1. Chapter 6 Measuring the price level
Chapter 5 covered the definition and measurement of the standard of living. We now turn our attention to the cost of living.
The cost of living is given by the average level of prices in the economy. To measure the average level of prices we use a price index, one of the most frequently used being the Consumer Price Index (CPI).

2. The CPI measures the average of the prices paid by urban consumers for a fixed market basket of consumer goods and services. The Bureau of Labor Statistics (BLS) publishes the CPI every month. The BLS checks the prices of 80,000 goods and services in the CPI market basket in 30 metropolitan areas.
The average expenditure on each item in the market basket is the weight that is attached to that item. E.g., if households on average spend 40% of their income of housing and 15% on food, then an increase in the price of housing should carry a weight of 40% and an increase in the price of food should be weighted 15% in determining the average overall increase in the cost of living.

3. There are three steps in calculating the CPI:
The CPI is defined to be equal to 100 in the reference base period. Currently the reference base period is If the CPI were then calculated to be, say, 105, in a later period, then this means that prices on average were 5% higher in that period than in the reference base period.
There are three steps in calculating the CPI:
1. Find the cost of the CPI market basket at base period prices.
2. Find the cost of the CPI market basket at current period prices.
3. Calculate the CPI for the base period and the current period.

4. To simplify the calculation, we will assume that consumers purchase only three goods: beer, pretzels and aspirins.
Also, we will construct an annual CPI rather than a monthly one.
For our calculation, the reference base period is assumed to be 2000 and the current period is 2006.

5. 1. The cost of the CPI market basket in the base period: 2000
Quantity consumed
Price per unit
Expenditure
beer 8
$2.00
$16.00
pretzels 5
$1.50
$7.50
aspirins 4
$0.50
Cost of basket at base period prices $25.50

6. 2. The cost of the CPI market basket at current period prices: 2006
Quantity consumed
Price per unit
Expenditure
beer 8
$2.50
$20.00
pretzels 5
$2.20
$11.00
aspirins 4
$1.00
$4.00
Cost of basket at current period prices $35.00

7. Thus, in 2000 (the reference base period),
3. Use the CPI formula to calculate the CPI in the reference base period and in the current period:
CPI = Cost of CPI basket at current period prices X 100
Cost of CPI basket at base period prices
Thus, in 2000 (the reference base period),
CPI = ($25.50/$25.50) X 100 = 100.
In 2006 (the current period),
CPI = ($35.00/$25.50) X 100 =
The interpretation of this number is that prices were 37.25% higher in the current year (2006) than they were in the reference base year (2000).

8. The formula for calculating the annual inflation rate is as follows:
The main purpose of the CPI is to measure changes in the cost of living over time, i.e., the inflation rate. The annual inflation rate is the percentage change in the price level from one year to the next.
The formula for calculating the annual inflation rate is as follows:
Inflation rate = CPI in current year – CPI in previous year X 100%
CPI in previous year

9. For example, in 1999 the CPI was 166
For example, in 1999 the CPI was ( = 100) and in 2000 it was Therefore the inflation rate for the year was:
Inflation rate =  X 100%
166.6
= 3.36%.

10. Problems with the CPI as a measure of the cost of living:
The cost of living is the amount of money that people would need to spend to achieve a given standard of living. The CPI is not an accurate measure of the cost of living for two reasons:
1. In calculating the CPI, quantities consumed are fixed. The CPI captures only changes in prices. But quantities do change from year to year and changes in quantity do affect the cost of living.

11. 2. Even those components of the cost of living that are measured by the CPI are not always measured accurately, i.e., the CPI is a biased measure of the cost of living. The sources of this bias are:
(a) New goods bias
(b) Quality change bias
(c) Commodity substitution bias
(d) Outlet substitution bias

12. In 1996 a Congressional Advisory Commission led by Michael Boskin of Stanford University (the “Boskin Commission”) calculated that the CPI overestimated inflation by 1.1 percentage points per year. So if the CPI gives an inflation rate of 2.9%, “true” inflation is probably only 1.8%.

13. Consequences of CPI bias
Many private contracts are indexed to the CPI. E.g., many union contracts specify that wages must increase at a rate equal to the inflation rate as measured by the CPI. If the CPI overestimates inflation, then indexed wages will rise more than enough to compensate workers for increases in the cost of living.
Many government expenditures, such as Social Security benefits, welfare payments and civil servant pensions, are indexed to the CPI and therefore increase by more than what is necessary to compensate recipients for the rising cost of living.

14. Using the CPI to convert nominal values to real values
“Nominal” versus “real”
It is misleading to compare dollar values paid at different dates because the purchasing power of the dollar decreases as a result of inflation, e.g., fifty years ago a dollar provided its holder with more command over goods and services than a dollar provides today.

15. To make valid comparisons of dollar amounts at different times, we need to measure real values, not nominal values.
A nominal value is one that is expressed in terms of current prices. A real value is one that is expressed in terms of the prices prevailing in a given year.

16. For example, suppose that consumption spending in 1997 was $5
For example, suppose that consumption spending in 1997 was $5.5 billion and in 2000 it was $6.8 billion. This means that in nominal terms consumption has increased by
$6.8 billion – $5.5 billion X 100% = 23.6%.
$5.5 billion
Does this mean that consumers are really buying 23.6% more goods and services? No! They are spending 23.6% more dollars, but, due to inflation, the purchasing power of those dollars in 2000 is not as high as that of the 1997 dollars.

17. In 1997 the CPI was 160. 5 (1982-84 = 100) and in 2000 the CPI was 172
In 1997 the CPI was ( = 100) and in 2000 the CPI was We can use these two numbers to calculate the relative value of a dollar in 1997 and This ratio is 172.2/160.5 = 1.073, i.e., prices were on average times higher in 2000 than in 1997.
We can use this ratio to convert the 2000 consumption spending into its 1997 equivalent, i.e., to express 2000 consumption spending in terms of 1997 prices:

18. Consumption spending in 1997 dollars =
(CPI in 2000)/(CPI in 1997)
= $6.8 billion
172.2/160.5
= $6.8 billion
1.073
= $6.34 billion.

19. This means that in 2000 consumers needed $6
This means that in 2000 consumers needed $6.8 billion to buy the same basket of goods and services that $6.34 billion would have bought back in 1997, i.e., at 1997 prices, because prices were times higher in 2000 than in 1997.
The $6.34 billion is real consumption expenditure in 2000 in terms of 1997 prices, whereas the $6.8 billion is nominal consumption spending in 2000 expressed in terms of current (2000) prices.

20. Thus, in our example, real consumption expenditure in constant 1997 dollars increased by:
$6.34 billion – $5.5 billion X 100% = 15.3%.
$5.5 billion
Recall that nominal consumption expenditure increased by 23.6% from 1997 to 2000, which simply means that consumers spent 23.6% more dollars in 2000 than they did in But those expenditures in 2000 only purchased 15.3% more real goods and services, once we remove the effect of the higher prices.

21. Nominal and real wage rates
In macroeconomics we focus on the average hourly wage rate. The nominal wage rate is the average hourly wage rate measured in current dollars. The real wage rate is the average hourly wage rate measured in the dollars of a given reference base year.

22. To convert a nominal wage rate into a real wage rate we use the following formula:
Real wage rate = Nominal wage rate
___________________________________________
(CPI in current year)/(CPI in reference base year)

23. For example, the nominal hourly wage rate in 2004 was $15. 68
For example, the nominal hourly wage rate in 2004 was $ What was the real hourly wage rate in terms of prices? The CPI for 2004 was The CPI for was of course Therefore,
Real wage rate in = $15.68
_________________
(188.9)/(100)
= $8.30.

24. Thus, $8. 30 is the 1982-84 equivalent of $15. 68 in 2004
Thus, $8.30 is the equivalent of $15.68 in This means that a worker needed to earn $15.68 in 2004 in order to buy the same basket of goods and services that he could have bought for $8.30 in , i.e., at prices, because prices were times higher in 2004 than they were in

25. We can calculate Mary’s annual salary in 1966 dollars:
But the reference base year is not necessarily Consider the following example:
Mary’s grandmother earned $8,000 per year in In 2004 Mary earned $41,000. Who was better off in real terms? The CPI in 1966 was 32.4 ( = 100). The CPI in 2004 was
We can calculate Mary’s annual salary in 1966 dollars:
Mary’s real 2004 salary in 1966 dollars = Mary’s nominal salary in 2004
___________________________
(CPI in 2004)/(CPI in 1966)
= $41,000
_____________
(188.9)/(32.4)
= $7,

26. Clearly, therefore, Mary’s grandmother, who earned $8,000 in 1966, was doing better than Mary whose real salary in 2004, in terms of 1966 prices, was only $7,
Alternatively, we can calculate Mary’s grandmother’s annual salary in terms of 2004 dollars:
Grandmother’s 1966 salary in 2004 dollars = Grandmother’s nominal salary
___________________________
(CPI in 1966)/(CPI in 2004)
= $8,000
____________
(32.4)/(188.9)
= $46,

27. Again, therefore, Mary’s grandmother, who, back in 1966, earned $46, in terms of 2004 dollars, was doing better than Mary who earned only $41,000 in 2004.
An increase in a worker’s nominal hourly wage rate tells us how many more dollars the worker is earning in an hour. An increase in the worker’s real hourly wage rate tells us how much more goods and services the worker is able to buy with that hourly wage.

28. As long as prices are rising, the nominal wage rate will grow faster than the real wage rate because the nominal wage rate includes inflation whereas the real wage rate removes the effects of inflation.
In general, to convert any nominal dollar amount into a real dollar amount, i.e., to deflate a nominal dollar value, we divide the nominal amount by a ratio of price indexes.

29. Nominal versus real interest rates
A nominal interest rate is the percentage return on a loan in dollars. A real interest rate is the percentage return on a loan in terms of purchasing power.
For example, suppose you deposit $100 in a bank account for one year at an annual interest rate of 10%. This interest rate, called the loan rate, is a nominal interest rate. It means simply that you will get back 10% more dollars at the end of the loan period than you initially deposited.

30. But now suppose that, over this same one-year period, prices on average increased by 4%. You would need $104 at the end of the year in order to be able to buy the same basket of goods and services that you were able to buy for $100 at the beginning of the year.
But since you are actually getting $110 at the end of the one-year period, the real interest you have earned is $6, i.e., you are able to buy 6% more goods and services at the end of the year than you were able to buy at the beginning of the year with the $100. You are getting an extra 6% of purchasing power, therefore the real interest rate in this case is 6%.

31. Real interest rate = 10% – 4% = 6%.
In general,
Real interest rate = Nominal interest rate – Inflation rate
In this case,
Real interest rate = 10% – 4% = 6%.