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Economics: Working with Three Variables on a Graph

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About this Lesson

  • Type: Video Tutorial
  • Length: 8:09
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 87 MB
  • Posted: 03/29/2010

This lesson is part of the following series:

Economics: Full Course (269 lessons, $198.00)
Economics: Introduction to Economic Thinking (18 lessons, $33.66)
Economics: Advanced Graphical Concepts (2 lessons, $2.97)

This video lesson shows you how to work with three variables on a graph. Taught by Professor Tomlinson, this video lesson was selected from a broader, comprehensive course, Economics. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/economics. The full course covers economic thinking, markets, consumer choice, household behavior, production, costs, perfect competition, market models, resource markets, market failures, market outcomes, macroeconomics, macroeconomic measurements, economic fluctuations, unemployment, inflation, the aggregate expenditures model, banking, spending, saving, investing, aggregate demand and aggregate supply model, monetary policy, fiscal policy, productivity and growth, and international examples.

Steven Tomlinson teaches economics at the Acton School of Business in Austin, Texas. He graduated with highest honors from the University of Oklahoma and earned a Ph.D. in economics at Stanford University. Prof. Tomlinson's academic awards include the prestigious Texas Excellence Teaching Award given by the University of Texas Alumni Association and being named "Outstanding Core Faculty in the MBA Program" several times. He has developed several instructional guides and computerized educational programs for economics.

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Thinkwell
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We've seen how economists use graphs to represent relationships between two variables. Now we'll see how an economist can represent a relationship among three variables in a two-dimensional graph. The trick is you only change two variables at a time.
Suppose we're interested in a relationship among three variables, and a good example would be making a map of a terrain. In this case, you've got three variables that change as you move across the terrain. One is your east/west coordinate, called your longitude. The other is your north/south coordinate, called your latitude. Finally, there is the distance that the terrain lies above sea level or below sea level - the altitude or the height of the point. As you move through a terrain, all three variables are changing - east/west, north/south, and height above sea level.
So when we draw a map, how do we represent these three variables? Let's look at a set of data points, and then we'll show how we represent them in a graph. Suppose we have a set of combinations of latitude and longitude for which the altitude remains constant. That is, let's look at points that have a constant altitude of 1,000 feet above sea level. If we identify a set of these points, we'll find that the latitude and longitude that give us an altitude of 1,000 can be written down in a table. Suppose that at a latitude of 200 feet north and 600 feet east we have an altitude of 1,000 feet. Suppose that at another point, a latitude of 100 feet north and 100 feet east, we have an altitude also of 1,000, and finally, a third combination. Notice the trick here is I'm holding my altitude constant as I change latitude and longitude. All of these combinations of latitude and longitude have a constant altitude of 1,000.
So let's move these numbers over to the box at the side, and then show how to represent them in a graph. On the vertical axis we will measure the distance north or south - or the latitude. On the horizontal axis, we'll measure the distance east and west - or the longitude. Altitude, we'll represent in a special way in the graph, and I'll show you in just a moment.
So let's look again at those points that we started with. Suppose that we are considering the point 60 east/west, 200 north/south, and an altitude of 1,000 that will lie in this picture in this way. First, put the longitude on the horizontal axis. The longitude of 60 means that we are at a point like this one. The latitude of 200 means that we are up here at 200, so I'll put a dot here to represent that combination of latitude and longitude. With 100 and 100, we also get the same altitude. And finally with 280, we get the same altitude. Each of these three dots represents a latitude and longitude combination with a constant altitude of 1,000. So what I can do to make it easier is I can connect all of the points that have an altitude of 1,000 and label this curve "1000." This collection of points is sometimes called an isoquant, from the word that means "same quantities." That is, each of the points on this curve represents a combination of latitude and longitude with a constant altitude of 1,000.
Now, this is not the only isoquant that we can draw. We can now change the altitude and find another set of combinations of latitude and longitude that have a different constant altitude. Let's consider another set of information here. Suppose we look at this table of numbers. Here are combinations of latitude and longitude that have a constant altitude of 2,000. Two hundred north and 200 east gives us an altitude of 2,000, the same with 140 and 300, and so forth. Each set of combinations here of latitude and longitude gives us a constant altitude of 2,000.
So now let's represent this set of points with a different isoquant in the same graph. Let's start with the combination of 200 and 200. With a longitude of 200 and a latitude of 200, we're going to get this point right here, and that has an altitude of 2,000. We also get an altitude of 2,000 with a longitude of 140 and a latitude of 300. That would be this point right here. Three hundred and 100 gives us another combination with an altitude of 2,000. Finally, one last point, here, at a latitude of 300 and a longitude of 380, we also have an altitude of 2,000.
Now, we can connect all of these dots to get another isoquant - that is, another collection of points where the altitude is constant, this time at an altitude of 2,000. However, notice this dot lies way up here; it doesn't appear to be on the same curve as these three dots. In fact, if I had more points what I would see is that this isoquant is actually an oval shape that comes around and connects to itself. Unlike this isoquant, which doesn't appear to bend back on itself, here's a complete set of points where all of these dots form a closed oval with an altitude of 2,000.
If I had other altitudes, I could form other isoquants; that is, other points with constant altitude. For example, this oval might represent the set of points that have an altitude of 3,000. Finally, here in the middle there might be a point at the top of our hill that has an altitude of 3,500. Here, then, is our isoquant map. What I've done is I've collected points together that have constant altitude. You can imagine here a topographical map where the altitude is rising as we move up to the northeast; and then after you go over the top of the hill, you begin to lose altitude. In fact, what you're seeing here are cross-sections of a hillside. Imagine a plane coming through and lopping off a hillside at a certain altitude. Here's what it would look like if it were lopped off at 1,000, here's what it would look like if it were lopped off at 2,000, here's the shape of all of those points with an altitude of 3,000, and so forth.
This is the way an economist represents three dimensions in a two-dimensional graph. We use the two axes to represent two of our dimensions - in this case east/west and north/south - and we use the third dimension in the graph, and we represent the third dimension in the graph as the numbers on the isoquant lines. Later, we'll be using this tool to represent consumer preferences as well as the trade-off between factors of production in the making of goods and services.
An Introduction to Economic Thinking
Advanced Graphical Concepts
Working With Three Variables on a Graph Page [2 of 2]

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