Graphing & Slopes

In this section, we briefly review the basics of graphing. The slope of a line is the rise over the run, or the change in y divided by the change in x, where the y axis is the vertical axis and the x axis is the horizontal axis.

In the first chart below, point A is situated at the (x,y) coordinate (2,4). Point B is at (4,8). Since we move up the Y axis four units while moving across the X axis 2 units, the slope is 4/2=2. Note that the slope is positive implying that X and Y are directly related. When X increases so does Y.

The second chart below shows point A at (5,10) while B is at (7,9). Y falls one unit while X rises by 2 units. The slope is -1/2. Here X and Y are inversely related. When X increases, Y decreases.

The third chart shows a flat line. Since the Y value does not change no matter how much X changes, the slope is zero.

The final chart shows a perfectly vertical line. This time the X value does not change, regardless of the Y value. Therefore, we divede by zero to calculate the slope which is infinite or undefined.

Use caution when reading graphs because the axis and scales can change and give misleading results when just glanced at.

Scarcity & Opportunity Cost

Wouldn't the world be a wonderful place if we could consume all the goods and services we wanted and never had to worry where the money would come from? Unfortunately, the world is not such a kind place. Each one of us has limited resources, and we must make choices as to how we will use those resources. The science of economics is concerned with the rationing of scarce resources.

Scarcity occurs when, at a zero price, quantity demanded is greater than quantity supplied. In other words, if the good were free, there would be a shortage of the good because more of the good would be demanded than supplied. Most goods and services are scarce. The concept of scarcity suggests the necessity of rationing goods and services in some manner. The most common way to do this is by using the price system. When a price is put on a good or service, people have to choose what products they will spend their income on.

There are a few things in life that are not scarce. Water and air are a few. These are two free goods for which there is usually no shortage. This statement, however, comes with certain provisios. "Clean" air may indeed be scarce. The same is true for "drinkable" water. We may be willing to pay for these resources.

Scarcity helps us to understand the idea that resources are limited and we cannot have everything that we want. Given our limited resources, we must make choices about where our resources should go. Every choice we make, then, involves a cost.

Opportunity Cost is the value of the next best alternative that is given up. Examples are choosing to go to the movies instead of going out to dinner, voting in elections, studying for an exam versus going out with friends, or going to college instead of woring full time. Every decision we make means sacrificing some other option. For example, going out to a movie on a Friday night may mean that the dinner at a restaurant has to be sacrificed due to lack of funds for both. The opportunity cost of the movie is the dinner given up.

What is the opportunity cost of going to college when your next best alternative is to work full time and live in an apartment? The full cost is not just the tuition. What else are you giving up? The answer is tuition ($2,000) + books ($500) + foregone income from not working. Tuition and books are the explicit resourses you must spend in order to attend college. But your time is also valuable and choosing to spend time in college means giving up time to work at a full time job.

Production Possibilities Frontier

We can represent the concepts of scarcity and opportunity costs in a graphical illustration. A Production Possiblilities Frontier (PPF) represents all possible combinations of the production of two goods given the available resources and technology.

Resources consist of

  1. Labor: human inputs to production
  2. Land: gifts of nature
  3. Capital: human-made inputs to production (i.e. machines, tools)

Notes:

  • Points on the line are efficient: absence of waste (pts. A,B,C)
  • Points inside the line are inefficient (pt. I)
  • Points outside the line are unattainable (pt. U)
  • Points on the line are not better than one another in terms of efficiency, but depend upon subjective preferences.
  • The slope of the line represents the opportunity cost of increasing the `X' good by one unit. For example, moving from A to B means gaining 50 defense units, but sacrificing 85 nondefense units. So the opportunity costs of moving from A to B is 85 nondefense units. This is what we have to give up.

Examples:

  1. Guns v. Butter debate: defense spending vs. domestic spending.
  2. Gender Equity in Sports: tradeoff between resources for women's and men's sports.
  3. FDA Regulation of Drugs: The FDA must decide to allow drugs and risk possibility of harming someone with a dangerous drug, or not allow drugs and risk the possibility of harming someone by keeping good drugs off the market. The possibility of harming someone with an approved drug is a Type I error. The other possibility of harming someone by restricting safe drugs is a Type II error. This is a tradeoff the FDA must deal with every day.
  4. Crime Prevention: How much should we spend on crime prevention? The tradeoff is between diminishing crime and sacrificing other goods & services, or having more crime and more of other goods & services. Even within a given budget for crime, decisions have to be made regarding how to spend the money, i.e. more equipment or more officers; more for crime prevention, or more to the court system?

The Principle of Increasing Costs

Why does the production possibilities frontier bow outward? We have intentionally drawn the curve this way to reflect the principle of increasing costs. The Principle of Increasing Costs says that as production of a good expands, the opportunity cost of producing another unit generally increases. This is because resources tend to be specialized so that some of their productivity is lost when they are transferred from what they do well to what they do poorly. One can see in the chart above that the opportunity cost of producing more and more defense goods increases.

When resources are not specialized, the principle of increasing costs does not apply and the production possibilities frontier is a straight line. This is represented in the chart below which plots the production of right shoes versus left shoes. Resources required to produce each of these products are very similar.

Economic Growth

Economic growth is the increase in the economy's level of production. Recall that the production possibilities frontier shows the possible production of two goods given the available resources and technology. Economic growth can occur because either the resource base expands, or the level of technology increases. Economies grow when population grows because labor is an important resource. The United States economy grew from a population of about 5 million in 1800 to over 90 million in 1900. This was a time of massive resource growth in our nation's history.

Economic growth also occurs when we learn how to use our existing resources more productively. This is what we call technological progress. For a given amount of resources, the economy's level of output increases. In either case, economic growth results in a shift outward of the production possibilities frontier.

This module has a Powerpoint slide show.