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The Good and Bad of Goods and Bads January 25, 2015

Posted by tomflesher in Micro, Teaching, Uncategorized.
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When students first hear the word “goods” pertaining to economic goods, they sometimes find it a little funny. When they hear some sorts of goods called “bads,” they usually find it ridiculous. Let’s talk a little about what those words mean and how they pertain to preferences.

Goods are called that because, well, they’re good. Typically, a person who doesn’t have a good would, if given the choice, want it. Examples of goods might be cars, TVs, iPads, or colored chalk. Since people want this good if they don’t have it, they’d be willing to pay for it. Consequently, goods have positive prices.

That doesn’t mean that everyone wants as much of any good as they could possibly have. When purchasing, people consider the price of a good – that is, how much money they would have to spend to obtain that good. However, that’s not because money has any particular value. It’s because money can be exchanged for goods and services, but you can only spend money once, meaning that buying one good means giving up the chance to buy a different one.

Bads are called that because they’re not good. A bad is something you might be willing to pay someone to get rid of for you, like a ton of pollution, a load of trash, a punch in the face, or Taylor Swift. Because you would pay not to have the bad, bads can be modeled as goods with negative prices.

Typically, a demand curve slopes downward because of the negative relationship between price and quantity. This is true for goods – as price increases, people face an increasing opportunity cost to consume one more of a good. If goods are being given away for free, people will consume a lot of them, but as the price rises the tradeoff increases as well. Bads, on the other hand, act a bit different. If free disposal of trash is an option, most people will not keep much trash at all in their apartments. However, as the cost of trash disposal (the “negative price”) rises, people will hold on to trash longer and longer to avoid paying the cost. Consider how often you’d take your trash to the curb if you had to pay $50 for every trip! You might also look to substitutes for disposal, like reusing glass bottles or newspaper in different ways, to lower the overall amount of trash you had to pay to dispose of.

As the cost to eliminate bads increases, people will suffer through a higher quantity, so as the price of disposal increases, the quantity accepted will also increase.

Perfectly Competitive Markets December 10, 2012

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When solving economic problems, the type of firm you’re dealing with can lead you to use different techniques to figure out the firm’s rational choice of action. This week, I’ll set up a thumbnail sketch of how to solve different firms’ types of problems, since a common exam question in intermediate microeconomics is to set up a firm’s production function and ask a series of different questions. The important thing to remember about all types of markets is that every economic agent is optimizing something.

In a perfectly competitive market, three conditions hold:

  • All goods are identical. If the seller is selling apples, then all apples are the same – there are no MacIntosh apples, no Red Delicious apples, just apples.
  • There are lots of sellers, so sellers can’t price-fix because there will always be another seller who will undercut.
  • There are lots of buyers, so a buyer boycotting won’t make a difference.

The last two conditions sum up together to mean that no one has any market power. That means, essentially, that no action an individual buyer or seller takes can affect the price of the goods. If ANY of these conditions isn’t true, then we’re not dealing with a perfectly competitive market – it might be a monopoly or a monopsony, or it might be possible to price-discriminate, but you’ll have to do a bit more to find an equilibrium.

Speaking of that, an equilibrium in microeconomics happens when we find a price where buyers are willing to buy exactly as much as sellers are willing to sell. Mathematically, an equilibrium price is a price such that QS(P) = QD(P), where QS is the quantity supplied, QD is the quantity demanded, and the (P) means that the quantities depend on the price P. Since the quantity is the same, economists sometimes call an equilibrium quantity Q* and the equilibrium price P*.

Consumers are optimizing their utility, or happiness. This might be represented using something called a utility function, or it might be aggregated and presented as a market demand function where the quantity demanded by everyone in the world is decided as a function of the price of the good. A common demand function would look like this:

QD(P) = 100 – 2*P

That means if the price is $0, there are 100 people willing to buy one good each; at a price of $1, there are (100 – 2*1) = 98 people willing to buy one good each; and so on, until no one is willing to buy if the price is $50. Demand curves slope downward because as price goes up, demand goes down. Essentially, a demand function allows us to ignore the consumer optimization step. Demand represents the marginal buyer’s willingness to pay; price equalling willingness to pay is something to remember.

Firms optimize profit, which is defined as Total revenue, minus total costs. If we have a firm’s costs, we can figure out how much they’d need to charge to break even on each sale. Let’s say that it costs a firm $39 to produce a each good. They won’t produce at all until they’ll at least break even – or, until their marginal benefit is at least equal to their marginal cost, at which point they’ll be indifferent. Then, as the price rises above $39, charging more will lead to more profit. Even if the firm’s marginal cost changes as they produce more unity, the price of the marginal unit will need to be at least as much as the marginal cost for that unit. Otherwise, selling it wouldn’t make sense.

The first condition to remember when solving microeconomics problems is that in a perfectly competitive market, a firm will set Price equal to Marginal Cost. If you have price and a marginal cost function, you can find the equilibrium quantity. If you have supply and demand functions, set QS(P) = QD(P) and solve for the price, or simply graph the functions and figure out where they meet.

When is a filibuster not a filibuster? December 7, 2012

Posted by tomflesher in Micro, Models, Teaching.
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A filibuster is a legislative technique where a lawmaker who is in the minority will block passage of the bill. Historically, that required talking continuously on the legislature floor, as that would prevent anyone else from doing anything. In the US Senate, a bill can be filibustered simply by declaring it so – the filibustering Senator doesn’t actually need to talk. The Senate is considering a rule change to move back to historical, “talking” filibusters. In either case, a filibuster can be broken by a 60-vote supermajority (called cloture), but a talking filibuster can also be broken by the filibustering Senator getting tired and quitting. What’s the economic difference between these two rules?

The fact is that talking imposes an extra cost on the filibustering party. When people are

The model:1

First, like all good economists, let’s make some simplifying assumptions. Say there are two parties, the Bears and the Bulls, and that there are 59 Bears and 41 Bulls. Assume that everyone votes strictly along party lines, so every vote comes out in favor of the Bears 59-41. That’s not enough for a 60% majority, so under the current system, the Bulls can filibuster every bill without stopping other legislation.

Parties aim to maximize their political capital, which is generated in two ways:

  • Passing bills. The more partisan a bill is, the more capital is generated. A bill that the entire country would agree to pass has zero partisanship; a bill only Bears would vote for has a very high partisanship. The minority party generates goodwill based on voting for bills, but it decreases when the bills are more partisan.
  • Public perception (goodwill). Filibustering leads to a negative public perception. This is directly related to how partisan a bill is – filibustering a totally nonpartisan bill (discount bus fares for war widows) would lead to a highly negative perception, but filibustering a very contentious bill would be offset. Similarly, a filibuster stops all business, so the longer it goes on, the angrier people get.

The Bulls’ capital generation would look like this, with the “talking filibuster” term last, P=Partisanship and D = Days spent filibustering:

C = - P^2+ 41*P - \frac{1}{P}*D^2

Under the current system, days spent filibustering is 0, since nobody actually has to filibuster. That is, the marginal cost of filibustering a bill is 0. If a bill passes, the Bulls generate 41 political capital per unit of partisanship for voting, but lose some capital for losing the vote. If a bill has Partisanship of 20.5, then the Bulls are indifferent between filibustering and allowing the vote; anything more partisan will definitely be filibustered, and anything less partisan will be voted on.

If talking filibusters are required, though, the whole thing gets much more complicated. Adding a marginal cost for being on TV filibustering makes the minority party far less likely to filibuster. The marginal political capital generated for filibustering for one day is

MCapital = -2*P + 41 + \frac{1}{P^2}

The Bulls are indifferent between filibustering and allowing the vote when Partisanship is about 20.5012. That’s just what we’d expect – that it takes a more contentious bill to justify a talking filibuster than a silent filibuster. Then, let’s take a look at a two-day filibuster:

MCapital = -2*P + 41 + \frac{4}{P^2}

A slightly longer filibuster requires a slightly more controversial bill, requiring Partisanship to be 20.5048. Finally, let’s take a look at a 90-day (3-month) filibuster:

MCapital = -2*P + 41 + \frac{8100}{P^2}

That would require a bill of partisanship 26.338. The model displays the expected features: that it takes a more contentious bill to merit a filibuster at all, and longer filibusters require much more contentious bills. If we raise the costs of doing something, it becomes used less often.

Note:
1 As far as I know, this isn’t stolen from anyone, but if it’s similar to one currently in the literature please let me know so I can do some reading and properly credit the inventor.

It’s For The Public Good December 6, 2012

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There are several types of goods in economics: private goods, public goods, club goods, and common goods. What defines which category a good will fall into?

The category can be determined knowing two things: Is the good rival? Is it excludable?

If a good is rival, one person using it prevents someone else from using it. This is a bit of a weird concept, since air can only be breathed by one person at a time, but air is so abundant as to be nonrival. Air in a SCUBA tank, though, would be rival, since only one person can breathe from it at a time. If a good is excludable, you can prevent someone from using the good if you don’t want them to. My apartment is excludable because I have a lock on the door.

Private goods are rival and excludable. Just about anything you can think of going to a store and buying is a private good. My TI-36X Pro calculator is rival (if you’re using it, I can’t) and it’s excludable (if I don’t want you to use it, I’ll just put it in my pocket). Private goods have some interesting properties and merit further discussion.

Public goods are defined as goods that are nonrival and nonexcludable. The classic example of a public good is military defense. If the Army exists and prevents other countries from invading the United States, then there’s no way to keep me from benefiting from that defense that doesn’t also prevent someone else (e.g., my no-good brother) from benefiting (so defense is nonexcludable). Similarly, defending the United States is nonrival because the fact that I’m defended doesn’t have any effect on how defended someone else is. I don’t use up military defense, so it doesn’t (in the simplest case) cost anything to defend my neighbor if I’m already being defended.

Club goods are excludable but nonrival. My landlord’s wireless internet connection is a club good. It’s excludable, because there’s a password on it; it’s nonrival, though, because up to a certain point it doesn’t matter how many people are connected to the network. My enjoyment of the internet doesn’t depend on whether my wife is online or not. (It would take a whole bunch of people, enough to cause congestion, to make my internet too slow to use.)

Common goods are pretty interesting, because there’s an intuitive concept called the tragedy of the commons. Common goods are rival, but nonexcludable. The classic example here is a meadow where you graze your sheep. Every one of us can use the meadow, since it’s public property, but if I graze my sheep here, they eat some of the grass and there’s less for your sheep. It’s in both of our interests  to conserve the meadow, but it’s also in both of our interests to cheat and consume as much as we want to. Common goods tend to get used up.

What goods seem to straddle the line between two of these categories, and how do you think that confusion can be resolved?

Scribbling in the Margins December 5, 2012

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3. Rational people think at the margin.

That’s one of Mankiw’s Ten Principles of Economics. (#3, in fact). What does it mean?

The usual definition of “marginal” is “additional.” In other words, the marginal cost of something is the cost of buying another one. So, we can rephrase Number Three as “Rational people think about the next one of whatever it is they’re thinking about.” We can also think about marginal benefits.

How much would you pay for a Dove Dark Chocolate bar?1 Whatever your answer, that’s the benefit that a Dove bar affords you. Currently, I have zero Dove bars, so the first Dove bar I bought would give me a benefit. Economists measure benefit in two ways: either in utility, which is an abstract concept of “happiness points,” or in dollars, which are, well, dollars. If I’d pay $1.50 for a Dove bar, then my marginal benefit for a Dove bar is $1.50. Because this sounds simple, economists sometimes make this sound more complicated by calling it money-metric utility.

After I eat the first Dove bar, I really wouldn’t want another 0ne – at least, not as much as the first. I’m willing to pay $1.50 for the first one, but $1.50 would be too much for the second. I might buy two if they’re on special for two for $2.50, but I wouldn’t pay much more than that. That means I value the second Dove bar at $1.00, or the benefit I’d get from two bars minus the benefit I’d get from one bar.2 This is pretty normal – marginal benefits, or marginal utility, is decreasing in quantity for most goods. That’s just a fancy way of saying that the second one isn’t as good as the first, and the third isn’t as good as the second. The technical term for that is diminishing marginal returns.

The marginal cost is just the cost of the additional bar. Usually, stores have one price per bar, no matter how many you buy. My local grocery store sells Dove Bars for $1.25 each. Since I’d pay $1.50 for that bar, I’d buy it, and I’d be better off to the tune of $0.25 because I got $1.50 worth of utility for only $1.25. (Economists call that $0.25 consumer surplus.)

Should I buy the second one?

If you make the decision all at once, you’d say that I value two bars at $2.50, so why not? Here’s the problem: that gives me a total benefit of $2.50 at a total cost of $2.50, for a consumer surplus of $0. If I buy the first bar, I get a consumer surplus of $0.25. Buying the second bar amounts to paying $1.25 for something I only value at $1, so I’d get a consumer surplus of -$0.25. Thinking at the margin allows me to spend that last $1 on something I actually value that much.

The fundamental criterion for making decisions in economics: do something  only if its Marginal Benefit is at least as much as its Marginal Cost. In other words, don’t buy something unless you’re at least breaking even.

Note:
1 Okay, that’s a 24-pack. How much would you pay for a 24-pack? Probably not more than 24-times-your-valuation. But we’ll chat about that later.
2 Mathematically, marginal benefit is defined as \frac{\Delta(Benefit)}{\Delta(Quantity)} , with Δ meaning “change.” Here, the change in benefit is $1.00 and the change in quantity is 1.

Really Interesting (Or Nominally Interesting, At Least) December 4, 2012

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Interest rates describe how much money you’ll have at the end of a year if you lend to someone. Mostly, you “lend” money to a bank by putting it in a savings account, but you might lend to the government by buying Treasury bonds or to your no-good brother by floating him $100. Currently, my bank pays 0.01%, although some commercial money market accounts pay around 1%; Treasuries pay about 0.18% for one-year bonds; my brother is currently paying me 10% (and the Mets are paying Bobby Bonilla 8%). Why the differences?

Borrowers need to pay the lender for two things: giving up the right to use his money for a year, and the risk that he won’t get his money back. The first element is pretty important for the lender: Patient Patricia will take a lower interest rate because she doesn’t need to buy stuff today – she’s willing to wait, especially if she can make a little money for waiting. On the other hand, Antsy Andrew wants to head right out and buy stuff, so asking him to wait a year for his stuff will cost a lot of money. Plus, I know there’s some inflation most years, so my brother will have to at least cover that.

That explains part of the difference between interest rates. A Treasury bond takes your money and keeps it for a full year, but my bank’s savings account allows me to withdraw my money at will. I’m not giving up much use of my money, so I don’t need to be paid much. When the Mets paid Bobby Bonilla 8% interest, they expected high inflation, when inflation turned out to be low.

It’s also really likely that, when I go to cash in my bond or take out my ATM card, the money’s going to be there. The government’s not going bankrupt1 and my bank deposits are insured. My no-good brother, though, might lose his job tomorrow. He’ll probably have the money to pay me, but he might not. That worries me, and I want him to pay for making me nervous. (In the real world, this also means I’ll get more money up front in an installment payment plan.)

That boils down to an important identity known as the Fisher Effect:

Nominal interest ≈ Real return + Expected inflation

When I expect inflation, that affects how much I’d rather have money now than later. My real return is how much I have to get from my no-good brother to compensate me for the risk that I’ll lose all my money. We can estimate inflation as being nearly zero today, so real returns (compensating for risk) explain almost all of the variation in interest rates.

But what about those banks paying 1%, when other banks (and the government) are paying much less? Banks need to hold reserves. A bank that’s nervous about how much money it has on hand will be willing to pay higher rates in order to get more deposits – in other words, if you need it, you’ll pay for it.

Note:

1 Okay, it might go bankrupt, but it’s reeeeaaaally unlikely to happen this month.

Increases in CPI: Good or bad? January 30, 2012

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One of the nice things about WordPress is that I get a nice summary of the search engine terms that led people to my page. Bobby Bonilla is popular, as always – it’s nice to know that people are curious about him – but another common way people end up on my blog is by looking for pros and cons of the Consumer Price Index. One searcher this week asked:

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.

Comparative Advantage April 8, 2011

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So far, we’ve done a lot of discussion of macroeconomics where the economy is closed – that is, we assume all trade takes place in the country, or, in plain terms, there’s no importing and no exporting. Now, we can extend that idea into allowing international trade.

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.

What’s so Gross about the Domestic Product? March 17, 2011

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The Gross Domestic Product (GDP) is one of the fundamental ideas of introductory macroeconomics. That’s because GDP is the core of one of the best ways to measure citizens’ well-being. We’ll get to that in a future post, though. For now, let’s talk about what GDP measures, and pretend that we’re not going to allow international trade. That makes this a closed economy model.

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

Y = C + I + G

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.

Shortcomings of CPI March 14, 2011

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In the previous post, we talked about the Consumer Price Index (CPI). Basically, the CPI is a number that indicates how much the price of a basket of goods purchased by the typical consumer has changed since a base year we choose when we calculate it. To review, in the base year, CPI is always 100, and in other years a number greater than 100 indicates that prices are higher than the base year while a number less than 100 indicates that the price level is lower than the base year.

One way to measure inflation is just by calculating the change in CPI. The percentage change in CPI – \% \Delta 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:

\%\Delta CPI = \frac{CPI_{current} - CPI_{base}}{CPI_{base}}

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.