Answers: Graphs Assignment
"Good graphics equals good thinking"

Part 1

1. Graphs represent one form of representing information visually and can, as we saw in the Cholera and Challenger examples, be very effective at conveying information to the reader. You job is to track down some graphs that will become part of your portfolio of the Best and Worst Graphics. At this point you need to track down one graph, from outside of economics, that you would like nominated for both categories. You also need a brief memo in which you indicate why you chose these graphs.

2. There has been much written about discrimination against women. The earnings data for males and females clearly indicates the following patterns. You are to determine the appropriate variables and then draw a graph that captures the essence of each of the statements.

In the left-side diagram the slope for the male line (maroon M) is steeper than the female line (blue F).  The slope gives the increase in income that a person earns by aging one year so a steep slope indicates that each year the increase is larger.  slope = D$/Dage

In the right-side diagram the slope for the single line (maroon S) is steeper than the married line (blue M).  The slope gives the increase in income that a person earns by aging one year so a steep slope indicates that each year the increase is larger.  slope = D$/Dage

The left hand diagram would work since the steeper slope for the M line signifies a greater age-premium for men.  This is what the situation would look like if the starting salaries were comparable.  If men received lower starting salaries, then the y-intercept on the F line would be above that of the M line.

d. The age premium for high school educated workers is lower than that for college educated workers.  Also the age premium for high school educated workers begins to decline at age 50 and turns negative by age 60. 

The secret here is to begin by recognizing that the age-premium is the slope of the line - it tells us how much earnings increase as a person ages one year.  The slope measures the annual raise.  If after age 50 the annual raises begin to fall, then the slope declines.  At age 60 the age premium turns negative which means that the level of earnings actually falls after age 60 so the slope would turn negative.

3. Population biologists often discuss the concept of survivorship. For populations information on survivorship is summarized in survivorship schedules which give the percentage of individuals surviving to each particular age. These tables, an example of which appears below, can be conveniently represented in graphs.

Survivorship Table

From the following descriptions, produce the appropriate survivorship graph. [Be sure you have the correct axes - survivorship probabilities and age]

• Species A: Accidental mortality is kept to a minimum. Death comes to most members only when they reach the upper limit of the life span.
• Species B: The probability of death remains constant at every age. A fixed fraction of each age group dies (due to predators, accidents,..) in each unit of time.
• Species C: The vast majority perish quickly. Those individuals that do survive have a good chance of reaching maturity.

The diagrams below would correspond to the statements. The one on the left has a sharp drop off which indicates at that age a large number of survivors die so that the percentage of the population surviving falls sharply. The flat section at the beginning of the line indicates that there is little change in the early period in the number of survivors which indicates that very few die during this period.  In the second diagram we have the picture of a constant rate of decline.  This should not be confused with a constant decline which would be a straight, negatively sloped line. The right-side graph show a sharp decline at early ages indicating that many die early and that after that the line is flat indicating that those who make it through the early years live long lives. 

4. Draw a graph that best describes the verbal descriptions of the following relationships.

The top left diagram below has a maximum value for tax revenue (T).  Before that point the slope is positive indicating that tax revenues increase as tax rates increase.  After that point the slope is negative indicating that the tax revenues decrease as tax rates increase. 

The top right diagram below is an example of a constant growth rate.  As the we move further to the right the actual increase in GNP gets larger because the base is larger. For example, a 2% growth rate on a base of 100 is 2 while a 2% growth rate on a base of 1,000 is 20.  The slope is the rate of change [ slope = DGNP/Dyear].    If the rate is constant then as the base gets bigger the DGNP ge6ts bigger so the slope would be greater.

The graph does appear below, but it would be a line with a slope of $1,000.  

d. The relationship between the number of calories burned per minute (C) of running and age (A) if there is a decrease of 2 calories burned per minute with each year we age.

The bottom left diagram below is an example of a constant change.  As the we move further to the right the actual decrease in calories remains the same - 2 calories for each minute. For example, in the first minute the savings is 2 calories while in the 20th minute the savings is also 2 calories.   The slope is the rate of change [ slope = Dcalories/Dminute].     If the change is constant then as the base gets bigger the Dcalories stays the same so the slope would be the same.

e. China's military power is currently less than the US but it is projected to grow at a faster rate than the US and some suggest that there will be a time in the 21st Century when China's military power will be greater than that of the US.

The bottom right diagram below has two curves, the maroon curve for the US and the blue curve for China.  The y-intercept is larger for the US which indicates the higher current level of power, but the greater slope for China indicates a greater growth rate for China.  The slope is the rate of change [ slope = Dpower/Dyears].    A greater slope means a bigger increase in power for any change in time which would be situation in China.

Here what you have are demand curves and the difference is in the slopes of the demand curves.  With price as the vertical axis and quantity on the horizontal axis you will get two negative slopes.  The curve for Mexico would be flatter signifying that the change in quantity would be larger for any change in price.  

4 You will soon learn to create your own spiffy graphs, but now you are going to create one that is largely done by someone else given the wonders of modern technology. You now have the ability to do in seconds what would have taken me hours to do not so many years ago.  To convince yourself that you can translate a picture (graph) into a story, I would like you to graph one economic variable which you can choose from the list at the Economic Time Series page.   For example what if you wanted to look at the unemployment rate.  You would go the the Federal Reserve, St. Louis and then choose US Employment Data.  Once there you can pull up the Unemployment Rate and you will follow the directions to construct a graph of the unemployment rate by selecting GIF chart of this data.  You will get the following graph (or something close to it since it will continually change). 

If you then follow directions and direct it to create a graph showing the unemployment rate since 1948 you get the following diagram.

You should pick one of the variables which you have a basic understanding of and then graph it and explain in a paragraph what you see in the graph.   A REALLY neat map of unemployment that can be found at this site.  Good luck.   (Please be sure to staple the graph to a typed paragraph - or integrate them into one document).

Part 2

1. So you want to create some graphs! The good news is that there are already some spreadsheets available electronically. You could go out and track down some tables on the Web-maybe using some of the locations identified on the Information Sources page or find some hard copy sources in the library. You are to construct one Pie, Bar, Stack, Area, Scatter, and Line graph which will be part of your portfolio for the course. As you develop your graphs, be sure that you choose data so that the graph which you choose is the best graph for that data.  Be most careful with the scatter diagram since this is the one which has traditionally caused people the most problem. 

You are on our own here, but you do have some examples of what you should be looking for.  Be most careful with the scatter diagram since this is the one which has traditionally caused people the most problem. 

2.  There are three parts to this question. Everyone should do one part based on the following scheme:

• 0,1,2              3a           
• 5, 6,7              3b 
• 3,4, 8,9          3c

Each of you should think of this as a question that will be answered with the use of some "new" data and a corrected graph.  

2a. You have heard much about the plight of the American worker, how the average earnings for workers in this country are falling. But what is the story? Do you buy into the story after you see the graph below. It is pretty clear that average wages have been rising since the end of W.W.II.

So you are tired of the whining? Before you make a rash judgment, however, remember that prices have been rising during this period. The real question is, Have wages been growing more or less rapidly than inflation? If wages have been rising, but slower than inflation, then you would expect an inflation adjusted measure to account for that. If you follow the appropriate method of conversion, we get the following graph for real (inflation adjusted) wages. As you can see, which variable we use makes an enormous difference.

2b. The 1980s was a boom-bust period for real estate in the US-especially in the Northeast. One of the explanations advanced for the speculative boom in the early 1980s was that banks had been burned by foreign loans to developing countries in the early 1980s and as a result turned their attention to real estate in the US and flooded the market with money. The problem facing the developing countries was that they were incapable of paying loans at the high rates that existed in the early to mid 1980s. My concern is that I can see that interest rates actually fell during this period as you can see in the diagram below. So where is the problem?

Once again we need to be careful of which data we are looking at. One issue which we will not look at is the exchange rate which would certainly have a bearing on the issue - especially if the loans were denominated in dollars. Here, however, we will focus our attention on the interest rates. What really matters to the borrower would be the real and not the nominal rate. If we look at the real rate we find that real rates were unusually high in the 1980s despite the falling interest rates. What happened was that inflation fell faster than interest rates - a reversal of the 1970s when inflation rose faster than interest rates.

2c. It is difficult not to notice what is happening in the stock market as it roars into uncharted territory. Things are so good in fact that some financial people are concerned we are reliving the 1920s and setting ourselves up for another stock market crash. Are we, or are we simply seeing a continuation of a rise that began as far back as the 1950s? What's the verdict given the past performance of the New York Sock Exchange Composite Index?

By now you should have a good idea where we are going. During this period when the stock market's prices were rising we were experiencing inflation - a general increase in the price level. If we adjust the stock price data for the change in the price level we find a different picture. The stock market rise which we are in the midst of appears to have begun in 1982 after more than a decade of decline.