/year compounded m times a year. Round your answe
Section 4.4
MULTIPLE CHOICE
1. Find the nth term of the arithmetic progression that has the given values of a = 7, d = 5, and n = 9.
a.
b.
c.
d.
ANS: B
PTS: 1
2. Find the nth term of the arithmetic pr
4
Mathematics of Finance
Compound Interest
Annuities
Amortization and Sinking Funds
Arithmetic and Geometric
Progressions
4.1
Compound Interest
Simple Interest Formulas
Simple interest is the int
5.4 Unconstrained optimization
For functions of two variables
z = f(x, y)
the optimum points are found by solving the simultaneous equations
f x ( x, y ) = 0 and f y ( x, y ) = 0
We can classify a opt
7.2 Applications of Partial Differentiation
Production function
A production function describes the output, Q, as a function of labour, L and
capital, K. That is
Q = f(L,K)
A production function that
Chapter 7
Functions of several variables
7.1 Partial Differentiation
Definition
A function, f, of two variables is written in the general form as
z = f(x, y)
where x and y are the independent variable
Chapter 4
Non-linear Functions and Applications
4.1 Quadratic, Cubic and Other Polynomial Functions
If the demand and supply graphs are curved and, in these circumstances, it is essential
to model the
4.2 The exponential functions
Definition
The exponential function to base a is
y = ax
f ( x) = a x
or
x is called the index, power or exponent, this is the variable part of the function
bx = b b L b
R
4.3 Logarithmic Functions
Definition
If
y = bx
then
logb y = x
and x is called the logarithm of y to base b.
Example
Evaluate
(a) log3 9
(b) log 4 2
1
log 7
(c)
7
(d) log10 100
Rules of Logarithms
1.
Chapter 6
Differentiation and Applications
6.1 Slope of a curve and Differentiation
In section 2.1 the slope of a straight line was defined to be the change in height
(y ) per unit increase in the hor
6.2 Applications of Differentiation
Marginal functions, Average Functions
In this section we concentrate on three main areas which illustrate differentiation
applicability in economics:
revenue and c
6.3 Optimization for functions of one variable
In this section we show how to locate maximum and minimum points of any
economic function. Look at the graph sketched in Figure. Points B, C, D, E, F and
6.4 Economic Applications of Maximum and Minimum Points
The task of finding the maximum and minimum values of a function is referred to as
optimization. This is an important topic in mathematical econ
6.5 Curvature and Other Applications
Second derivative and curvature
The first and second derivatives (y' and y") have already been used to find maximum
and minimum points of various functions. In thi
6.6 Further Differentiation and Applications
dy
= ex
dx
Rule 5
If y = e x then
Rule 6
If y = ln( x) then
dy 1
=
dx x
Example
Determine the first, second and third derivatives of the following function
4.2
Annuities
Annuity is amount of equal (mostly) payments made at regular intervals
of time.
So there is NO PRINCIPAL.
Example:- Monthly deposits into a savings account.
Monthly home mortgage payment