Graphs and Their Meaning Ch1Graphs and Their Meaning Ch1

GraphsGraphs: Used to illustrate economic : Used to illustrate economic models; Illustrate relationships.models; Illustrate relationships.– Generally Generally twotwo variables illustrated variables illustrated **Consumption > as income >Consumption > as income >

*Horizontal: determining factor*Horizontal: determining factor

Vertical: depends on Vertical: depends on incomeincome

IndependentIndependent variable=Horiz. variable=Horiz.

DependentDependent variable=Vertical variable=Vertical

Consumption

Income Y

$100 200 300 400

400

300

200

100

0Aa

bc

d$$

Graphs Graphs

Direct relationshipDirect relationship (Positive): the (Positive): the two variables (consumption & two variables (consumption & income) change in the income) change in the samesame direction.direction.– >consumption = >income>consumption = >income– <consumption= < income<consumption= < income– 2 variables change positively they 2 variables change positively they

always graph as an always graph as an upslopingupsloping line. line.

GraphsGraphs() () Inverse relationshipInverse relationship

Attendance in 1000’s

0 4 8 12 16 20 30

60

50

40

30

20

10

0

Ticket

Price

(P)

2 Variables change in opposite directions.

*Ticket prices < attendance >

*Ticket prices > attendance <

*Inverse relationship causes the line to slope downward.

“Which variable is the cause

and which is the effect???”

ab

c

de

f

Ceteris ParibusCeteris Paribus

Ceteris ParibusCeteris Paribus=“=“– All other things being equal.”All other things being equal.”

Plots relationship between two variables and Plots relationship between two variables and assumes ceteris paribus.assumes ceteris paribus.

In reality: All “other things” are not equalIn reality: All “other things” are not equal– What could change attendance other What could change attendance other

than ticket prices?than ticket prices?

Slope of LineSlope of Line SlopeSlope = Vertical change/Horizontal = Vertical change/Horizontal

chg.chg.

Slope= VC/HCSlope= VC/HC Between points B/C:Between points B/C:

Vertical: +$50Vertical: +$50 Horizontal: +$100Horizontal: +$100 +50/+100=1/2=.5+50/+100=1/2=.5

Consumption

400

300

200

100

0

Income Y

Aab

c

Positive Slope of LinePositive Slope of Line

Slope is positive .5 because Slope is positive .5 because consumption and income increase in consumption and income increase in the the same directionsame direction; Consumption ; Consumption and income are and income are directlydirectly or positively or positively related.related.– Slope of .5 tells us the following:Slope of .5 tells us the following:

$1 increase in consumption for every $2 $1 increase in consumption for every $2 increase in income.increase in income.

$2 decrease in income there will be a $1 $2 decrease in income there will be a $1 decrease in consumption.decrease in consumption.

Negative SlopeNegative Slope

Slope=VC/HC (Points c and d)Slope=VC/HC (Points c and d)VC = -10 drop HC = +4VC = -10 drop HC = +4 Ticket prices & Ticket prices &

attendance have anattendance have an

inverseinverse relationship relationship..

-10/+4=-2 ½ or -2.5-10/+4=-2 ½ or -2.5

What does it say?What does it say?

60

50

40

30

20

10

0

a b

c

de

Attendance in 1000’s

4 8 12 16 20

Ticket

Price

P

Slope and Marginal AnalysisSlope and Marginal Analysis

MarginalMarginal=Adding one more/less unit.=Adding one more/less unit.The .5 slope shows that $.50 of extra The .5 slope shows that $.50 of extra

(marginal) consumption is associated (marginal) consumption is associated with each $1 change in income.with each $1 change in income.

The -2.5 slope shows that $10 increase The -2.5 slope shows that $10 increase in ticket prices will result in a 4,000 in ticket prices will result in a 4,000 decrease in attendance. decrease in attendance.

A $10 decrease in attendance will result A $10 decrease in attendance will result in an increase in attendance.in an increase in attendance.

Vertical Vertical InterceptIntercept

Vertical InterceptVertical Intercept: of a line is the point : of a line is the point where the line meets the vertical axis. where the line meets the vertical axis.

VI=$50VI=$50

If current income=0; still If current income=0; still spend? spend? 400

300

200

100

0Aa

bc

$ Income (Y)$100 200 300 400

$$

Consumption

Infinite SlopeInfinite Slope

Infinite slopeInfinite slope: Variables are unrelated or : Variables are unrelated or independent of one another.independent of one another. Ex. The purchase of wrist watches is not related to the Ex. The purchase of wrist watches is not related to the

price of bananas.price of bananas. Slope of line is parallel to vertical axis.Slope of line is parallel to vertical axis. Same quantity of watches is purchased regardless of Same quantity of watches is purchased regardless of

price of bananas.price of bananas.

0

Price Ban

Watches bought

Slope=

InfiniteSlope = 0

Divorce Rate

Consumption

Linear RelationshipLinear Relationship

If we know the vertical intercept and If we know the vertical intercept and slope, we can describe a line in slope, we can describe a line in equation form.equation form. C=a+bxC=a+bx

a=vertical intercepta=vertical intercept C=consumptionC=consumption b=slope of lineb=slope of line x=independent variablex=independent variable

Slope of Nonlinear CurveSlope of Nonlinear Curve

Slope of straight line is the same at all points.Slope of straight line is the same at all points. Slope of nonlinear line changes from point to Slope of nonlinear line changes from point to

point. Lines are called point. Lines are called curvescurves..

Measure slope=draw line tangent to curveMeasure slope=draw line tangent to curve

*Slope of the curved line =slope of tangent*Slope of the curved line =slope of tangent20

15

10

5

0

0 5 10 15 20

a

bb

ba

A

B