BUSI1007

Introduction to Microeconomics and

Accounting

+

BROAD COURSE OUTLINEEconomics of production and industry organizationCosts of production: Total, average, variable, fixed, marginal, economies of scale, Economic versus accounting profit , Forms of business organizations

Market structures:Market structures: Perfect competition, Monopoly, Price discrimination, Oligopoly and Monopolistic competition, Introduction to game theory

Time Value of moneyCapital Investment analysis

Introduction to MacroeconomicsIntroduction to macroeconomics, National income, GDP, Consumer price index, The tax system and public policy  

MATH SKILLS FOR INTRODUCTORY ECONOMICS

Mathematics plays an important part in economics and serves, as a basic means of explaining and analyzing behaviour in an economy.

MATH REVIEW LEARNING OUTCOME

Identify different points on a graph using coordinates.Identify the point of intersection between two lines on a graph. Determine points of tangency on a straight line and use them to calculate the slope of the curve. Determine whether a straight line (or portion of a curve) has a positive, negative, or zero slope. Identify maximum and minimum points of a curve

MATH SKILLS FOR INTRODUCTORY ECONOMICS

1. Graph Basics

8

y

THE CARTESIAN PLANE IS DIVIDED INTO FOUR QUADRANTS.

III

III IV

Cartesian Plane

Formed by intersecting two real number lines at right angles. Divides space into 4 quadrants

POINTS AND THEIR COORDINATES

9

y

Cartesian Plane

Horizontal line = X axis

Vertical line =

Y axis

y axis

x axisorigin

11

y

PLOTTING POINTS IN THE CARTESIAN PLANE

1. Begin at origin

2. Use ordered pair (coordinates) to draw point (x,Y) e.g. (5,6)

3. (5, 6) is an example of an ordered pair 5 is the X coordinate and 6 is the Y coordinate

(5,6)5

6

12

yPLOTTING THE POINT (-3, 4)

(– 3, 4)(– 3, 4)

left 3

up 4

x

13

y

PLOT THE FOLLOWING POINTS.

A(– 4, 6) A(– 4, 6)A

B(2, – 3)

B(2, – 3)

C(– 6, – 4)

C(– 6, – 4)

D(7, 3)

D(7, 3)

These points all lie in different quadrants.

A(– 4, 6)

D(7, 3)

B(2, – 3)

14

y

PLOT THE FOLLOWING POINTS.

F(0, 6) F(0, 6)

E(5, 0)

H(0, – 3)

G(– 7, 0)

H(0, – 3) E(5, 0)

These points all lie on the axes, not in quadrants.

• What point is on the y-axis?

• What point is labeled (20,60)?

• What point(s) have a y-coordinate of 30?

• What point has the largest x- coordinate value?

GRAPH BASICS - QUICK REVIEW

VARIABLES

In economics, measurable characteristics such as prices, outputs, income, etc., are measured by numerical values.Since these values can vary we call these characteristics "variables.” We express a relationship between two variables, X and Y, by stating the following for example:

The value of the variable Y depends upon the value of the variable X.

VARIABLES

For example, the total price you pay for a particular sized pizza (Y) depends upon the number of toppings (X) you order.

We can write the relationship between variables in an equation for a straight line like this:

Y = a + bX If we know that X and Y represent variables, then what are a and b?

(a and b) are CONSTANTS in (Y = a+bX)

a and b are constants. They are fixed values which specify how X relates to Y. In our pizza example, "a" is the price of a plain pizza with no toppings and "b" is the cost of each topping. A graph of this particular relationship between X and Y, will show all the combinations of X and Y that fit the equation. When plotted, the result is a straight line graph

VARIABLES

If plain pizza (a) is $50.00 and the cost of each topping (b) is $10, then given Y = a + (b)(X) we get the following table:

Final cost = plain pizza + topping cost X # of toppings

$ 50 $50 $10 0$ 60 $50 $10 1$ 70 $50 $10 2$ 80 $50 $10 3$ 90 $50 $10 4$100 $50 $10 5

GRAPH - COST OF PIZZA

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

102030405060708090

100

Cost of Pizza with Toppings

Number of toppings

Fina

l Cos

t

(0,50)(1,60)

(2,70)(3,80)

(4,90)

(5,100)

COMPONENTS OF GENERAL EQUATION FOR STRAIGHT LINE

y = a + b x

Pizza: y = 50+10x

variable variable

Y intercept slope

SLOPE (Gradient or Rise over Run)

The slope of a curve is used to tell us how much one variable (y) changes in relation to the change in another variable (x). This can be written as follows:

Slope = ∆Y/ ∆X Slope = ∆ Vertical axis ∆ in Horizontal Axis

The slope tells us how much the cost of a pizza changes as the number of toppings changes.

4

3

2

1

10 20 30 40

A

B

C

D

X=30, Y=3

X=10, y=1

Y

X

SLOPE = 1/10WHAT IS THE SLOPE OF THIS LINE?

COMPONENTS OF GENERAL EQUATION FOR STRAIGHT LINE

y = a + b x

Pizza: y = 50+10x

variable variable

Y intercept slope

SLOPEExamples:

Y = 20+30x y intercept is 20

slope is 30 y = 4 – 10x

y intercept is 4 slope is (-10)

Y = 1.3x + 1/2y y intercept is? slope is?

SLOPE OF PIZZA GRAPH

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

102030405060708090

100

Cost of Pizza with Toppings

Number of toppings

Fina

l Cos

t

A

(0,50)(1,60)

(2,70)(3,80)

(4,90)

(5,100)

Y=50+10(X)

B

FINDING THE EQUATION OF A STRAIGHT LINE

We need to find the values of a and b to substitute into the formula y = a + bxFinding a is easy

b is the slope – thedifference betweenany 2 points on the line

the point at which the line crosses the

y axis (value of y)

= xin change The yin change The

9

1 2 3 4 5 6 7 8

12345678

-8 –7 –6 –5 –4 –3 –2 –1 -1-2-3-4-5-6

x

We can simply read off the value of b

a = 3

y = 2x +3

b = xin change The yin change The

y

b = or

b = 2

48

12

FINDING THE EQUATION OF A LINE

THE SLOPE

Slope can be positive or negative …

3

2y

x

b = 2/3

3

-2 yx

b = - 2/3

3

1

y

x

b = 3

-3

1

y

x

b = - 3

CALCULATING SLOPE OF LINE FROM THE COORDINATES OF TWO POINTS ON THE LINE

Example: Let's say that points (8, 15) and (7, 10) are on a straight line. What is the slope of this line?

The change in y = 10 -15 = -5

The change in x = 7 - 8 = - 1

Put them together:

Change in y -5 change in x -1

Therefore slope = -5 / -1 = 5

A B

ACTIVE LEARNING: Finding Equation of a Straight Line

Joining (2, 3) & (-1, -3)

Joining (-4, -1) & (4, 1)

Joining (-1, 4) & (2, -2)

Find the gradient and intercept of the lines ..

Hence write down the equations for each line

Joining (2, 3) & (-1, -3)

PICTORIAL REPRESENTATION OF THE SLOPE OF A LINE: POSITIVE, NEGATIVE, INFINITE OR ZERO

PositiveSlope

NegativeSlope

InfinitySlope

Y

X

ZeroSlope

Y

X

IDENTIFYING THE INTERSECTION OF TWO straight LINES

Represents More than one relationship between the X and Y variables.

the two lines have the same (x, y) values simultaneously at point B the point of intersectionX

SLOPE OF NONLINEAR RELATIONSHIPS

We usually calculate the slope of a curve at just one point. Why? Because the slope of the curve changes as you move along it.

SLOPE OF NONLINEAR RELATIONSHIPS

To measure slope, we introduce the concept of a tangent. A straight line that touches a non linear curve at a pointThe point where the tangent line just touches the curve is called the point of tangency.

37

4

3

2

1

10 20 30 40

AY=2

X=30 X

YSLOPE AT A POINT ON A NON LINEAR CURVE

X=

38

20

15

10

5

25 50 75 100

AY=

X=

-10

X

YSLOPE OF NONLINEAR RELATIONSHIPS

DIRECT RELATIONSHIP BETWEEN TWO VARIABLES?

When one variable increases, the other increases or when one variable decreases the other decreases

EXPENDITURE FOR PERSONAL COMPUTERAT DIFFERENT ANNUAL INCOMES

Personal Expenditure

Annual Income

$1,000$2,000$3,000$4,000

$10,000$20,000$30,000$40,000

Direct Relationship

41

4321

10 20 30 40

A

B

C

D

Y=1X=10

Y

X

GRAPH OF DIRECT RELATIONSHIP

0

INVERSE RELATIONSHIP BETWEEN TWO VARIABLES?

When one variable increases, the other decreases or when one variable decreases the other in

QUANTITY OF COMPACT DISCS CONSUMERS PURCHASED AT DIFFERENT PRICES

Price per compact disc

Quantity of compact discs

$20$15$10

25,000,00050,000,00075,000,000

$5 100,000,000Inverse Relationship

44

20

15

10

5

25 50 75 100

A

B

C

D

Y=20

X=25X

YGRAPH OF INVERSE RELATIONSHIP

INDEPENDENT RELATIONSHIP BETWEEN TWO VARIABLES?

When one variable changes, the other variable remains unchanged

EXPENDITURE FOR TOOTHPASTEAT DIFFERENT ANNUAL INCOMES

Personal Expenditure

Annual Income

$20$20$20$20

$10,000$20,000$30,000$40,000

Independent Relationship

47

40

30

20

10

10 20 30 40

A B C D

Y=0X=10

X

YGRAPH OF INDEPENDENT RELATIONSHIP

MAXIMUM POINT ON A CURVE

A maximum point is the point on the curve with the highest y-coordinate value and a slope of zero. What point is maximum?

MINIMUM POINT ON A CURVE

A minimum point is the point on the curve with the lowest y-coordinate value and a slope of zero

What point is minimum?

GENERAL QUESTIONS

What is a direct relationship between two variables?What is the slope of a line?What is an inverse relationship between two variables?What is an independent relationship between two variables?Can slope vary along a curve?

MATH REVIEW LEARNING OUTCOME

Identify different points on a graph using coordinates. Match a graph of a straight line with the appropriate equation. Match an equation of a straight line with the appropriate graph. Calculate the slope of a straight line a. from the equation

b. from two points c. from the graph Determine whether the slope of a straight line is positive, negative, zero, or infinite.