Quantitative Reasoning: Consumer Price Index (CPI) Project

QR CPI Instructions

Learning Outcomes for this Project

  1. Understand how the CPI Index is constructed and what it means.
  2. Compare two prices for the same commodity from different years using the CPI index.
  3. Make a graph of a series of prices or wages in nominal and constant dollars.
  4. Develop your skills at interpreting graphs in nominal and constant dollars.
  5. Apply critical thinking skills to interpret graphs from the media.

CPI Background

The first thing that needs to be done is for you to understand the concept of the CPI and how to use it. Open the Word document QR.CPI Tutorial and read it very carefully. It provides a brief overview of the CPI,an explanation on converting prices to constant year dollars and shows graphically why we must convert to constant dollars. Without understanding this material, you may find this project much more difficult to complete.So, please do not proceed any further until you have mastered this material.

After you complete the above reading, please

Open the Word document QR CPI Answer Form [Hereafter called the “Answer Form”]. You will enter your typed answers into this document as directed.

Part AConverting to Constant Dollars

Open the file QRCPI Data.xls. This file provides the CPI in the US for every year from 1912 to 2003. Use the data in this file to answer the CPI questions for Part A.

Complete Part A on the Answer Form by answering the following CPI Questions. Briefly explain your reasoning for each answer and show your computations. No credit will be given if you do not show the relevant computations.

Once again, to answer the following questions you need to have read the QR.CPI Tutorial document.

  1. The average price of a gallon of regular unleaded gasoline in 1976 was $0.64. In 1998 it was $1.06. Use constant 1998dollars to determine your answers.
  • How much was one 1976 dollar worth in 1998?
  • How much was $0.64 in 1976 worth in 1998?
  • Isthe price of gasoline in 1998 more or less than in 1976? Why?

2.In 1989, red delicious apples cost on average $0.57 per pound. In 1995, they cost $0.83 per pound. Use constant 1995 dollars to determine your answers.

  • How much was one 1989 dollar worth in 1995?
  • How much was $0.57 in 1989 worth in 1995?
  • Were apples more or less expensive in 1995 than in 1989? Why?

3.The official definition of "poverty level" is supposed to be adjusted for the effects of inflation. For a family of four, the poverty level was an income of $3,743 in 1970 and $5,050 in 1975. Use constant 1975 dollars to determine your answers.

  • How much was one 1970 dollar worth in1975?
  • How much was $3,743 in 1970 worth in 1975?
  • Do the poverty level incomes in 1970 and 1975 have approximately equal buying power in their respective years (as they should if "poverty level" had the same meaning in both periods)? Why?

4.For a family of four, the poverty level was an income of $5,050 in 1975 and $16,100 in 1997. Use constant 1997 dollars to determine your answers.

  • How much was one 1975 dollar worth in 1997?
  • How much was $5.050 in 1975 worth in 1997?
  • Is a poverty level family better or worse off with $16,100 in 1997? Why?

Part B Minimum Wage Graphs in Nominal and Constant Dollars

Now open the file QR CPI MinWageData. This file contains the minimum wage rate for the US starting in 1938 when it was instituted. [An excellent source of information on the minimum wage in the United States is Department of Labor's page on the topic.]

Minimum Wagein Nominal Dollars Graph Construction

1.We now want to graph the nominal minimum wage data against the year using Excel.

  • Highlight the data in columns A and B from row 8 to row 73.
  • Use the Chart Wizard to make a graph of this data.
  • Under Chart Type choose an XY Scatter plot for this graph.
  • Then choose the fifth subtype. Click Next twice.
  • Title the chart “US Minimum Wage Data 1938 to 2003 in Nominal Dollars”.
  • Label the x-axis“Year” and the y-axis “Wage”.
  • Click Next and select and check the button “As object in” and click Finish.
  • You can now move the chart around on the page by grabbing anyone of the little black boxes and dragging.
  • Remove the small box within the chart by clicking on it and pressing the delete key.

A sample graph from 1938 to 1970 is presented below. Your graph will look like this except it will go through the year 2003.

Sample Graph

Paste your graph into your Answer Form document in part B, #1.

Make sure that your graph display is at least as large as the sample graph.

Minimum Wage Graph in Nominal DollarsInterpretation

  1. Make some observations from the graph you made in Part B,#1.
  • What is the overall trend of the graph (increasing or decreasing)?
  • Identify three periods when the minimum wage rate was increasingvery rapidly and identify the $ change.
  • Identify three periods when it wasnot increasing at all.

You may look at the actual data to answer these last two items

Complete part B, #2 on the Answer Form.

3. Is the graph you made in Part B, #1an accurate portrayal of the buying power of the minimum wage? Briefly explain why or why not. Refer to Part C of the “CPI Tutorial” for assistance.

Complete part B, #3 on the Answer Form.

Minimum Wagein Constant 2003 $ Graph Construction

4. We now want to make a graph of the minimum wage rate in constant 2003 dollars. To do this, we need to convert nominal dollars to constant dollars for each year. We use an Excel spreadsheet to do this quickly.

  • Open the file QRCPI Data.xls (CPI file), a file that contains the consumer price index (CPI-U base year 1982-84)from 1913 to the present.
  • Open the file QRMinWageData.xls (MinWage file). From the CPI file, Copy the CPI values from 1938 to 2003 in columnB from row 38 to row 103.
  • Paste the CPI values in column C,starting at cell C8, next to the minimum wage column B in MinWage file. (The years for the data from both files should correspond)
  • In cell C6, type the heading “CPI”.
  • Add a column D which contains the minimum wage in constant 2003 dollars. In cell D8, enter the formula =B8*184/C8(See the CPI tutorial for the discussion on converting to constant dollars.), press Enter and then left click on the right bottom corner of cell D8 and drag down to cell D73.
  • In cell D6 type the heading“2003 $”.

The top of the spreadsheet should look like this.

Sample

US Minimum Wage Rates 1938-Present
[Rates are those that were in effect at the end of each year.
The minimum wage was instituted under the Fair Labor Standards Act in 1938.
Amendments in 1961 and 1966 extended coverage to more workers.]
Year / Wage / CPI / 2003 $
1938 / $0.25 / 14.1 / 3.26
1939 / $0.30 / 13.9 / 3.97
1940 / $0.30 / 14.0 / 3.94

Minimum Wage in Constant Dollars Graph Construction

Tomake a graph of the minimum wage in constant 2003 dollars, follow the instructions in Part B, #1above for the above spreadsheet, except replace the first instruction with the one below.

  • Highlight the data in columns A and D. First Highlight the data in column Aand then holding down the Control key,highlight the data in column D.

A sample graph from 1938 to 1970 is presented below. Your graph will look like this except it will go through the year 2003.

Sample Graph

Paste your chart into your Answer Form document in part B, #4.

Minimum Wage Graph in Constant Dollars Interpretation

5.Make some observations from the graph you made in Part B, #4. Enter your answers in your Answer Form document in Part B, #5.

  • Describe in whatperiods of time the basic trend of the graph is essentially upward.
  • Describe in what periods of time the basic trend of the graph is essentially downward.
  • Determine the largest minimumwage
  • Determine the smallest minimum wage.
  • Determine what year you wish you were living in if you were earning the minimum wage? Why?
  • Look at years1950-1955 and 1981-89 in your nominal dollar wage graph when the actual minimum wage rate did not change. Then look at the constant dollar wage graph and describe what happened to the minimum wage rate in constant dollars during those same years. Explain whatcaused this pattern to occur.
  • Contrast the different perspectives that the two graphs present to a viewer of the minimum wage over the entire time period.
  • Using the ideas developed in sections C and D of the “CPI Tutorial”, explain why the Nominal graph does not present a realistic understanding of the minimum wage over time?

Part C Interpreting a Media Graph

The Federal Hourly Minimum Wage graph below was widely distributed in September of 1997 when the last minimum wage hike was instituted. Based on our understanding gleaned from the “CPI Tutorial” and what we have done in this project so far, we want to critique this graph to determine whether it presents a realistic depiction of the minimum wage over time.

Answer the following questions in your Answer Form document in Part C.

  • What initial impression does this graph give about the minimum wage over time?
  • This initial impression is due to a serious error that the graph’s presentation contains. Find the error and describe it (Hint: Look at the dates at the bottom of the graph).
  • How does the impression from this graph differ from the impression made by your Nominal Dollar Wage graph in Part B, #1?
  • How does the impression from this graph differ from the impression made by your Constant Dollar Wage graph in Part B, #4?
  • Does “The Federal Hourly Minimum Wage” graph shown above present a realistic depiction of the minimum wage? Why?

Submit your completed Answer Form by e-mail to the Instructor or post it to your private conference by the designated due date.
Make sure your e-mail has your full name on it and make the subject of the e-mail or the posting “CPI”.
Your facilitator will tell you whether to e-mail or to post your complete Answer Form document.

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