Appendix I HOW TO READ GRAPHS
A picture is wort” a thousand Word Chinese Proverb
Before you can master economics, you must have a working knowledge of graphs, Then are as indispensably to the economist as a hummer is to a carpenter. So if you arc not familiar with the use of diagrams. invest some time ill learning ! how to read them-it will be time: well spent.
What is a graph? It is a diagram showing- how two or more sets of data or variables an’ related to one another, Graphs are essential in economics because.among other reasons. they allow us to analyze economic concepts and examine historical trends.
You will encounter many different kinds of graphs in this book. Some graphs show how variables change over time (see. for example. the inside of the front cover): other graphs show the relationship between different variables (such .IS the example we will turn 10 in a moment). Each graph in the’ hook will help You understand an important economic relationship
THE PRODUCTION·POSSIBILITY FRONTIER
The first graph that you encountered in this text was the production-possibility frontier .. As we showed in the bod}’ of this chapter, the production-possibility frontier, or f>PF. represents the maximum amounts of a pair of goods or services that can both be produced with an economy’s given resources, assuming that all resources arc fully employed.
Let’s follow up an important application. that of choosing between food’ and machines. The essential data for the PPF are shown ill Table l A-I. which is very much like the example in Table I-I.Recall that each of the possibilities gives one ‘level of food production and one level of machine production.As the quantity produced increases.the production of machines falls. Thus. if the economy produced HI units of food. it could produce a maximum of ).I() machines, but when the output of food is 20 units, only 120 machines can be manufactured.
Production-Possibility Graph. The data shown in Table IA·I can also be presented as a graph. To construct the graph,we represent each of the table’s pairs of data by a single point on a two-dimensional plane. Figure l A-I displays in a graph the relationship between’
The table shows six potential pairs of outputs that Can be produced with the given resources of a he country.the country can choose one of the six possible combinations.
This figure shows the data of table lA-1 in graphical form.The data are exactly the same, but the visual display presents the data more vividly.
It Is easy to calculate slopes for straight lines as “rise over run.” Thus in both (a) and (b),the numerical value of the slope is rise/run = CD/Be = s/1 = s. Note that in (a), CD is neg-,alive, indicating a negative slope, or an inverse relationship between X and Y.
FIGURE IA-4. Steepness is not the Same as Slope
Note that even though (a) looks steeper than (b).they display the same ‘relationship.Both have a slope of 112 but the X axis has been stretched out in (b).
The key points to understand about slopes are the following:
1. The slope can be expressed as a number. It measures the change in }’ per unit change in X, or “the rise over the run,”
2. If the line is ‘straight, its slope is constant everywhere.
3. The slope of the line indicates whether the relationship between X and Y is direct or inverse. Direcl relationship occur when variables move in the same direction (that is, they increase or decrease together); inverse relationships occur when the variables move in opposite directions (that is, one increases as the other decreases), .
Thus a negative slope indicates the X-l’relation i~ inverse, as it is in Figure l A-3(a). Why? Because an increase in X calls for a decrease in Y.
People sometimes confuse slope with the appearance of steepness, This conclusion is often but not always valid. The steepness depends on the scale
of the graph. Panels (a) and (b) in Figure IA-4 both portray exactly the same relationship. But in (b),the horizontal scale has been stretched out compared with (a). If you calculate carefully, you will see that the slopes are- exactly the same (and are
equal to 12)’
Slope of Q Curved Line. A curved or nonlinear line is one whose slope changes. Sometimes we want to mow the slope at a given point, such as point B in Figure IA-5. We see that the slope at point B is positive,but it is not obvious exactly how to calculate the slope. To find the slope of a smooth curved line at a point, we calculate the slope of the straight line that
just touches, but does not cross, the curved line at the point in question, Such a straight line is called a tang-mt to the curved line. Put differently, the slope of a curved line at a point is given by the slope of the straight line that is tangent to the curve at the given point. Once we draw the tangent line, we find the slope of the tangent line with the usual right-angle measuring technique discussed earlier.
To find the slope at point B in Figure IA-5, we simply construct straight line FBJ as a tangent to the curved line at point B. We then calculate the slope of the tangent as a NJ/MN. Similarly, the tangent line GH gives the slope of the curved line at point D.Another example of the slope of a nonlinear line is shown in Figure IA-6. This shows a typical microeconomics curve, which is dome-shaped and has a maximum at point c. We can use our method of slopes-as-tangents to see that the slope of the curve
·is always positive-In the region where the curve is rising and negative in the falling region, At the peak or maximum of the curve, the slope is exactly zero.A zero slope signifies that a tiny movement in the X variable around the maximum has no effect on the value of the Y variable.
J For those who enjoy algebra, the slope \>fa line can be remembered as follows: A straight line (or linear relationship) is written as Y = a + bX. For this line, the slope of till’ curve is b, which measures the change in Y per unit change in X.A curved line or nonlinear relationship is one in”,Mn~ terms other than constant. and the X term. An example of a nonlinear relationship is the quadratic equation Y’= (X – 2)2.You can very!)’ that the slop” of this equation is negation X< 2 and positive for X> 2. slope for.x = 2? For those who know calculus: A zero slope Collies where the derivative of a smooth curve is equal to zero. For example, plot and use calculus to find zero-slope point of a curve defined by the function Y = (X – 2)2.
By constructing a tangent line, we can calculate the slope of a curved line at a given point. Thus the line FBMJis tangent to smooth curve ABDE at point B. The slope at B is calculated as the slope or the tangent line, that is, as NJ/MN.
Many curves in economics first rise, then reach a maximum,then fall. In the rising region from A to C the slope is positive (see point ll). In the falling region from C to E the slope is negative (see point D). At the curve’s maximum,point C, the slope is zero. (What about a U-shaped curve? What is the slope at its minimums?}
Shifts of and Movement Along Curves.
An important distinction in economics is that between shifts of curves and movement along curves. We can examine this distinction in figure 1A-7. The inner production-possibility frontier reproduces the PPF in figure 1A-2. At point D society chooses to produce 30 units of food and 90 units of machines. If society decides to consume more food with a given PPF then it can m oven along the PPF to point E. this movement along the curve represents choosing more food and fewer machines.
suppose that the i inner PPF represents society’s production possibilities for 1990. If we return to the same country in 2000 , we see that the PPF has shifted form the nee 1990 curve to the outer 2000 curve. (This shift would occur because of technological change or because of an increase in labor or capital available.) In the later year , society might choose robe at point G, with more food and machines than at either D or E.
In using ,graph~, it is essential to distinguish movement along a curve such as a from high-investment D to low-investment f. r from a shift of a curve (as from D in an early)’ear to G ill .& later year).
curve, while in the second case (from D to &) we see a shift of the curve.
Some Special Graphs. The PPF’ is one of the most important graph~ of economics, one depicting the relationship between two economic variables (such as food and machines or guns and butter). You will encounter other types of graphs ill the pages that follow.
Time Series.Some graphs show how a particular variable has changed over time. look, for example, at till’ graphs (Ill the inside front cover of this text The left-hand graph shows a lime series. since the American Revolution. of a significant macroeconomic variable, the ratio of the federal government debt to total gross domestic product, or GDP- this ratio is the df’bt-GDP ratio. Time-series graphs have time Oil the horizontal axis and variables of interest (in this case, the debt-GDP ratio) on the vertical axis. This graph shows that the debt-GDP ratio has risen . sharply <luring every major war.
Scatter Diagrams. Sometimes individual pairs of point’ will he plotted. as in Figure lA-I. Often. combination of variables for different years will be plotted.An important example of a scatter diagram from macro economics is the consumption junction, shown in Figure IA-8. This scatter diagram shows the nation’s total disposable income on the horizontal axis
and total consumption (spending.by households on good~ like food. clothing, and housing) on the vertical axis. Note that consumption is very closely linked to income, a vital clue for understanding changes in national income and output.
Diagrams with More Than One Curve. Often It useful to put two curves in the same graph, thus obtaining a “multicultural diagram.” The most important example is the supply-and-demand diagram, shown in Charier S (see page 47). Such graphs can show different relationships simultaneously, such as ho consumer purchases respond to price (demand) an how business production responds to price (supple) By graphing the two relationships together. we c determine the price and quantity that will hold in a market.
FIGURE IA·8, Seatter.’. Diagram of Consumption Function Shown Important Macroeconomic Law
observed points of consumption spending call near the CC line , Which displays average behavior over time. Thus , the blue colored point for 1999 is so near the CC line that it could have been quite accurately predicted from that line even before the year was over. Scatter diagrams allow us to se how close the relationship is between two variables.
This concludes our brief excursion into graphs.Once you have mastered these basic principles. the graphs in this book, and in other areas, Can be hot fun and instructive.
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