CS 110: Introduction to Computer Science Lab Module 7 Index Numbers: Gasoline and Inflation Why We Need the Consumer Price Index When were gas prices their highest? Quantitative Concepts and Skills Percentages Ratios Proportions Relative Change Graph: XY scatter plot Prepared for SSAC by Semra Kilic-Bahi, Colby-Sawyer College, New London NH Modified by Fred Annexstein © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2005 1
Background Index numbers are used to standardize measurements made at different times or different places so they can be directly compared. This module focuses on the use and meaning of index numbers. In particular, it examines the gasoline price index and consumer price index. The index number is defined as a value relative to a reference value The reference value is the value, chosen at one particular time or place, to which values at other times and/or other places will be compared. The equation assigns an index number of 100 to the reference time or location. Making comparisons with Index Numbers: The main purpose of index numbers is to make comparisons. One can compare the prices in one particular year to the prices in the reference year for a particular product or service. Comparisons can also be made when neither value is the reference value: 2
Overview The Consumer Price Index (CPI) applies to a wide variety of consumer goods and services. The Bureau of Labor Statistics (BLS) measures two consumer price indices. The Urban Consumers Price Index (CPI-U) covers all urban consumers, about 80% of the U. S. population. The Wage Earners Consumer Index (CPI-W) is based on the purchasing habits of only wage earners. This module will use the CPI-U. Because the CPI is used as an economic indicator and a means of adjusting dollar values, it affects many aspects our lives. The relative change in the CPI from one year to the next is referred as the rate of inflation. If we want to compare prices fairly we must take inflation into account: we must adjust prices for inflation. To adjust for inflation, we find the equivalent price in a later year. Slide 4 poses the problem: Was gasoline really more expensive in 2005 than it was in 1980? Slides 5 -7 explore the problem by building and using a Gas Price Index. Slides 8 -13 uses the Consumer Price Index to compare the cost of gasoline with the inflation of costs in general, and Slides 14 and 15 chart the cost of gasoline in 2005 dollars for 1978 -2005. Slides 16 -17 give the end-of-module assignments. 3
The Cost of Gasoline Problem: Is gasoline more expensive now (2005) than it has been in the past? Recreate this spreadsheet and graph that show the cost of a gallon of gasoline year by year from 1978 through 2005. Color convention throughout this module = Cell with a number in it = Cell with a formula in it It certainly looks like it, doesn’t it? But what about inflation? 4 Resource: Bureau of Labor Stat. http: //data. bls. gov/cgi-bin/surveymost? ap. The value for 2005 is estimated.
Exploring the Question: Making a Gasoline Price Index We can construct a Gasoline Price Index (GPI) using 1978 as a reference. Add a column to the spreadsheet and calculate the Gasoline Price Index for each year since 1978. =(C 4/$C$4)*100 Compare these cell formulas to the formula for an index number on Slide 2. =(C 12/$C$4)*100 Because we want all of the formulas to point back to the value for 1978, we use an absolute cell reference (the dollar signs). For more information on absolute and relative cell references in EXCEL, see “cell reference” in the EXCEL help file. The graph of the GPI is the same shape as the graph of the cost of gasoline on Slide 4. Why? In 2005, the price of gasoline was 357% of the price of gasoline in 1978 – an increase of more than 2. 5 times! 5
Using the GPI to Make Comparisons Suppose it cost $12 dollars to fill a gas tank in 1980. How much would it have cost to fill the same tank in 2005? We can answer the question by using the GPI (Gasoline Price Index) that we developed in Slide 5. First we divide the GPI for year 2005 by the GPI for 1980 to find a comparison factor (it will be a multiplier) that will express the cost of gasoline in 2005 relative to the cost of gasoline in 1980: . Thus the 2005 price is almost twice the 1980 price. Next you multiply what you would have paid for gas in 1980 by the comparison factor to find what you would have paid in 2005. Thus, if you had filled your gas tank for $12 in 1980, you would have paid $12. 00 × 1. 91 = $22. 92 to fill your gas tank in 2005 Be prepared to discuss this calculation using the words ratio and proportion 6
Making More Comparisons If we can answer the question for 2005, we can answer it too for any year that we know the GPI. So, if it cost $12 dollars to fill a gas tank in 1980, how much would it have cost to fill the same tank for each year from 1978 to 2005? Add another column in the spreadsheet to show the price for each year. We are not showing a graph of the $12 tank of gas vs. time, because it would be yet another rescaled version of the graph of GPI. But now we can come to the point: How would these graphs of gasoline prices differ from graphs of consumer prices in general over those years? What about inflation? Compare this cell formula to the formula for the price of gas in 2005 on slide 6. 7
Consumer Price Index We have observed that the price of gasoline has increased over time. But the price of consumer goods in general may have increased even more. If so, the cost of gas in 2005 might actually cost less relative to everything else in 2005 than it did earlier. The way to find out is to look at the Consumer Price Index. Click on the object to create this spreadsheet. Now graph the Consumer Price Index vs. Time. Certainly there has been an inexorable rise in prices in general from 1978 to 2005. How do the across-the-board prices in 2005 compare specifically to those in 1980? 8
Using the CPI to Make Comparisons We wish to compare the cost of goods and services in 1980 to the cost of goods and services in 2005. According to these tabulated values of the CPI-U, what would have cost $82. 40 in 1980 would have cost $194. 90 in 2005. In general, costs in 2005 were how many times the costs in 1980? Recall (Slide 4) a gallon of gas cost $1. 22 in 1980. In general, things that cost $1. 22 in 1980 (“in 1980 dollars”) cost $1. 22 × 2. 36 = $2. 89 in 2005 (“in “ 2005 dollars”). But a gallon of gas cost $2. 32 in 2005. So gasoline was not relatively more expensive in 2005 than it was in 1980. We can have Excel make this kind of comparison for every year since 1980 from our data on CPI and GPI. 9
Comparing the GPI and the CPI Add the four columns of cell equations to recreate this spreadsheet. Columns E and F are the indexes relative to the 1980 value. Columns G and H are the percentage increases of the indexes since 1980. For comments on this table, see next slide. 10
Comparing the changing GPI to inflation: Table This says costs in 1989 were 1. 5 x the costs in 1980. This says there was 50% inflation between 1980 and 1989. This says gas actually decreased 13% over the same period. Now graph Columns E and F vs. year to see the change in CPI and GPI relative to their values in 1980. 11
Comparing the changing GPI to inflation: Graph Over the 1980 -2005 period, gas prices started out tracking the CPI, but then they fell far behind as the CPI rose but the GPI did not – until recently, that is, when the GPI has been rising faster than the CPI. This graph of the rising CPI shows the amount of inflation since 1980. When speaking of “graphs of inflation, ” however, one generally is referring to the annual inflation (“inflation rates”). Inflations rates are different – they are the relative change over a one-year period (for example, a 10% change over a 10 -year period is vastly different than a 10% change over a one-year period). To draw a graph of the annual inflation rate from 1980 to 2005, we need to go back to the data of Slide 8. 12
Inflation Rate Retrieve your data from the spreadsheet of Slide 8, add two columns of cell equations to track the year-to-year inflation rate, and graph inflation rate vs. time. Note: the CPI of 1979 (72. 6) is 11. 35% higher than the CPI of 1978 (65. 2), so we are saying that the inflation rate during 1978 was 11. 35%. 13
Adjusting Gasoline Prices for Inflation We can make the comparison a different way. We can ask how much a gallon of gasoline back then “was worth” in the dollars of 2005. For example, in 2005 you would have had to pay 194. 9/82. 4 = 2. 37 times what you would have paid for the same goods in 1980. So the $1. 22 you would have paid for a gallon of gas in 1980 would buy 2. 37×$1. 22 = $2. 89 worth of goods in 2005 (whereas gas cost “only” $2. 32 a gallon). Retrieve your data for the CPI (Slide 8) and the Price of a Gallon of Gas (Slide 5), and add a column of cell equations to calculate how much a gallon of gas worth year by year in 2005 dollars. Now graph the gas price and the 14 adjusted gas price vs. time
Adjusting Gasoline Prices for Inflation Here is the answer to our question. The graph shows the cost of a gallon of gasoline in 2005 dollars from 1978 through 2005. Gas was more expensive in 1979 -1982 than in was in 2005 according to these data. 15
End of Module Assignments 1. Expand the table in Slide 5 to give the gasoline price index over the period 1978 to present (use $2. 20 for 2006 and $2. 79 for 2007). Also, use 1988 as the reference year. Multiplot the GPI with the 1988 reference year with the GPI with the 1978 reference year (Slide 5). What do you observe? How do the graphs differ? Explain what you observe. 2. Redo the calculations in Slide 7 to find the equivalent of gasoline which cost $12 in 1980 for each year over the period 1978 to present using 1988 as the reference year and compare it to the results from using 1978 as a reference year. What do you observe? Does the result make sense? Explain! 3. Expand the table in Slide 8 and create a scatter plot of the CPI from 1913 to present (See ftp: //ftp. bls. gov/pub/special. requests/cpiai. txt) 4. Redo the calculations in Slide 15 by evaluating the equivalent price of an item which cost $1 in 1988 for each year since 1913. In what year was the purchasing power of 1988’s $1 the highest? 5. Use your table from assignment 3 to calculate and graph (scatter plot) the rate of inflation since 1913. What do you observe? Write a paragraph discussing the behavior of the rate of inflation in terms of major national and world events during this period. Compare your graph with the CPI graph of assignment #4. 16
End of Module Assignments 7. Find the average price of an item or a service from 1970’s and adjust its price to today’s dollars. 8. Find out about the Housing Price Index and write a brief summary about how it is used. Compare the price of a house in another town to a house in your own town. 9. Find out about the Consumer Confidence Index and write a brief summary describing it. Describe any recent trends in the Consumer Confidence Index. References Using and Understanding Mathematics: A Quantitative Approach, by Jeffrey Bennett and William Briggs Contemporary College Algebra, by Don Small For All Practical Purposes, Mathematical Literacy in Today’s World, by COMAP Bureau of Labor Statistics Website http: //data. bls. gov/ Gas station picture: http: //cgi. ebay. com/ws/e. Bay. ISAPI. dll? View. Item&item=7113368463&category=834 17
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