Graphs in Economics

   If you glance quickly through this text, you will find many graphs. Some seem sim­ple, while others seem more complicated. They are included to help you visualize and understand economic relationships. Physicists and chemists sometimes illustrate their theories by building arrangements of multicolored wooden balls, representing protons, neutrons, and electrons, which are held in proper relation to one another by wires or sticks. Economists most often use graphs to illustrate their models. By understanding these “pictures,” you can more readily comprehend economic relationships. Most of our principles or models explain rela­tionships between just two sets of economic facts, which can be conveniently rep­resented with two-dimensional graphs.

Construction of a Graph
   A graph is a visual representation of the relationship between two variables. In economics we represent the independent variable on the horizontal axis and the dependent variable on the vertical axis. If the graph is a straight line we say the relationship is linear.

Direct and Inverse Relationships
   By a direct relationship (or positive relation­ship) we mean that two variables—in this case, consumption and income—change in the same direction. An increase in consumption is associated with an increase in income; a decrease in consumption accompanies a decrease in income. When two sets of data are positively or directly related, they always graph as an upsloping line.
   In contrast, two sets of data may be inversely related. Consider the relationship between the price of basketball tickets and game attendance at ST. University (SU). Here we have an inverse relationship (or negative rela­tionship) because the two variables change in opposite directions. When ticket prices decrease, attendance increases. When ticket prices increase, attendance decreases.Observe that an inverse relationship always graphs as a downsloping line. 

Dependent and Independent Variables
   Although it is not always easy, economists seek to determine which variable is the “cause” and which is the “effect.” Or, more formally, they seek the independent variable and the depend­ent variable. The independent variable is the cause or source; it is the variable that changes first. The dependent variable is the effect or outcome; it is the variable that changes because of the change in the independent variable. As noted in our income-consumption example, income generally is the independent variable and consumption the dependent variable. Income causes consumption to be what it is rather than the other way around. Similarly, ticket prices (set in advance of the season) determine attendance at SU basketball games; attendance at games does not determine the ticket prices for those games. Ticket price is the independent variable, and the quantity of tick­ets purchased is the dependent variable.
   You may recall from your high school courses that mathematicians always put the independ­ent variable (cause) on the horizontal axis and the dependent variable (effect) on the vertical axis. Economists are less tidy; their graphing of independent and dependent variables is more arbitrary. Their conventional graphing of the income-consumption relationship is consistent with mathematical presentation, but economists put price and cost data on the vertical axis. Hence, economists graphing of SU’s ticket price-attendance data conflicts with normal mathe­matical procedure.

 

Other Things Equal
   Our simple two-variable graphs purposely ignore many other factors that might affect the amount of consumption occurring at each income level or the number of people who attend SU basketball games at each possible ticket price. When econo­mists plot the relationship between any two variables, they employ the ceteris paribus (other things equal) assumption. In reality, “other things” are not equal; they often change. Specifically, the lines we have plotted would shift to new locations.
   Consider a stock market “crash.” The dra­matic drop in the value of stocks might cause people to feel less wealthy and therefore less willing to consume at each level of income. The result might be a downward shift of the con­sumption line.
   Similarly, factors other than ticket prices might affect SU game attendance. If SU loses most of its games, attendance at SU games might be less at each ticket price.

Slope of a Line
   Lines can be described in terms of their slopes and their intercepts. The slope of a straight line is the ratio of the vertical change (the rise or drop) to the horizontal change (the run) between any two points of the line, or “rise” over “run.”

 SLOPES AND MARGINAL ANALYSIS
   Recall that economics is largely concerned with changes from the status quo. The concept of slope is important in economics because it reflects marginal changes— those involving one more (or one less) unit.

INFINITE AND ZERO SLOPES
      Many variables are unrelated or independent of one another. For example, the quan­tity of wristwatches purchased is not related to the price of bananas. The graph of their relationship is the line parallel to the vertical axis, indicating that the same quantity of watches is pur­chased no matter what the price of bananas. The slope of such a line is infinite.
   Similarly, aggregate consumption is completely unrelated to the nation’s divorce rate. We put consumption on the vertical axis and the divorce rate on the horizontal axis. The line parallel to the horizontal axis represents this lack of relatedness. This line has a slope of zero.

 

   Equation of a Linear Relationship
   If we know the vertical intercept and slope, we can describe a line succinctly in equation form. In its general form, the equation of a straight line is

y = a + bx where

y = dependent variable

a = vertical intercept

b = slope of line

x = independent variable

Slope of a Nonlinear Curve

      We now move from the simple world of linear relationships (straight lines) to the more complex world of nonlinear relationships. The slope of a straight line is the same at all its points. The slope of a line representing a nonlinear relationship changes from one point to another. Such lines are referred to as curves. Consider the downsloping curve. Its slope is negative throughout, but the curve flattens as we move down along it. Thus, its slope constantly changes; the curve has a different slope at each point.
   To measure the slope at a specific point, we draw a straight line tangent to the curve at that point. A line is tangent at a point if it touches, but does not intersect, the curve at that point. The slope of the curve at a point is equal to the slope of the tangent line.

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Factors that Affect PPC

UNEMPLOYMENT AND PRODUCTIVE INEFFICIENCY

Almost all nations have at one point(ex. Great Depression) or another experienced widespread unem­ployment of resources. That is, they have operated inside of their production pos­sibilities curves. In the last half of the 1990s, several countries (for example, Argentina, Japan, Mexico, and South Korea) operated inside their production possibilities curves, at least temporarily, because of substantial declines in economic activity. Economies that experience substantial discrimination based on race, ethnicity, and gender do not achieve productive efficiency and thus operate inside their pro­duction possibilities curves. Because discrimination prevents those discriminated against from obtaining jobs that best use their skills, society has less output than otherwise. Eliminating discrimination would move such an economy from a point inside of its production possibilities curve toward a point on its curve. Similarly, economies in which labor usage and production methods are based on custom, heredity, and caste, rather than on efficiency, operate well inside their production possibilities curves.

TRADEOFFS AND OPPORTUNITY COSTS

Many current controversies illustrate the tradeoffs and opportunity costs indicated in movements along a particular production possibilities curve. (Any two categories of “output” can be placed on the axes of production possibilities curves.) Should scenic land be used for logging and mining or preserved as wilderness? If the land is used for logging and mining, the opportunity cost is the forgone benefits of wilderness. If the land is used for wilderness, the opportunity cost is the lost value of the wood and minerals that society forgoes.

Should society devote more resources to the criminal justice system (police, courts, and prisons) or to education (teachers, books, and schools)? If society devotes more resources to the criminal justice system, other things equal, the oppor­tunity cost is forgone improvements in education. If more resources are allocated to education, the opportunity cost is the forgone benefits from an improved criminal justice system.

SHIFTS IN PRODUCTION POSSIBILITIES CURVES

Our World has recently experienced a spurt of new technologies relating to computers, communications, and biotechnology. Technological advances have dropped the prices of computers and greatly enhanced their speed. Cellular phones and the Internet have increased communications capacity, enhancing production and improving the efficiency of markets. Advances in biotechnology, specifically genetic engineering, have resulted in important agricultural and medical discoveries. Many economists believe that these new technologies are so significant that they are con­tributing to faster-than-normal economic growth (faster rightward shifts of the pro­duction possibilities curve).

In some circumstances a nation’s production possibilities curve can collapse inward. An example can be war among Kosovo and Yugoslavia, in the late 1990. Yugoslavia’s economy was hurt because of this war. Allied bombing inflicted great physical damage on Yugoslavia’s production facilities and its system of roads, bridges, and communica­tion. Consequently, Yugoslavia’s production possibilities curve shifted inward.

Effect of International Trade and Specialization on PPC (summary)

Production possibilities analysis implies that a nation is limited to the combinations of output indicated by its production possibilities curve. But we must modify this principle when international specialization and trade exist.

An economy can avoid, through international specialization and trade, the output limits imposed by its domestic production pos­sibilities curve. International specialization means directing domestic resources to out­put that a nation is highly efficient at producing. International trade involves the exchange of these goods for goods produced abroad. Specialization and trade enable a nation to get more of a desired good at less sacrifice of some other good. Specialization and trade have the same effect as having more and better resources or discovering improved production techniques; both increase the quan­tities of capital and consumer goods available to society.

Important Assumptions Related to Production Possibilities Curve

Let’s now discard the first three assumptions underlying the production possibili­ties curve and see what happens.

Unemployment and Productive Inefficiency

    The first assumption was that our economy was achieving full employment and pro­ductive efficiency. Our analysis and conclusions change if some resources are idle (unemployment) or if least-cost production is not realized.Any points on PPC represent maximum outputs possible to be produced; they illustrate the combinations of goods that can be produced when the economy is operating at full capacity—with full employment and productive efficiency. With unemployment or inefficient pro­duction, the economy would produce less than each alternative shown in the table.

Graphically, we represent situations of unemployment or productive inefficiency by points inside the original production possibilities curve.  A move toward full employment and pro­ductive efficiency would yield a greater output of one or both products.

A Growing Economy

   When we drop the assumptions that the quantity and quality of resources and tech­nology are fixed, the production possibilities curve shifts positions—that is, the potential maximum output of the economy changes.

INCREASES IN RESOURCE SUPPLIES

    Although resource supplies are fixed at any specific moment, they can and do change over time. For example, a nation’s growing population will bring about increases in the supplies of labour and entrepreneurial ability. Also, labour quality usually improves over time. Historically, the economy’s stock of capital has increased at a significant, though unsteady, rate. And although we are depleting some of our energy and mineral resources, new sources are being discovered. The development of irrigation programs, for example, adds to the supply of arable land.

The net result of these increased supplies of the factors of production is the ability to produce more goods . Thus, 20 years from now, there  may be greater abundance of resources ,therefore, this will result in a greater potential output of one or both products at each alternative. Soci­ety will have achieved economic growth in the form of an expanded potential output.

But such a favourable change in the produc­tion possibilities data does not guarantee that the economy will actually operate at a point on its new production possibilities curve. Some 15 million jobs will give China full employment now, but 10 or 20 years from now its labour force will be larger, and 15 million jobs will not be sufficient for full employment. The produc­tion possibilities curve may shift, but at the future date the economy may fail to produce at a point on that new curve.

ADVANCES IN TECHNOLOGY

     Our second assumption is that we have constant, unchanging technology. In reality, technology has progressed dramatically over time. An advancing technology brings both new and better goods and improved ways of producing them. For now, let’s think of technological advances as being only improvements in capital facilities— more efficient machinery and equipment. These advances alter our previous dis­cussion of the economic problem by improving productive efficiency, thereby allowing society to produce more goods with fixed resources. As with increases in resource supplies, technological advances make possible the production of more goods.

Thus, when either supplies of resources increase or an improvement in technol­ogy occurs, the production possibilities curve shifts outward and to the right. Such an outward shift of the production possibilities curve represents growth of economic capacity or, sim­ply, economic growth: the ability to produce a larger total output. This growth is the result of (1) increases in supplies of resources, (2) improvements in resource qual­ity, and (3) technological advances.

The consequence of growth is that our full-employment economy can enjoy a greater output of goods. While a static, no-growth economy must sac­rifice some of one product in order to get more of another, a dynamic, growing economy can have larger quantities of  products.

Economic growth does not ordinarily mean proportionate increases in a nation’s capacity to produce all its products.

Terms:

ECONOMIC Growth An outward shift in the production possibil­ities curve that results from an increase in resource supplies or quality or an improvement in technology.