Macroeconomic Measurements Cost of Living Calculating the Rate of Inflation Page 1 of 3 Now, here’s a mystery. On page one of the Wall Street Journal, the inflation rate is reported at 2.5%, and on page fourteen of the same day’s journal it says we’ve had 0% inflation for the last year. Now, how can both of these numbers be correct? Is there an error or is there something I’m missing? Hold on, on page one it says that the 2.5% inflation rate is based on the GDP deflator; whereas, on page fourteen in says that the 0% inflation rate is based on the consumer price index. Now, I know that these two indexes are different, and maybe that accounts for the difference in their measures of inflation. After all, the consumer price index measures only the prices of a subset of goods – goods that are purchased regularly by households, things like food and clothing – whereas, the GDP deflator includes all of the goods and services produced in the economy. So, since the consumer price index is based on the prices of fewer goods maybe that’s why the number is different than the inflation rate measured by the GDP deflator. However, it turns out that there’s something else going on. What’s going on is that even if the GDP deflator and the consumer price index were based on exactly the same set of goods, you could get different numbers because of differences in the way in which the two indexes are calculated. I think I can make this point very clear with a simple example. Consider an economy that produces only two goods, food and clothing. We’re choosing food and clothing because these are goods that consumers purchase, so the consumer price index is based on the price of these goods, and since these are the only goods produced in the economy, the GDP deflator depends also only on the price of these two goods. Now let’s look at the gross domestic product data for two consecutive years, the year 2000 and the year 2001. In the year 2000, ten units of food are produced, and the price per unit is $10 for food. So, $10 times ten units is $100 worth of food production. Clothing: $20 per unit times ten units is $200 from clothing production. $200 plus $100 gives us a gross domestic product of $300 in the year 2000. Now, as we move to the year 2001, notice that two things have changed. First, the prices of goods have changed. Food is now selling for $20 a unit and clothing for $35 a unit. The next thing that’s changed is that quantities have changed. There’s more food produced and more clothing produced, so the gross domestic product is going to be larger because prices are bigger and quantities are bigger. Let’s go ahead and calculate the gross domestic product for the year 2001. $20 per unit of food times fifteen units of food gives us a GDP from food of $300. Over here under clothing, we’ve got $35 a unit times fifteen units for $525 worth of clothing produced. $525 plus $300 gives us a gross domestic product for the year 2001 of 825. Now, I’m interested in what’s happening to prices between the year 2000 and the year 2001. Now, since there are two different goods being produced, our overall measure of prices has got to be some kind of weighted average of the change in prices, and the way in which that weighted average is calculated is what distinguishes the consumer price index from the GDP deflator. Let’s look first at the method used in calculating the consumer price index. The intuition behind a consumer price index is how much would you have to pay to get the same goods you got last year at this year’s prices, so we’re using the quantities from last year but the prices from this year. Let’s look, then, at how the consumer price index is calculated. Macroeconomic Measurements Cost of Living Calculating the Rate of Inflation Page 2 of 3 The question is what would it cost you to buy last years goods at this years prices? So, let’s look first, then, at that amount of money that you’d have to spend. What I’m going to do is take the quantities from the year 2000 and move them forward to the year 2001 and calculate the spending I would have to do at 2001 prices in order to buy the year 2000 quantities. So, in the year 2001, food is now $20 a unit, $20 a unit times the original ten units of food that we were buying last year is $200 you’re going to have to spend to get the same food that you were buying last year. What about clothing? Last year you had ten units of clothing so this year when you have to pay $35 a unit for clothing, you’re going to have to spend $350 to get the same amount of clothing that you had last year. So, $350 on clothing, $200 on food gives us a grand total of $550 that you have to spend in the year 2001 when prices are higher to get the same goods that you were buying back in the year 2000. Now, let’s calculate the consumer price index. The consumer price index is a ratio. It’s a ratio of the amount of money that you’d have to spend this year to get that basket relative to how much you have to spend in the base year, the year whose quantities you’re considering. So, let’s calculate, $550, the amount we’d have to spend in the year 2001, divided by $300, the amount we had to spend in our base year, the year 2000, multiply that by one hundred and you get the consumer price index, which in this case is 183. So, the consumer price index for the year 2001 is 183. That’s the amount by which prices have increased from one year to the next, but we’re interested in percentage increase, the amount by which prices have increased in percentage terms because that’s the inflation rate. So, what we do to calculate the inflation rate using this method is we take the consumer price index for the year 2001, and we subtract from it the consumer price index from the year 2000. Now, the year 2000 is our base year, remember, where it costs $300 to buy that basket of goods and services. So, divide $300, which is the amount you have to spend in the year 2000, by $300, which is the amount you have to spend in the base year, and you get one hundred. The CPI for the base year by definition is always 100%, it’s equal to itself. So, subtract 100 from 183. So, this is the CPI for the year 2001 minus the CPI for the year 2000, the base year. And divide by the base year amount which is 100, and that’s going to give us the rate of inflation. One hundred eighty three minus 100 is 83 divided by 100 is equal to 83%. The rate of inflation measured according to the method of the CPI is 83%. The CPI has increased by 83% from the year 2000 to the year 2001. The price of that market basket of goods and services has gone up by 83%; that’s the inflation rate measured with this method. Now, let’s look at the other method for calculating the inflation rate. This one is based on the GDP deflator. Remember, the GDP deflator is the ratio between the nominal GDP in a particular year and the real GDP for that same year. The way you calculate the real GDP, you’ll remember, is to find the value of the goods and services produced in a particular year using the market prices from the base year. So, the nominal GDP for the year 2001 is 550, but the real GDP is calculated using the year 2000 prices. So, let’s go ahead and put the year 2000 prices into our equation and use the year 2001 quantities. So, this means that the real GDP for the year 2001 is $10 times fifteen units of food or $150, plus $20 times fifteen units of clothing worth $300. $300 plus $150 gives us a real gross domestic product of $450. Now, to find the GDP deflator take the nominal GDP and divide by the real GDP, and this should give us, then, after we multiply by 100, some notion of on average how much prices have risen between the year 2000 and the year 2001. And the answer is 122. So, 122 is the GDP deflator for the year 2001. Macroeconomic Measurements Cost of Living Calculating the Rate of Inflation Page 3 of 3 To calculate the inflation rate, now, we have to see how the GDP deflator has changed between the two years. So, we now want to do a percentage change calculation. So, let’s do that. 122 is the GDP deflator for the year 2001. What’s the year 2000 GDP deflator? Well, it’s the base year. So, in the base year the GDP deflator is always going to be 100% because you’re comparing that year with itself. So, subtract 100 from 122 and divide by 100 and that’s going to give us an inflation rate of 22%.