■using graphs in economic analysis 1 analysis toolkit 1 analysis toolkit

■Using Graphs in Economic Analysis■Using Graphs in Economic Analysis

1Analysis Toolkit

1Analysis Toolkit

Using Graphs in Economic AnalysisUsing Graphs in Economic Analysis

● Display large quantity of data quickly

● Facilitate data interpretation and analysis

● Important relationships more apparent than from written descriptions or long lists of numbers

● Display large quantity of data quickly

● Facilitate data interpretation and analysis

● Important relationships more apparent than from written descriptions or long lists of numbers

Two-Variable DiagramsTwo-Variable Diagrams

● Variable = an entity that can assume different values.

● Variable can be independent (usually represented on the X-axis) or dependent (usually represented on the Y-axis)

● In microeconomics, we will study such variables as prices, quantity, revenue, cost and profit.

● Variable = an entity that can assume different values.

● Variable can be independent (usually represented on the X-axis) or dependent (usually represented on the Y-axis)

● In microeconomics, we will study such variables as prices, quantity, revenue, cost and profit.

Quantities of Natural Gas Demanded at Various Prices

Quantities of Natural Gas Demanded at Various Prices

Qu

anti

ty

Price (a)

7 6 5 4 3 2 1 0

20

40

60

80

100

120

D

D

b

a

Q

P Pri

ce

Quantity (b)

140 120 100 80 60 40 20 0

1

2

3

4

5

6

View two variables together to see if they exhibit a relationship

View two variables together to see if they exhibit a relationship

QD=QD(P) P=P(QD)

P

Q

If a relationship is found, say via a function QD=QD(P). the inverse function, P=P(QD), can be found by rearranging the terms.

Hypothetical Supply CurveHypothetical Supply Curve

QS=QS(P) P=P(QS)

140 120 100 80 60 40 20 0

1

2

3

4

5

6

Quantity

Pri

ce

What is held constant along this supply curve?

The Definition and Measurement of SlopeThe Definition and Measurement of Slope

● Slope = ratio of vertical change to horizontal change♦Rise divided by Run=

♦ Measure of steepness of a relationship

● Slope = ratio of vertical change to horizontal change♦Rise divided by Run=

♦ Measure of steepness of a relationship

Y

X

The Definition and Measurement of SlopeThe Definition and Measurement of Slope

● The slope of a straight line♦ Negative slope = one variable rises while the

other variable falls■ The two variables move in opposite directions.

♦ Positive slope = two variables rise and fall together■ The two variables move in the same direction.

● The slope of a straight line♦ Negative slope = one variable rises while the

other variable falls■ The two variables move in opposite directions.

♦ Positive slope = two variables rise and fall together■ The two variables move in the same direction.

Negative SlopeNegative Slope

Negative slope

0 X

Y

Positive SlopePositive Slope

Positive slope

0 X

Y

The Definition and Measurement of SlopeThe Definition and Measurement of Slope

♦ Zero slope = the variable on the horizontal axis can be any value while the variable on the vertical axis is fixed■ Horizontal line

♦ Infinite slope = the variable on the vertical axis can be any value while the variable on the horizontal axis is fixed■ Vertical line

♦ Zero slope = the variable on the horizontal axis can be any value while the variable on the vertical axis is fixed■ Horizontal line

♦ Infinite slope = the variable on the vertical axis can be any value while the variable on the horizontal axis is fixed■ Vertical line

Zero SlopeZero Slope

Zero slope

0 X

Y

Infinite SlopeInfinite Slope

Infinite slope

0 X

Y

The Measurement of SlopeThe Measurement of Slope

● The slope of a straight line♦ Slope is constant along a straight line.

♦ Slope can be measured between any two points on one axis and the corresponding two points on the other axis.

● The slope of a straight line♦ Slope is constant along a straight line.

♦ Slope can be measured between any two points on one axis and the corresponding two points on the other axis.

How to Measure SlopeHow to Measure Slope

3 — 10 Slope =

1 — 10 Slope =

(b) (a)

A

X

B

C

13 3 0

Y

8

11

X

A B

C

13 3 0

Y

8 9

The Definition and Measurement of SlopeThe Definition and Measurement of Slope

● The slope of a curved line♦ Slope changes from point to point on a

curved line.■Curved line bowed toward the origin has a

negative slope.● Variables change in opposite directions.

■Curved line bowed away from the origin has a positive slope.

● Variables change in the same direction.

● The slope of a curved line♦ Slope changes from point to point on a

curved line.■Curved line bowed toward the origin has a

negative slope.● Variables change in opposite directions.

■Curved line bowed away from the origin has a positive slope.

● Variables change in the same direction.

Negative Slope in Curved LinesNegative Slope in Curved Lines

Negative slope

0 X

Y

Positive Slope in Curved LinesPositive Slope in Curved Lines

Positive slope

0 X

Y

The Definition and Measurement of SlopeThe Definition and Measurement of Slope

● The slope of a curved line♦ A curved can have both a positive and

negative slope depending on where on the curve is measured.

♦ The slope at a point on a curved-line is measured by a line tangent to that point.

● The slope of a curved line♦ A curved can have both a positive and

negative slope depending on where on the curve is measured.

♦ The slope at a point on a curved-line is measured by a line tangent to that point.

Behavior of Slope in Curved Lines

Behavior of Slope in Curved Lines

Negative slope

Positive slope

0 X

Y

Negative slope

Positive slope

0 X

Y

How to Measure Slope at a Point on a Curve

How to Measure Slope at a Point on a Curve

r

r

t

t

A B

R

M

G T

E

F

D

C

Y

X 10 9 8 7 6 5 4 3 2 1 0

8

7

6

5

4

3

2

1

Rays Through the Origin and 45-degree LinesRays Through the Origin and 45-degree Lines

● Y-intercept = point at which a line touches the y axis, i.e. when x =0

● X-intercept = point at which a line touches the x axis, i.e. when y =0

● Ray through the origin = straight line graph with a y-intercept of zero

● Y-intercept = point at which a line touches the y axis, i.e. when x =0

● X-intercept = point at which a line touches the x axis, i.e. when y =0

● Ray through the origin = straight line graph with a y-intercept of zero

Rays through the OriginRays through the Origin

1 – 2 Slope = +

Slope = + 1

Slope = + 2

B

E

K

A C

D 0

5

4

3

2

5 4 3 2 1

1

Y

X

Y =X Y =2 X

Y =1 / 2 X

Squeezing 3 Dimensions into 2: Contour MapsSqueezing 3 Dimensions into 2: Contour Maps

● Some problems involve more than two variables

● Economic “contour map” a.k.a. indifference map or level set.♦ Shows how variable Z changes as we change

either X or Y

● Some problems involve more than two variables

● Economic “contour map” a.k.a. indifference map or level set.♦ Shows how variable Z changes as we change

either X or Y

An Economic Contour Map An Economic Contour Map

Z = 40

Z = 30

Z = 20

Z = 10

Ya

rds

of

Clo

th p

er

Da

y

Labor Hours per Day

Y

X 80 70 60 50 40 30 20 10 0

10

20

30

40

50

60

70

80

B

A

An Economic Contour Map An Economic Contour Map