Variables and relationships in economics include the price of a good or service in the entire economy, and the price level, also exhibits this inverse or negative. Positive correlation exists when two variables move in the same direction. In macroeconomics, positive correlation exists between consumer spending and gross domestic product (GDP). Microeconomics, which analyzes individual consumers and firms, features many instances of positive. Graphs Used in Economic Models B) negative relationship, also called an inverse rela- tionship. C) positive relationship, also called a direct relation- ship.
A nonlinear curve A curve whose slope changes as the value of one of the variables changes.
Negative Correlation - Variables that Move in Opposite Direction
The relationship she has recorded is given in the table in Panel a of Figure The corresponding points are plotted in Panel b. Clearly, we cannot draw a straight line through these points. Instead, we shall have to draw a nonlinear curve like the one shown in Panel c. This information is plotted in Panel b. This is a nonlinear relationship; the curve connecting these points in Panel c Loaves of bread produced has a changing slope.
Inspecting the curve for loaves of bread produced, we see that it is upward sloping, suggesting a positive relationship between the number of bakers and the output of bread. But we also see that the curve becomes flatter as we travel up and to the right along it; it is nonlinear and describes a nonlinear relationship. How can we estimate the slope of a nonlinear curve? After all, the slope of such a curve changes as we travel along it. We can deal with this problem in two ways.
One is to consider two points on the curve and to compute the slope between those two points. Another is to compute the slope of the curve at a single point. When we compute the slope of a curve between two points, we are really computing the slope of a straight line drawn between those two points.
They are the slopes of the dashed-line segments shown. These dashed segments lie close to the curve, but they clearly are not on the curve. After all, the dashed segments are straight lines. When we compute the slope of a nonlinear curve between two points, we are computing the slope of a straight line between those two points. Here the lines whose slopes are computed are the dashed lines between the pairs of points.
Every point on a nonlinear curve has a different slope. To get a precise measure of the slope of such a curve, we need to consider its slope at a single point. To do that, we draw a line tangent to the curve at that point.
A tangent line A straight line that touches, but does not intersect, a nonlinear curve at only one point. The slope of a tangent line equals the slope of the curve at the point at which the tangent line touches the curve.
Consider point D in Panel a of Figure We have drawn a tangent line that just touches the curve showing bread production at this point. It passes through points labeled M and N. The vertical change between these points equals loaves of bread; the horizontal change equals two bakers.
The slope of our bread production curve at point D equals the slope of the line tangent to the curve at this point. In Panel bwe have sketched lines tangent to the curve for loaves of bread produced at points B, D, and F. Notice that these tangent lines get successively flatter, suggesting again that the slope of the curve is falling as we travel up and to the right along it.
In Panel athe slope of the tangent line is computed for us: Generally, we will not have the information to compute slopes of tangent lines.
We will use them as in Panel bto observe what happens to the slope of a nonlinear curve as we travel along it. We see here that the slope falls the tangent lines become flatter as the number of bakers rises.
Notice that we have not been given the information we need to compute the slopes of the tangent lines that touch the curve for loaves of bread produced at points B and F. In this text, we will not have occasion to compute the slopes of tangent lines. Either they will be given or we will use them as we did here—to see what is happening to the slopes of nonlinear curves.
In the case of our curve for loaves of bread produced, the fact that the slope of the curve falls as we increase the number of bakers suggests a phenomenon that plays a central role in both microeconomic and macroeconomic analysis. As we add workers in this case bakersoutput in this case loaves of bread rises, but by smaller and smaller amounts. Another way to describe the relationship between the number of workers and the quantity of bread produced is to say that as the number of workers increases, the output increases at a decreasing rate.
In Panel b of Figure Indeed, much of our work with graphs will not require numbers at all. We turn next to look at how we can use graphs to express ideas even when we do not have specific numbers. Graphs Without Numbers We know that a positive relationship between two variables can be shown with an upward-sloping curve in a graph. A negative or inverse relationship can be shown with a downward-sloping curve. Some relationships are linear and some are nonlinear.
The supply curve shows that when prices are high, producers or service providers are prepared to provide more goods or services to the market; and when prices are low, service providers and producers are interested in providing fewer goods or services to the market. The aggregate expenditure, or supply, curve for the entire Canadian economy the sum of consumption, investment, government expenditure and the calculation of exports minus imports also shows this positive or direct relationship.
Construction of a Graph You will at times be asked to construct a graph, most likely on tests and exams. You should always give close attention to creating an origin, the point 0, at which the axes start. Label the axes or number lines properly, so that the reader knows what you are trying to measure. Most of the graphs used in economics have, a horizontal number line or x-axis, with negative numbers on the left of the point of origin or 0, and positive numbers on the right of the origin.
Figure 2 presents a typical horizontal number line or x-axis.
In economics graphs, you will also find a vertical number line or y-axis. Here numbers above the point of origin 0 will have a positive value; while numbers below 0 will have a negative value. Figure 3 demonstrates a typical vertical number line or y-axis. When constructing a graph, be careful in developing your scale, the difference between the numbers on the axes, and the relative numbers on each axis. The scale needs to be graduated or drawn properly on both axes, meaning that the distance between units has to be identical on both, though the numbers represented on the lines may vary.
You may want to use single digits, for example, on the y-axis, while using hundreds of billions on the x-axis. Using a misleading scale by squeezing or stretching the scale unfairly, rather than creating identical distances for spaces along the axes, and using a successive series of numbers will create an erroneous impression of relationship for your reader. If you are asked to construct graphs, and to show a knowledge of graphing by choosing variables yourself, choose carefully what you decide to study.
Here is a good example of a difficulty to avoid. Could you, for example, show a graphical relationship between good looks and high intelligence? I don't think so. First of all, you would have a tough time quantifying good looks though some social science researchers have tried! Intelligence is even harder to quantify, especially given the possible cultural bias to most of our exams and tests.
Finally, I doubt if you could ever find a connection between the two variables; there may not be any. Choose variables that are quantifiable. Height and weight, caloric intake and weight, weight and blood pressure, are excellent personal examples.
The supply and demand for oil in Canada, the Canadian interest rate and planned aggregate expenditure, and the Canadian inflation rate during the past forty years are all quantifiable economic variables.
Negative relationship - Wikipedia
You also need to understand how to plot sets of coordinate points on the plane of the graph in order to show relationships between two variables. One set of coordinates specify a point on the plane of a graph which is the space above the x-axis, and to the right of the y-axis.
For example, when we put together the x and y axes with a common origin, we have a series of x,y values for any set of data which can be plotted by a line which connects the coordinate points all the x,y points on the plane. Such a point can be expressed inside brackets with x first and y second, or 10,1. A set of such paired observation points on a line or curve which slopes from the lower left of the plane to the upper right would be a positive, direct relationship.
A set of paired observation or coordinate points on a line that slopes from the upper left of the plane to the lower right is a negative or indirect relationship. Working from a Table to a Graph Figures 5 and 6 present us with a table, or a list of related numbers, for two variables, the price of a T-shirt, and the quantity purchased per week in a store.
Note the series of paired observation points I through N, which specify the quantity demanded x-axis, reflecting the second column of data in relation to the price y-axis, reflecting first column of data. See that by plotting each of the paired observation points I through N, and then connecting them with a line or curve, we have a downward sloping line from upper left of the plane to the lower right, a negative or inverse relationship.
We have now illustrated that as price declines, the number of T-shirts demanded or sought increases. Or, we could say reading from the bottom, as the price of T-shirts increases, the quantity demanded decreases.
We have stated here, and illustrated graphically, the Law of Demand in economics.
Now we can turn to the Law of Supply. The positive relationship of supply is aptly illustrated in the table and graph of Figure 7. Note from the first two columns of the table that as the price of shoes increases, shoe producers are prepared to provide more and more goods to this market. The converse also applies, as the price that consumers are willing to pay for a pair of shoes declines, the less interested are shoe producers in providing shoes to this market.
The x,y points are specified as A through to E. When the five points are transferred to the graph, we have a curve that slopes from the lower left of the plane to the upper right. We have illustrated that supply involves a positive relationship between price and quantity supplied, and we have elaborated the Law of Supply.
Now, you should have a good grasp of the fundamental graphing operations necessary to understand the basics of microeconomics, and certain topics in macroeconomics.
Many other macroeconomics variables can be expressed in graph form such as the price level and real GDP demanded, average wage rates and real GDP, inflation rates and real GDP, and the price of oil and the demand for, or supply of, the product.
Don't worry if at first you don't understand a graph when you look at it in your text; some involve more complicated relationships. You will understand a relationship more fully when you study the tabular data that often accompanies the graph as shown in Figures 5 and 7or the material in which the author elaborates on the variables and relationships being studied.
Gentle Slopes When you have been out running or jogging, have you ever tried, at your starting pace, to run up a steep hill? If so, you will have a good intuitive grasp of the meaning of a slope of a line. You probably noticed your lungs starting to work much harder to provide you with extra oxygen for the blood. If you stopped to take your pulse, you would have found that your heart is pumping blood far faster through the body, probably at least twice as fast as your regular, resting rate.
The greater the steepness of the slope, the greater the sensitivity and reaction of your body's heart and lungs to the extra work. Slope has a lot to do with the sensitivity of variables to each other, since slope measures the response of one variable when there is a change in the other. The slope of a line is measured by units of rise on the vertical y-axis over units of run on the horizontal x-axis. A typical slope calculation is needed if you want to measure the reaction of consumers or producers to a change in the price of a product.
For example, let's look at what happens in Figure 7 when we move from points E to D, and then from points B to A. The run or horizontal movement is 80, calculated from the difference between and 80, which is Let's look at the change between B and A. The vertical difference is again 20 - 80while the horizontal difference is 80 - We can generalize to say that where the curve is a straight line, the slope will be a constant at all points on the curve.
Figure 8 shows that where right-angled triangles are drawn to the curve, the slopes are all constant, and positive. Now, let's take a look at Figure 9, which shows the curve of a negative relationship.