Mathematics 505D

Data Analysis and Probability

Summer 2011

Projects

Gross Domestic Product

When we talk about the United States’ economy, we are talking about an enormously complex system that must be studied in many different ways and from many different points of view in order to be well understood. One key indicator of the United States’ economic health is the gross domestic product (GDP), a statistic that tells us the total monetary value of all goods and services produced in the United States during a given period of time. (This is slightly different from the gross national

product (GNP), a metric that tells us the value of all goods and services produced by people and corporations from the United States, regardless of where these things are produced.) In this project, you will explore how GDP correlates with some other indicators of economic health, such as inflation, and some policies which are believed to strongly affect our economy, such as the minimum wage.

You have been given a data sheet with GDP figures from 1947 to the present, along with other data such as the minimum wage, the consumer price index (CPI), and unemployment figures. (Most of these figures are from the U.S. Department of Labor.)

Answer the following questions:

1. The consumer price index is a statistic that tells us the cost, in U.S. dollars, of a certain “market basket” of commonly purchased goods at a given time. As inflation occurs, goods and services become more expensive, and the CPI increases. In 1947, the CPI was 22.3. In 1973, the CPI was 44.4, about twice the 1947 figure. Suppose Sam worked in the year 1947 and made $0.60 per hour. If Sam’s son Tim worked in the year 1973, how much money would Tim have had to make per hour in order to have the same purchasing power as Sam?

2. Suppose Sam made $1200.00 in the year 1947. How many 2010 dollars was this worth? (In other words, determine how many 2010 dollars you would need to have in order to have the same purchasing power Sam had.)

3. Use the CPI data given in the table to convert all of the monetary figures in the data sheet (GDP, minimum wage) into 2010 dollars. (In other words, for each dollar amount, determine what amount of 2010 dollars would have the same purchasing power.) We will call the original, unadjusted figures “nominal GDP” and “nominal minimum wage.” We will call the new figures, which have been adjusted for inflation, “real GDP” and “real minimum wage.”

4. The annual inflation rate in a given year is the percentage by which the given year’s CPI exceeds the previous year’s CPI. For example, the CPI in 1973 was 44.4, and the CPI in 1974 was 49.3. So the inflation rate in the year 1974 was

= ≈ 11.04%.

Use Excel to compute the annual inflation rate in each year from 1948 to 2010.

5. The annual GDP growth rate in a given year is the percentage by which the United States’ real GDP in the given year exceeds the real GDP in the previous year. Use Excel to compute the annual GDP growth rate in each year from 1948 to 2010.

6. Use the given data to answer the following questions:

(a) Is there a correlation between nominal GDP and nominal minimum wage? If so, what reasons might there be for this correlation?

(b) Is there a correlation between real GDP and real minimum wage? If so, what reasons might there be for this correlation?

7. Notice that increases in the (nominal) minimum wage occur very infrequently; usually, when the minimum wage increases in several consecutive years, it is because of an increase in the minimum wage that has been graduated over several years. Is there a relationship between annual GDP growth rate and when increases in the nominal minimum wage occur?

8. Political conservatives often warn lawmakers against increasing the minimum wage because doing so makes labor less affordable for business owners; this, in turn, causes unemployment to increase. Use the data to investigate this claim.

9. Conservatives also express concern that minimum wage increases can cause severe inflation. Investigate this claim.

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