## Correcting Economic Variables For The Effects Of Inflation

The purpose of measuring the overall lex-el of prices in the economy is to permit comparison between dollar figures from different times. Now that we know how price indexes are calculated, let's see how we might use such an index to compare a dollar figure from the past to a dollar figure in the present.

Indexation the automatic correction by la« or contract of a dollar amount for the cflecti of inflation

Dollar Figures from Dipperent Times

We first return to the issue of Babe Ruth's salary. Was his salary of \$80.000 in 1931 high or low compared to the salaries of today's players?

To answer this question, wc need to know the level of prices in 1^31 and Ihe level of prices today. Part of the increase in baseball salaries compensates players for higher prices today. To compare Ruth's salary to those of today's players, we need to inflate Ruth's salary to turn 1931 dollars into today's dollars.

The formula for turning dollar figures from year T into today's dollars is Ihe following:

Amount in today's dollars - Amount in yea» T dollars x 1 1

A price index such as ihe consumer price index measures the price Wei and thus determines the size of the inflation correction.

Let's apply the formula to Ruth's salary. Government statistics show a consumer price index of 15.2 for 1931 and 207 for 2007. Thus, the overall level of prices has risen by a factor of 13.6 (which equals 207/15.2). We can use these numbers to measure Ruth's salary in 2007 dollars, as follows:

Salary in 2007 dollars - Salary in 1931 dollars X I/'"' I*'"'1.

Price level in 1931

We find that Babe Ruth's 1931 salary is equivalent to a salary today of over \$1 million. That is a good Income, but it is less than a quarter of Ihe median Yankee salary today and only 4 percent of what the Yankees pay A-Rod. Various forces, induding overall economic growth and the increasing income shares earned by superstars, have substantially raised the living standards of Ihe best athletes.

Let's also examine President Hoover's 1931 salary of \$75,000. To translate thai figure into 2007 dollars, we again multiply the ratio of Ihe price levels in Ihe 2 years. We find lhat Hoover's salary is equivalent to \$75.0lX) x (207/15-2), or \$1,021,382, in 2007 dollars. This is well above Presxlent Ceorge W'. Bush's salary of \$4!X>/KM1. It seems that President Hoover did have a pretty good year after all.

### Indexation

As we have just seen, prkr indexes are used to correct for the effects of inflation when comparing dollar figures from different limes. This type of correction shows up in many places in Ihe economy. When some dollar amount is automatically corrected for changes in the price level by law or contract, the amount is si id lo be indexed for inflation.

For example, many long-term contracts between firms and unions include partial or complete indexation of the wage to the consumer price index. Such a provision iscalled a con-cf-hzinx allmcance, or COLA. A COI.A automatically raises the wage when the consumer price index rises.

Indexation is also a feature of many laws. Social Security benefits, for example, are adjusted every year to compensate the elderly for increases in prices. The bracket* of the federal income tax—tlx; income levels at which the tax rates change—are also indexed for inflation. ! here arc, however, many ways in whkh the tax system is not indexed for inflation, even when perhaps it should be. We discuss these issues more fully when we discuss the costs of inflation later in this book.

Real and Nominal Interest Ratf.s

Correcting economic variables for the effects of inflation is particularly important, and somewhat tricky, when we look at data on interest rates. The very concept of an interest rate necessarily involves comparing amounts of money at different points in lime. When you deposit your savings in a bank account, you give the bank some money now, and the bank returns your deposit with interest in the future. Similarly, when you borrow from a bank, you get some money now, but you will have to repay the loan with interest in the future. In both cases, to fully understand the deal between you and the bank, it is crucial to acknowledge that future dollars could have a different value than today's dollars. I hat is. you have to correct for the effects of inflation.

Let's consider an example. Suppose Sally Saver deposits MAW in a bank account that pays an annual interest rate of 10 percent. A year later, after Sally has accumulated \$100 in interest, she withdraws her \$1,11X>. Is Sally \$1IM1 rkher than she was when she made the deposit a year earlier?

nominal interest rat« tli« interest rati as usually reported without a correct! on tor the *(f«ct5 of inflation teal ¡nterett rat« tlie interest rate corrected for the offsets of Inflation

The answer depends on what we mean by "richer." Sally does have \$100 more than she had before. In other words, the number of dollars in her possession has risen by 10 percent. But Sally does not care about the antouni of money itself: She cares about what she can buy with it. If prices have risen while her money was in the bank, each dollar now buys less than it did a year ago. In this case, her purchasing power—tlie amount of goods and services she can buy—has not risen by II) percent.

To keep things simple, let's suppose that Sally is a music fan and buys only music CPs. When Sally made her deposit, a CD at her local music store cost \$10. Her deposit of \$1,000 was equivalent to 100 CDs. A year later, after getting her ll) percent interest, she has \$1,100. How many CDs can she buy now? It depends on what has happened to the price of a CD. Here are some examples:

• Zero inflation: If the prfce of a CD remains at \$10, the amount she can buy has risen from 100 to 110 CDs. The 10 percent increase in the number of dollars means a 10 percent increase in her purchasing power.

• Six percent inflation: If the price of a CD rises from \$10 to \$10-60, then the number of CDs she can buy has risen from 100 to approximately 104. Her purchasing power has increased by about 4 percent.

• Ten percent inflation: If the price of a CD rises from \$10 to \$11, she can still buy only HXlCDv Even though Sally's dollar wealth has risen, her purchasing power is the same .is it was a year earlier.

• Twelve percent inflation: If the price of a CD increases from \$10 to SI 1.20, the number of CDs she can buy has fallen from 100 to approximately

Even with her greater number of dollars, her purchasing power has decreased by about 2 percent.

And if Sally were living in an economy with deflation—foiling prices—another possibility could arise:

• Two percent deflat'ion: If the price of a CD falls from \$10 to \$9.80, then tin-number of CDs she can buy rises from 100 to approximately 112. Her purchasing power increases by about 12 percent.

These examples show that the higher the rate of inflation, the smaller tin- increase in Sally's purchasing power. If the rate of inflatkm cxcccds the rate of interest, her purchasing power actually falls. And if there is deflation (that is, a negative rateof inflation), her purchasing power rises by more than the rale of interest.

To understand how much a person earns in a savings account, we need to consider both the interest rate and the changc in the priccs. The interest rate that measures the change in dollar amounts iscalkd the nominal interest rale, and the interest rate corrected for inflation is called the real interest rate. The nominal interest rate, the real interest rate, and inflation are related approximately as follows:

Real interest rate = Nominal interest rate - Inflation rale

The real interest rate is the difference between the nommal interest rate and the rate of inflation. The nominal interest rate tells you how fast the number of dollars in your bank account ri>es over time, while the real interest rate tells you how fast the purchasing power of your bank account rises over time-

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