Chapter 22 The CPI and Cost of Living (Inflation)
A. Inflation
1. Inflation – a general increase in overall price level. It is measured by utilizing something called the consumer price index.
2. Consumer Price Index (CPI) – this is a bundle of goods that a typical HH purchases in a year. By monitoring the changes in the price of this basket we get a sense of how overall prices are changing from year to year. It contains roughly 80,000 G/S and is measured in about 30 metro areas. It does so every month.
Note: a base year of prices (reference base period) is given and the basket is updated every 2-4 years for the inclusion of G/S that are currently being purchased. Currently the base period is 1982-84.
Mathematically: CPI = P basket of Specific Yr / P basket Base Yr
3. Inflation Formula:
Note: It measures the rate of change in prices from one year to the next. It is not the change in prices, but the rate of change in prices.
Mathematically: Inflation = [(CPI yr 2- CPI yr 1) / CPI yr 1] * 100
-since 1965 the rate of inflation has been somewhere between 2-5%
4. Bias of the CPI
a. Fixed Basket Problem or New Product bias – the basket is relatively fixed for a time period and may not be able to account for changes in what a HH purchases currently as it happens. It is attempted to be held constant but is not perfect.
b. Substitution bias – as the relative prices change from month to month HH may purchase more or less of G/S due to this change in prices. This is not accounted for since the price of some items may be similar even though the value of the basket may change.
c. Increase or Change in Quality – this is not accounted for in the CPI. So as prices increase due to the change in quality the CPI cannot control for this.
d. Outlet bias – the more we have of outlets or discount stores the more HH tend to purchases these G/S. This is not counted in the CPI either since they measure things purchased from retail stores.
5. Costs of Inflation
a. Lenders- if inflation is not accounted for properly it can cost them
b. taxpayers – if inflation occurs they may see a rise in investment price and have to pay taxes even though this is not really an increase in value.
c. currency holders – those who decide to hold $ and not invest
d. it can artificially alter how firms and HH spend money due to uncertainty.
e. generally causes uncertainty like when Government changes funding and budgets based on values that include inflation.
f. people on non-indexed incomes lose purchasing power as inflation goes up.
6. Other terms
a. deflation – an overall drop in price level. Has not been a problem in the US.
b. hyperinflation –very raid inflation changes. This is on the order of 10% or greater each year. It has been a problem in Germany after WWII & South America recently.
c. cost of living index – another name for the CPI since it measures how much we must pay for a certain amount of G/S.
d. Nominal wage rate – average hourly wage in current year prices
e. Real wage rate – hourly wage rate as measure in a base year.
7. CPI is used for:
(a) Policy target – it is used by the government to target inflation
(b) To index payments to
(c) To translate nominal to real values
Mathematically :
1)Real value = (nominal value / CPI of that yr ) * 100
Note: A special case is interest rates where:
2) Real interest rate = nominal rate – inflation
-inflation does not change the average purchasing power in the economy, but it may re-distribute it should it not be fully anticipated by all parties.
8. Other measures of Price Level
a. GDP Deflator – average of the current prices of all the G/S included in GDP expressed in base year prices.
-uses all G/S measured in GDP used
b. PCE Deflator – an average of the current items included in GDP in C expressed in base year prices.
**both measures use current year quantities and therefore adjust for new product bias. In general the values are very close with CPI measurement being the most conservative (i.e. overstate inflation)
B. Practice Problems for Inflation, CPI, and Interest Rates
1. Calculate CPI:
Suppose we want to calculate CPI and we are given that the basket of goods to produce this are 2 televisions sets, 4 bottles of shampoo, and 20 pizzas. If you are given the prices of these items as follows calculate:
a. The CPI for each year assuming that 2004 if considered your base year.
b. For each example given calculate the rate of inflation for each year.
Table 1: Given Information
Year/Goods / Pizza / TV / Shampoo2004 / 10 / 300 / 1
2005 / 11 / 350 / 1.50
2006 / 14 / 450 / 2.25
To calculate the CPI for each year we must do so in a 3 step process as follows:
Step 1: Get the total value of the market basket for the yr
Step 2: Divide each year’s market basket price by the base years total market basket value.
Step 3: Multiply each year by 100 to get the CPI. Note that the base year’s value is always going to be 100.
To get inflation we simply use the following formula:
Inflation = (CPI yr 2- CPI yr 1)/ CPI yr 1 * 100
So using this equation we obtain the values for inflation in 2005 and 2006. Note: we cannot calculate the rate of inflation for 2004 with the information given. To do so we would need the prior years CPI.
Table 2: Calculating CPI and Inflation
Year/Goods / Pizza / TV / Shampoo / Value of Basket / CPI(a) / Inflation (in %)
(b)
2004 / 10 / 300 / 1 / 20*10+4*1+2*300=804 / 100 / -
2005 / 11 / 350 / 1.50 / 20*11+4*1.5+2*350=926 / 115 / 15
2006 / 14 / 450 / 2.25 / 20*14+4*2.25+2*450=1189 / 148 / 28.4
2. Calculate Real interest in the following situations:
a. Bob buys a one-year corporate bond that pays him a nominal interest rate of 10%. Over that year inflation is 7%.
b. A Bank makes a loan out at a nominal interest rate of 6%. Over the life of the loan inflation averages 8%.
Answers:
(a) To obtain the real rate of interest we use the formula:
Real interest = Nominal interest – inflation = 10 – 7= 3%
(b) Again, using the same formula: Real interest = Nominal interest – inflation = 6 – 8= -2%. Given this information it is probably unwise to make such a loan since the value that you will receive later on is going to be less in present value terms than what you lent it at.
1