Is an increase in CPI good or bad?

As with all economics, the answer is, “It depends,” but let’s start by asking a refining question: Good or bad for whom?

• The Government: Good.
  

An increase in the CPI represents an increasing cost of living, which is related to inflation. Inflation, as measured by an increase in the CPI, means that the government can sign contracts to pay employees or purchase materials in current dollars and then pay them back in inflated dollars; that is, if I sign a contract today, January 30, 2012, to pay you $100 on January 30, 2013, then the $100 I have now is worth more than the $100 I’ll pay you back with. (This is one reason for interest payments.) Of course, if everyone expects the inflation, they’ll take that into account when contracting with the government and demand higher payments. A government can, in fact, use large unexpected inflation to cut their costs this way – it’s called an inflation tax, and we’ll talk about it a little later on – but it’s not  a strategy that works well or often.

• Businesses: Good.

Businesses can take a beating if they’re contracting with governments, but consider wage contracts – when I worked at a factory, pay rates were set by position in January, so my only hope of getting a raise was to move to a higher position. If CPI rose over the course of the year, which it almost always did, I took what was effectively a pay cut until the next round of  cost-of-living adjustments in January. That means that the business could negotiate contracts throughout the year for supplies and sales, but its real wage expenses actually fell.

• Consumers: Bad (mostly).

And who takes the brunt of the drop in real wages? Households, or consumers. Since I lack the power to demand my wages rise throughout the course of the year, then my wages on January 1 are going to buy fewer goods than my wages on December 31, even though they’re nominally the same amount of money.

On the other hand, a small, predictable amount of inflation allows for a few things to happen. If it’s small, it means that prices more or less stay the same. (A large inflation rate would make it impossible for me to keep the same wage from January 1 to December 31 without built-in monthly or quarterly raises, for example.) If it’s predictable, we avoid a couple of ugly problems like the inflation tax or surprises when repaying loans. If it’s inflation, rather than deflation, people and businesses have a smaller incentive to hold on to their money to wait for prices to drop, so there’s an argument, weak though it is, to be made that inflation encourages spending.

All told, an increase in CPI means that a household has to spend more dollars to maintain the same standard of living; that’s mostly bad for the households, but it can be good for businesses and the government.

Start with the plain-sense definition of a budget. Most people think of a budget – quite correctly – as a list of planned expenses by category. I might plan out my week’s spending as:

• $30: gas
• $200: planned monthly expenses (rent, insurance, utilities)
• $50: groceries
• $40: a meal out
• $30: savings
• $50: petty cash (Starbucks, forgot my lunch, that sort of thing)

That comes out to $400. What does that tell me? Well, for it to be a good budget, I’d better not make any less than $400 a week! Otherwise, I’m planning to spend more than I make, and that’s going to get me into trouble shortly. (If I spend myself into a deficit, I’ll need to plan to get out at some point.) It also tells me that I expect to make no MORE than $400 this week. After all, I have a spot for savings and a spot for petty cash, so I have places for overflow. Petty cash is what some people call slack,where anything “extra” would go.

Let’s simplify just a little. Let’s say I have that same $400 income, but I can only spend it on two things: coffee and sweaters. Sweaters cost $25 each, and coffee costs $2 per cup. I have a couple of choices – in fact, an infinite number of them – for how I can spend that money. For example, if I want to spend all my money on coffee, I can buy

cups of coffee. If I want to spend all my money on sweaters, I can buy

of them. Of course, there’s no reason to spend all my money on one of those two goods. I can buy any combination, subject to the budget constraint that I don’t create a deficit: that is, that

Think back to when we talked about opportunity cost: if I have the same budget either way, then think about how many cups of coffee I have to give up to get a sweater. There are a couple of ways to do this, but the easiest is to compare the prices: for $25, I get one sweater or 12.5 cups of coffee, so the opportunity cost of one sweater is 12.5 cups of coffee. Similarly, for $2, I get one cup of coffee or 1/12.5 = .08 sweater, so my opportunity cost of buying a cup of coffee is 8% of a sweater. Note that this is the same as dividing the total quantities I can buy:

Basically, we can use a budget constraint to determine opportunity costs by imagining that we spend our entire budget on each of two goods and then comparing the quantities, or simply by comparing prices. Opportunity costs represent budgeting decisions on a much smaller – some might say marginal – scale.

The standard example goes like this: I like books, so I want to turn my passion into a job and open a bookstore. To do so, I need to rent a storefront and buy some inventory; for now, I’m going to run the bookstore myself. I’ll be open eight hours a day, so I’ll quit my current job at the box factory and do the bookstore job instead. Easy peasy, right? I even have $100,000 in the bank to get myself started.

Let’s look at the costs. The first thing to consider is the actual money I’m laying down to run this business. Say rent is $1,000 per month. If I don’t want to bother with discounting – and for now, I don’t – then that means I’ve spent $1,000 x 12 = $12,000 on rent this year. Then, imagine that in order to meet demand and still have a decent inventory, I need to spend $43,000 on books. That brings me up to $55,000 worth of cash that I’m laying out – my explicit costs, otherwise known as accounting costs, are $55,000.

But accounting costs don’t show that I had to give up my job at the box factory to do this, and I could have made $45,000. They also don’t account for the interest income I’m giving up by pulling my money out of the bank to live on it. Even if interest rates are only 1.25 APR (that’s annual percentage rate), I’m losing $1,250 in interest income. So, for simplicity (I don’t want to bother with compounding, either), let’s assume that in January I take out this year’s $45,000 in salary and keep it under my mattress. I buy my inventory and pay my rent. I’ve given up $1,250 in interest income and $45,000 in salary, so even though I haven’t laid out that cash, I have to count it as a cost. Accountants won’t write down what I gave up on a balance sheet, but my implicit costs, or opportunity costs, are $46,250.

Total costs are simple – just add implicit and explicit costs. My total costs for starting the business are $55,000 + $46,250 = $101,250.

The key to understanding opportunity cost is that it’s a measure of what you gave up to make a choice, and so it shows how much something is worth to you. If I offer you a free Pepsi, your opportunity cost is zero, so you might as well take it. If I offer you a Pepsi for your Dr. Pepper, we can infer two things:

1. I value Dr. Pepper at least as much as Pepsi, and
2. I can figure out how much you value Dr. Pepper, relatively, based on your decision. If you accept, then you must value Pepsi at least as much as Dr. Pepper; if not, you must value Dr. Pepper more (and would thus be rational, since Dr. Pepper is superior to Pepsi).

Opportunity cost is very useful for determining preferences. We’ll talk about that a little more later on. In the meantime, just remember this distinction:

• Explicit costs are things you paid money for
• Opportunity costs are how much you’d value your best alternative
• Total costs are the sum of explicit and opportunity costs.

In 1999, the Mets owed outfielder/first baseman Bobby Bonilla $5.9 million dollars. They wanted to be rid of Bonilla, who was a bit of a schmoe, but they couldn’t afford to both give him his $5.9 million in the form of a buyout and meet payroll for the next year. No problem! The Mets sat down with Bonilla and arranged a three-part deal:

1. The Mets don’t have to pay Bonilla until 2011.
2. Starting in 2011, Bonilla will receive the value of the $5.9 million as an annuity in 25 annual installments.
3. The interest rate is 8%.

Let’s analyze the issues here.

First of all, the ten-year moratorium on payment means that the Mets have use of the money, but they can treat it as a deposit account. They know they need to pay Bonilla a certain amount in 2011, but they can do whatever they want until then. In their case, they used it to pay free agents and other payroll expenses. In exchange for not collecting money he was owed, Bonilla asked the Mets to pay him a premium on his money. At the time, the prime rate was 8.5%, so the Mets agreed to pay Bonilla 8% annual interest on his money. That means that Bonilla’s money earned compound interest annually. After one year, his $5.9 million was worth (5,900,000)*(1.08) = $6,372,000. Then, in the second year, he earned 8% interest on the whole $6,372,000, so after two years, his money was worth (6,372,000)*(1.08) = (5,900,000)*(1.08)*(1.08) = $6,881,760. Consequently, after ten years, Bonilla’s money was worth

The prime rate didn’t stay at 8.5%, of course, as the Federal Reserve Economic Data (FRED) webpage maintained by the St. Louis Fed shows. This is a monthly time series of prime rates, which are graphed to the right. The prime rate  can be pretty volatile, so it was a bit of an odd choice to lock in a rate that would be effective for 35 years. As it turns out, the prime rate fluctuated quite a bit. Taking the annualized prime rate by dividing each monthly rate by 12 and adding them together, we can trace how much a bank account paying the full prime rate would have paid Bonilla:

So since his agreement with the Mets paid him $12,737,657.48 and he could have invested that money by himself to earn around $10,891,903.26, Bonilla is already better off to the tune of (12737657.48 – 10891903.26) or about 1.85 million.

In addition, we can measure the purchasing power of Bonilla’s money. Using FRED’s Consumer Price Index data, the CPI on January 1, 2000, was 169.3. On January 1, 2011, it was 221.062. that means the change in CPI was

So, the cost of living went up (for urban consumers) by 30.57% (or, equivalently, absolute inflation was 30.57% for an annualized rate of around 3%). That means that if the value of Bonilla’s money earned a real return of 30.57% or more, he’s better off than he would have been had he taken the money at the time.

Bonilla’s money increased by

Bonilla’s money overshot inflation considerably – not surprising, since inflation generally runs around 3-4%. That means that if Real return = Nominal return – Inflation, Bonilla’s return was

Because Bonilla’s interest rate was so high, he earned quite a bit of real return on his money – 85% or so over ten years.

Bonilla’s annuity agreement just means that the amount of money he holds now will be invested and he’ll receive a certain number of yearly payments – here, 25 – of an equal amount that will exhaust the value of the money. The same 8% interest rate, which is laughable now that the prime rate is 3.25%, is in play.

In general, an annuity can be expressed using a couple of parameters. Assuming you don’t want any money left over, you can set the present value equal to the sum of the discounted series of payments. That equates to the formula:

where PV is the present value of the annuity, PMT is the yearly payment, r is the effective interest rate, and t is the number of payments. Bonilla will receive $1,193,248.20 every year for 25 years from the Mets. It’s a nice little income stream for him, and barring a major change in interest rates, it’s one he couldn’t have done by himself.

Equilibrium has a connotation of balance. The idea is that two (or more) things need to be balanced for some definition of balance that makes sense in the discussion. In economics, we generally think of equilibrium as representing a point where everything that’s produced is consumed. In a market for an individual good, that means we need to find a point where enough of those goods are produced so that everyone who wants to buy a good can do so.

That’s not very exact, though – it’s very rare that we see a goods market where everyone who wants the good can get it. There has to be some sort of incentive for the item to be produced, and generally that isn’t the satisfaction of seeing people using your trinket. (Sometimes it is – for example, the satisfaction of producing this blog and the fact that it forces me to think clearly are incentives for me to produce.) In general, that incentive is a price for the good – by producing, you get the opportunity to sell the good and get some money in exchange. That also provides a mechanism by which people self-select whether or not they participate in the market – at a certain price, people are willing to buy if they value the product at least that much. If the price is too high, they might still want the item, but they aren’t willing to pay for it so they’re no worse off.

How does that generalize to a macroeconomy, where we’re concerned about lots of goods and lots of prices? Well, it can be difficult to do so. That’s part of what makes grad macro so difficult. We, however, are going to make a couple of simplifying assumptions.

First of all, think back to the idea of the GDP Factory, where everyone works. Instead of producing individual goods, imagine that everyone just produces Stuff. The Stuff goes out on the market and is sold for money, the money is used to pay workers, and the workers go back to work and produce more Stuff. So, we can think of all goods as being part of the larger concept of production. So, everything we produce is supplied to the market. Remember that the supply equation is

where is Stuff supplied, A is technological knowledge, K is capital, H is human capital, N is natural resources, and L is labor.

Then, remember that all the Stuff we produce has to be bought, stored in inventory, or exported, so our demand equation is

where is Stuff demanded, C is consumption, I is investment, G is government spending, and NX is Stuff exported less Stuff imported.

In order to find an equilibrium, we need to make another pair of assumptions:

• The more you can sell for, the more you want to produce.
• The more goods cost, the less you’ll want to buy.¹

Since we’re simplifying away from individual goods, instead of a price, think about the price level of the economy as a whole (which we’ll abbreviate as PL). Also since we’re not thinking too much about individual goods, we don’t have to worry too much about changes in relative prices. (We can talk about those a little bit later.) So, basically, we’re looking at things statically – we don’t need to figure out what happens if coffee’s price goes up more than tea, for example.

The price level determines, on average, how much Stuff sells for. As the price level increases, we’ll produce more. As the price level decreases, we’ll buy less. There’s just one more condition we need to allow an equilibrium:

• At 0 production, we need an incentive to produce more. So, at 0 production, demand is greater than 0 and supply is 0 by definition. At infinite production, demand is less than infinite.

So, these conditions say 2 things: At a low level of production, demand outstrips supply. As the price level increases, we produce more and demand less. These conditions guarantee that there’s a price level at which we’ll want to supply exactly as much as we want to demand – a little bit lower in price and more will be demanded than produced, and a little bit higher and more will be produced than demanded. So, at that price level,

Supply equals demand.

Equilibrium.

¹Mathematically,

To answer that question, think back to how electricity is produced. There’s a small amount of input electricity that’s required to produce any extra electricity, along with natural resources like coal and water to produce steam. It’s possible to recapture some of the electricity produced and use it as input in the next procedure. Note that this doesn’t imply there’s some sort of perpetual motion machine or a finite amount of electricity being used to produce an infinite amount, just that sometimes you need to use a small amount of the final product to prepare more of it. In that case, we could say that the amount of electricity produced is a function of the inputs, which are coal, water, land to produce the plant, and electricity.

In the same way, businesses produce goods and services. There’s a fancy term for production. It’s … production. You can also think of production as real GDP, which is equivalent to the amount of stuff produced in a certain division. Generally GDP will be production within a country over the course of one year.

The input factors for production can be a couple of things. First of all, you need money, but what do you use the money for? Generally, companies use money to buy one of a couple of different things.

• A factory, for example, requires machinery. Even offices need machinery, like copiers and printers. That’s called capital (more properly, physical capital) and (because Marx wrote Das Kapital in German) abbreviated K.
• Any company needs well-trained people who have skills and can operate the machinery or perform services. That’s called human capital and abbreviated H. Human capital is, at the broadest level, synonymous with special skills or (especially) education. It refers to talent or skill, not to the people themselves.
• Companies need to know how to produce whatever it is they produce. This is called technological knowledge and abbreviated with the letter A or occasionally z. Technological knowledge allows everyone to be more productive.
• Companies need natural resources, abbreviated N, to operate their machinery or keep their employees comfortable.
• Finally, companies need people to do the work. This is called labor and abbreviated L.

There are many ways to express this relationship. The broadest is to say that we can put a bunch of machines and raw materials in a room with some laborers, some people who have special talent, and the energy to run them, and the people will produce something. How much they produce is a function of how much of each of those factors of production is available, and then there will be a bonus for extra technological knowledge that represents what level of production our factory was already at. We can express that mathematically, using Y to represent output as usual, as

This represents all of the production of our factory or country. We could, then, figure out how much we’re producing per worker. This has a special name: productivity. We can represent productivity mathematically simply by dividing each factor through by the number of workers (which is the exact plain-sense meaning of “production per worker”):

(This requires an assumption called constant returns to scale, which is in turn related to the assumption that when we produce, we produce at around an optimal point where we’re as efficient as we can be given our current level of technology.)

Basically, we produce goods, which are a form of capital. To do so, we use capital and natural resources, which can be used up, along with technological knowledge, labor, and the special skills and talents we call human capital, none of which are used up. Any economy can continue to grow as long as it continues to operate efficiently. That means, as we mentioned in the Comparative Advantage entry, that a country like the US, which has easy access to capital and human capital, should produce things that make the best use of those factors. China, on the other hand, is best off producing labor-intensive goods. India is spread thin with respect to natural resources but has a lot of labor and a lot of human capital.

The key here is that we may see changes in what a country produces over time, but growth can continue indefinitely, as long as we make good choices about production.

The first question, though, is why would we want to do any international trade at all? Why shouldn’t we – the United States – produce all the goods we need at home instead of sending money outside the country to buy things produced somewhere else?

The first thing to think about is called absolute advantage. In some cases, goods are just cheaper to produce in another country than here. An example might be labor-intensive goods (those are goods produced using more human input than machinery). A lot of clothes purchased in the US are produced in India and Bangladesh, for example, and that makes sense: there are many people, wages are relatively low, and so it’s cheaper to produce goods that can be made by people. On the other hand, the US is more adept at producing capital-intensive goods. An example might be circuitboards, which require a lot of machinery to produce right. It’s easier to substitute people for sewing machines than to substitute them for photoengraving equipment.

However, that ignores some possibilities. If we only took absolute advantage into account, we’d come to the conclusion that a few very smart, very productive nations should do just about everything. Breaking this down to individuals, imagine an economy where there are only two people: a writer and her teenage neighbor. The writer can produce 80 pages of quality material in eight hours and do her dishes in an hour. The teenager can produce 8 pages in eight hours and they aren’t very good, and it takes him two hours to do the dishes. (Not a very productive kid.) If the writer wants a novel, she should do it, and if the writer’s dishes need to be washed, then under the theory of absolute advantage, she should do them, since her absolute cost to do so is lower.

Still, that leaves her with two fewer hours to write, kicking her down to only seven hours and 70 pages. The kid has six pages written and one load of dishes. She’s had to give up 10 pages of production – that’s her opportunity cost, or the best thing she gave up to go mow the lawn. It’d be fair to say that doing the dishes cost her 10 pages of writing. The tally: 76 pages plus two set of dishes (70 + 1 from the writer, and 6 + 1 from the kid).

Suppose instead that the writer negotiates with the kid – she’ll do all his writing, and he’ll do all her dishes. She writes 80 pages. He does two loads of dishes. The total: 80 pages plus two loads of dishes, PLUS the kid has five hours free to put together another five pages of material. We have 85 pages and two loads of dishes. That’s an extra 9 pages. Everyone’s better off.

This is called comparative advantage. The kid isn’t faster than the writer at anything, but his opportunity cost to do a load of dishes – two hours of time – could only produce two pages of writing. The writer’s opportunity cost for a load of dishes is 10 pages. So, since his opportunity cost is lower, the teenager’s comparative advantage is in doing dishes. On the other hand, the opportunity cost to the writer of writing 10 pages is one load of dishes. The opportunity cost to the teenager of writing 10 pages is five loads of dishes. The writer’s opportunity cost is lower, so her comparative advantage is in writing.

You can extend that same idea to two different countries. In some, there are lower opportunity costs to produce goods. It’s correct in a quick and dirty way to say that the opportunity cost of producing labor-intensive goods in the US is higher than in India, and vice versa for capital-intensive goods. Basically, the theory of comparative advantage tells us that even if we have the capability to produce something good, we should allow another country to produce it and then import it if we can produce something better.

Let’s start with a simple premise: Everything that’s produced is purchased by someone. That makes sense in a couple of ways. A household can buy something, another business can buy something, the government can buy something, or… businesses can produce goods and store them for future use. For now, let’s treat this as the business buying its own goods to resell later.

GDP is defined as the market value of all final goods and services produced within a country in a given period of time. If we’re talking about the United States’ GDP for 2010, then it amounts to the prices of everything that was made in the US in 2010. The word ‘final’ means that if one company produces something that’s used as an input for another product, then only the last product counts. That means that some goods, like flour, might be final goods sometimes and intermediate goods other times. If I own a bakery, then I’ll buy a five-pound sack of flour to use in making bread, and so the flour is intermediate (since it’s used to produce another, final good). If I buy flour to make the same loaf of bread at home, then the flour might be used in home production, but since home-produced goods aren’t sold, then the flour is last sold to a consumer, and so it’s a final good. Since a consumer makes the purchase, it’s called Consumption.

Imagine that a box factory produces 600 boxes on December 31, 2010 and then sells them on January 1, 2011. Then, we have a sale of final goods, but the final goods weren’t produced in 2011, so they can’t count toward 2011 GDP. This requires the idea of inventory, which can be defined as goods that are produced but not sold. Inventory sales need to be subtracted from spending when calculating GDP.

Spending by businesses is on two things: intermediate goods (to produce final goods) and capital production (that is, stuff that allows them to be more efficient). All together, we call this spending by businesses Investment, which has a special definition in macroeconomics. Make sure not to confuse ‘investment’ in macro with the idea of putting money in stocks and bonds and hoping it grows. When taking a macro class, ‘investment’ pretty much means ‘spending by businesses.’ Inventory gets subtracted from investment, because it represents using past-produced goods. Those goods would have been counted as GDP in a previous year, so they need to be subtracted now even though a consumer purchased them.

Consumption and business spending aren’t the only things that need to be counted, though. Sometimes a business will produce a good that isn’t bought by a consumer. (I, for example, have never purchased a space shuttle, even though clearly someone’s producing them.) This is why we need to count Government spending.

Everything that’s produced is purchased, as long as we define ‘purchased’ to include ‘stored in inventory,’ and then we can subtract inventory sales from future GDP. Even though someone consumes a good that might have been produced in the previous year, subtracting it as inventory spending allows us to maintain the definition of GDP as ‘everything produced in the US in 2010′ while at the same time having an easy way to calculate it: just add up everything we buy!

This leads directly to the expenditure method for calculating GDP: just add up all the spending by consumers, by businesses, and by the government. In math, the letter Y is often used to represent output, and GDP represents the production (i.e. output) in an economy. So, we can use the formula

where C is consumption spending, I is business spending (including subtracting inventory) and G is government spending. (In an open economy we’d need to account for imports and exports. That will come later.)

These two definitions (“the final market value of all goods and services produced in an economy in a given period of time” and “C + I + G”) are equivalent. In a future post, we’ll talk about how to put that to use.

One way to measure inflation is just by calculating the change in CPI. The percentage change in CPI – – can be calculated by figuring the year you’re interested in as the base year and then just subtracting 100 from the current CPI. However, if you’re using other data where the base year is already calculated (such as from FRED), you can use the regular percentage change formula:

However, the nature of the CPI leads to a few problems. They stem from the use of the basket of goods, which has to stay constant from one year to another in order for the comparisons to be meaningful. That means that whatever we decide to use as the basket of goods in 2007 has to be what we calculate the value of in 2011. There are some immediate problems that come to mind.

First, think about the changes in relative prices of goods to each other. Let’s say the basket contains a pound of flank steak. A lot of people use that as the filling for tacos, so a substitute good might be roast pork. If those goods are around the same price, people are indifferent between them. What if the price of pork increases a little, but the price of flank doubles? In that case, a lot of people will stop buying flank steak and switch over to pork instead. The basket doesn’t reflect this, though, so the CPI will rise a lot more than the relative cost of living does, so the CPI doesn’t really accurately reflect the change in the cost of buying what a typical household buys. This is called substitution bias.

Second, I’m addicted to my iPad. When the current basket was created in 2007, it didn’t exist. Now, it’s practically a requirement for a grad student. The basket can’t account for the introduction of new goods like this, since in order for it to be a useful comparison, the basket has to stay the same from year to year.

Finally, I think it’s fair to say that some goods are getting more durable. An iPod Touch, for example, lasts longer than it did when it was introduced in 2007. It offers more features than it used to (such as voice control and a camera). Even if prices had stayed the same,  fourth-generation Touch is worth far more than a first-generation Touch. The same expenditure generates a lot more happiness, and so the quality of goods isn’t accounted for in the CPI.

CPI isn’t a perfect measure of inflation or the cost of living, but it’s a common and important one. Know how to calculate it, and know its shortcomings.

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

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:

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