1 Analysis Toolkit Using Graphs in Economic Analysis

Using 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

Two-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.

Quantities of Natural Gas Demanded at Various Prices

View two variables together to see if they exhibit a relationship QD=QD(P)  P=P(QD) D 120 6 100 5 Q 80 4 Quantity Price Q P a 60 3 b 40 2 20 1 P 1 2 3 4 5 6 7 20 40 60 80 100 120 140 Price (a) Quantity (b) 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 Curve QS=QS(P)  P=P(QS) 6 5 4 Price 3 2 1 20 40 60 80 100 120 140 Quantity What is held constant along this supply curve?

The Definition and Measurement of Slope 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 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.

Negative Slope Y Negative slope X

Positive Slope Y Positive slope X

The 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 Y Zero slope X

Infinite Slope Y Infinite slope X

The 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.

How to Measure Slope Y Y 3 — 10 Slope = C 11 B C 9 1 — 10 Slope = B 8 X X 3 13 3 13 (a) (b)

The 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.

Negative Slope in Curved Lines Y Negative slope X

Positive Slope in Curved Lines Y Positive slope X

The 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.

Behavior of Slope in Curved Lines Y Y Negative slope Positive slope Negative slope Positive slope X X

How to Measure Slope at a Point on a Curve Y r 8 D 7 E 6 R t F 5 C 4 G T 3 M 2 1 A B X 1 2 3 4 5 6 7 8 9 10

Rays 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

Rays through the Origin Y =2 X Y =X Slope = + 2 5 Slope = + 1 4 B Y =1 / 2 X C D 3 A 2 1 – 2 Slope = + K 1 E X 1 2 3 4 5

Squeezing 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

An Economic Contour Map

An Economic Contour Map Y Z = 40 80 Z = 30 70 Z = 20 Z = 10 60 50 Yards of Cloth per Day A 40 30 B 20 10 X 10 20 30 40 50 60 70 80 Labor Hours per Day