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It’s For The Public Good December 6, 2012

Posted by tomflesher in Micro, Teaching.
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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

Posted by tomflesher in Finance, Teaching.
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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

Posted by tomflesher in Macro, Teaching.
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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.

Budgets and Opportunity Cost January 19, 2012

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In the previous entry, we talked a little about opportunity cost. In short, it’s what someone gives up in order to acquire something else. What does that have to do with budgeting?

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

\frac{400}{2} = 200

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

\frac{400}{25} = 16

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

2*(cups\:of\:coffee) + 25*(sweaters) \le 400

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:

16\:sweaters = 200\:cups

1\:sweater = \frac{200}{16}\:cups

1\:cup = \frac{16}{200}\:sweaters

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.

Opportunities and What They Cost December 23, 2011

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One of the fundamental concepts in economics is that of opportunity cost. In order to understand opportunity cost, though, we need to take a step back and think about costs in a more general way.

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.

Bobby Bonilla’s Deferred Deal: A Case Study August 2, 2011

Posted by tomflesher in Finance, Macro, Teaching.
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Note: This is something of a cross-post from The World’s Worst Sports Blog.  The data used are the same, but I’m focusing on different ideas here.

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

5,900,000 \times (1.08)^{10} = 12,737,657.48

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:

\begin{tabular}{c||cc}  Year& Annualized interest rate & Current Value \\  \hline  2000& 0.09233 & 6444766.67 \\  2001& 0.06922 & 6890851.93 \\  2002& 0.04675 & 7212999.26 \\  2003& 0.04123 & 7510355.16 \\  2004& 0.04342 & 7836429.74 \\  2005& 0.06187 & 8321243.53 \\  2006& 0.08133 & 8998038.00 \\  2007& 0.08050 & 9722380.06 \\  2008& 0.05088 & 10217006.15 \\  2009& 0.03250 & 10549058.85 \\  2010& 0.03250 & 10891903.26 \\  \end{tabular}

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

\frac{221.062 - 169.300}{169.300} \times 100 = 30.57 \%

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

\frac{12,737,657.48 - 5,900,000}{5,900,000} \times 100 = 115.89 \%

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

115.89 - 30.57 = 85.32 \%

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:

PV = PMT \times [\frac{1 - \frac{1}{(1 + r)^t}}{r}] \\  12737657.48 = PMT \times [\frac{1 - \frac{1}{(1.08)^25}}{.08}] \\  PMT = 1193248.20

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 in Macroeconomics April 22, 2011

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One of the things macroeconomists focus on quite a bit is calculating equilibrium conditions, or equilibria. Sometimes these account for random shocks or long-term growth – these have names like Dynamic stochastic general equilibrium and they’re outside the scope of this blog, which has so far focused on introductory-level material. We’re going to develop an idea of what an equilibrium is supposed to be and show how to figure out an equilibrium in a simple, open macroeconomy.

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

Y^S = A \times f(K,H,N,L)

where Y^S 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

Y^D = C + I + G + NX

where Y^D 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,

Y^D = Y^S

Supply equals demand.

Equilibrium.

1Mathematically,

\frac{\partial Y^D}{\partial PL} > 0
\frac{\partial Y^S}{\partial PL} < 0

Don’t Make A Production About GDP April 11, 2011

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I’ve often heard people complain that economics growth models assume that the economy can grow infinitely. Some of these arguments sound plausible – what happens when we run out of resources? – but others seem to fall into the fallacy that wealth exists and is spread around, rather than created. The title of this post – Where does growth come from? – might well be restated as, “How is wealth created?”

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

Y = A \times F(K, H, N, L)

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”):

\frac{Y}{L} = A \times F(\frac{K}{L}, \frac{H}{L}, \frac{N}{L}, 1)

(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.

Comparative Advantage April 8, 2011

Posted by tomflesher in Macro, Teaching.
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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.