## What Good is the Consumer Price Index, Anyway? March 14, 2011

Posted by tomflesher in Macro, Teaching.
Tags: , , , , , ,

One of the first things people learn in their Intro Macro course is that prices change. Before we get into why that happens, let’s think about one of the other things we’ve already talked about: purchasing power and the associated concept, purchasing power parity. One way to measure purchasing power is to look at how much a dollar buys, but in my Beerflation post I referred to how the relative price of beer may have increased since the 70s but the relative price of laptops has decreased. So, let’s consider how we can solve that problem.

One common way to do so is to consider not the price of one good, like a beer at a bar or a can of black beans or a copy of Introduction to Modern Economic Growth, but the overall price of many goods. Think about, for example, the hypothetical cost of being a new college student. I’ll ignore tuition for now (since that’s variable based on where you go to school and how you did in high school) and only consider things a typical freshman would need to buy over the course of the year.

First, the student needs a place to sleep and food to eat. At my current employer, the University at Buffalo, a double room costs $5928. A meal plan with 14 meals per week plus$300 in flexible spending costs $1950 per semester or$3900 for the year. Then, the student needs clothes to wear. A typical wardrobe might be five pairs of jeans, five t-shirts, five polo shirts, ten pairs of underwear, ten pairs of socks, and a winter jacket. If purchased at Target, Wal-Mart and Old Navy, this would run a total of about $250. As for actual academic expenses, the student will need books for about eight to ten classes (let’s settle on 9 for now). Assuming the price of books is around$80 each (allowing for a class or two that has a novel as the assigned text and two math classes that might use the same book, like Calculus I-II), that puts book expenditure around $720. The Calculus class probably allows the use of a graphing calculator, which currently runs about$100 at Amazon.

Finally, the biggie will be the student’s computer. I tend to go cheap and pick up laptops around $450 from Best Buy, so let’s use that number. If we add up all of these numbers, we get$11,348, which is a fair number to use when we discuss “the out-of-pocket cost of being a college student.”1 Then, we can compare the cost to last year’s rates and next year’s rates and look at how the out-of-pocket cost of being a college student changes from year to year.

That’s basically what the CPI does. It looks at what’s called in technical terms a “basket of goods.” That is, it assumes that people buy more or less the same goods every year and then looks at the changes in the total price of those goods.2 In order to make things easier to deal with, they perform a mathematical trick called normalizing. That allows us to use an index, or a single number, to show changes. It’s easier remembering that CPI in the base year is defined as 100 than trying to remember what a particular year’s total cost was. They choose a base year and divide that total cost for the basket of goods by the base year’s total cost. So, the formula for CPI in a given year is

$CPI \equiv \frac{Cost_{current}}{Cost_{base}} \times 100$

So, there are two things to note here. The first is that when the current cost equals the base cost, the CPI will equal 100 (so, CPI is  always 100 in the base year). The second is that we can find the approximate percentage change in prices – that is, the approximate level of inflation – using either of the following formulas:

$\%\Delta CPI = \frac{CPI_{current} - CPI_{base}}{CPI_{base}} \times 100 = (\frac{CPI_{current}}{CPI_{base}} - 1) \times 100$

So, summing up, the Consumer Price Index (CPI) is a number that represents how the price of a certain basket of goods has changed since a chosen base year. The basket of goods is meant to represent typical products purchased by a typical household in a given year. It’s one way to measure inflation, since the goods are the same from year to year so the real value should stay the same even if the prices change.

Notes.
1 Note that this is explicitly the out-of-pocket cost. The opportunity cost is much different and would have to take into account the wages that the student gave up to go to college, but wouldn’t necessarily take into account a computer or clothing since those would need to be bought anyway. Again, this cost is an estimate and many of the numbers are estimated or rounded. If anyone cites this as “the cost of going to college,” I’ll be very sad.

2 If we have a model economy where we know that we have a well-defined basket of goods x1, x2, …, xn with associated prices p1, p2, …, pn, then the price of the basket would be

$\displaystyle\sum\limits_1^n x_n \cdot p_n$