## The Good and Bad of Goods and BadsJanuary 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. ## Don’t Discount the Importance of PatienceApril 9, 2013 Posted by tomflesher in Micro, Teaching. Tags: , , add a comment Uncertainty is one explanation for why interest rates vary. Tolerance for uncertainty is called risk aversion, and it can be pretty complicated. (We’ll talk about it a little bit later on.) Another big concept is patience. Willingness to wait is also pretty complicated, but that’s our topic for today. It’s easy to imagine some reasons that people would have different levels of patience. For one, you’d expect a healthy thirty-year-old (named Jim) to be more patient than a ninety-year-old (named Methuselah). What if someone (named Peter) offered us a choice between$100 today or a larger amount of money a year from now? How much would it take for Jim and Methuselah to take the delayed payoff? Would they take $100 a year from now? A lot can change in a year: • There could be a whole bunch of inflation, and the$100 will be worth less next year than it is now. Boom, we’ve lost.
• We could put the money in the bank and earn a few basis points of interest. Boom, we’ve lost.
• We could die and not be able to pick up the money. Boom, we’ve lost.
• Peter could die and we wouldn’t be able to collect. Boom, we’ve lost.

Based on these, we’ll want a little bit more money next year than this year in order to be willing to take the money later instead of the money now. Statistically, though, Jim is more likely than Methuselah to be there to pick up the money.

Neither would take any less than $100 next year, but that’s just a lower limit. According to Bankrate.com, Discover Bank is paying 0.8% APY, which means that the$100 would be worth .8% more next year – just by putting the money in the bank, we can trade the risk that the bank goes bust (really unlikely) for the risk of Peter dying. That’s an improvement in risk and an improvement in payoff, so there’s no reason to take any less than $100.80. Again, though, this is a lower bound. Peter still has to pay for making them wait. That’s where the third point comes into play. Methuselah is probably not going to live another year. It’s much more likely that he’ll get to spend the$100 than whatever he gets in a year; in order to make it worth the wait, the payoff would have to be huge. Methuselah views money later as worth a lot less than money today. He might need $200 to make it worth the wait. Jim, on the other hand, might only need$125. He has more time, so he’s much more patient.

This level of patience is called a discount rate and is usually called β. You can do this sort of experiment to figure out someone’s patience level. You’d then be able to set up an equation like this, where the benefit is the $100 and the cost is what you give up later: $100 = \beta \times Payoff$ Methuselah, then, would have $100 = \beta \times 200$ so β = 1/2. Jim would have the following equation: $100 = \beta \times 125$ so β = 4/5. Based on this, we can say that Methuselah values money one year from now at 50% of its current value, but Jim values money one year from now at 80% of its current value. Everyone’s discount rate is going to be a little bit different, and different discount rates can lead people to make different choices. If Peter offers$100 today or $150 tomorrow, Jim will wait patiently for$150. Methuselah will jump at the $100 today. Both of them are rational even though their choices are different. ## Evaluating Different Market StructuresDecember 13, 2012 Posted by tomflesher in Micro, Teaching. Tags: , , , , , , , , , , add a comment Market structures, like perfect competition, monopoly, and Cournot competition have different implications for the consumer and the firm. Measuring the differences can be very informative, but first we have to understand how to do it. Measuring the firm’s welfare is fairly simple. Most of the time we’re thinking about firms, what we’re thinking about will be their profit. A business’s profit function is always of the form Profit = Total Revenue – Total Costs Total revenue is the total money a firm takes in. In a simple one-good market, this is just the number of goods sold (the quantity) times the amount charged for each good (the price). Marginal revenue represents how much extra money will be taken in for producing another unit. Total costs need to take into account two pieces: the fixed cost, which represents things the firm cannot avoid paying in the short term (like rent and bills that are already due) and the variable cost, which is the cost of producing each unit. If a firm has a constant variable cost then the cost of producing the third item is the same as the cost of producing the 1000th; in other words, constant variable costs imply a constant marginal cost as well. If marginal cost is falling, then there’s efficiency in producing more goods; if it’s rising, then each unit is more expensive than the last. The marginal cost is the derivative of the variable cost, but it can also be figured out by looking at the change in cost from one unit to the next. Measuring the consumer’s welfare is a bit more difficult. We need to take all of the goods sold and meausre how much more people were willing to pay than they actually did. To do that we’ll need a consumer demand function, which represents the marginal buyer’s willingness to pay (that is, what the price would have to be to get one more person to buy the good). Let’s say the market demand is governed by the function QD = 250 – 2P That is, at a price of$0, 250 people will line up to buy the good. At a price of $125, no one wants the good (QD = 0). In between, quantity demanded is positive. We’ll also need to know what price is actually charged. Let’s try it with a few different prices, but we’ll always use the following format1: Consumer Surplus = (1/2)*(pmax – pactual)*QD where pmax is the price where 0 units would be sold and QD is the quantity demanded at the actual price. In our example, that’s 125. Let’s say that we set a price of$125. Then, no goods are demanded, and anything times 0 is 0.

What about $120? At that price, the quantity demanded is (250 – 240) or 10; the price difference is (125 – 120) or 5; half of 5*10 is 25, so that’s the consumer surplus. That means that the people who bought those 10 units were willing to pay$25 more, in total, than they actually had to pay.2

Finally, at a price of $50, 100 units are demanded; the total consumer surplus is (1/2)(75)(100) or 1875. Whenever the number of firms goes up, the price decreases, and quantity increases. When quantity increases or when price decreases, all else equal, consumer surplus will go up; consequently, more firms in competition are better for the consumer. Note: 1 Does this remind you of the formula for the area of a triangle? Yes. Yes it does. 2 If you add up each person’s willingness to pay and subtract 120 from each, you’ll underestimate this slightly. That’s because it ignores the slope between points, meaning that there’s a bit of in-between willingness to pay necessary to make the curve a bit smoother. Breaking this up into 100 buyers instead of 10 would lead to a closer approximation, and 1000 instead of 100 even closer. This is known mathematically as taking limits. ## Duopoly and Cournot EquilibriumDecember 12, 2012 Posted by tomflesher in Micro, Teaching. Tags: , , , , add a comment A few days ago, we discussed perfectly competitive markets; yesterday, we talked about monopolistic markets. Now, let’s expand into a case in between – a duopolistic, or two-seller, market. This is usually called a Cournot problem, after the economist who invented it. We’ll maintain the assumption of identical goods, so that consumers won’t be loyal to one company or the other. We’ll also assume that each company has the same costs, so we’re looking at identical firms as well. Finally, assume that there are a lot of buyers, so the firms face a market demand of, let’s say, QD(P) = 500 – 2P, so P = 250 – QD(P)/2. Since the firms are producing the same goods, then QS(P) = q1(P) + q2(P). Neither firm knows what the other is doing, but each firm knows the other is identical to it, and each firm knows the other knows this. Even though neither firm knows what’s going on behind the scenes, they’ll assume that a firm facing the same costs and revenues is rational and will optimize its own profit, sothey can make good, educated guesses about what the other firm will do. Each firm will determine the other firm’s likely course of action and compute its own best response. (That’s the one that maximizes its profit.) Now, let’s take a look at what the firms’ profit functions will look like. Recall that Total Profit = Total Revenue – Total Cost, and that Marginal Profit = Marginal Revenue – Marginal Cost. Companies will choose quantity to optimize their profit, so they’ll continue producing until their expected Marginal Profit is 0, and then produce no more. Firm 1’s total revenue is Pxq1 – revenue is always price times quantity. Keeping in mind that price is a function of quantity, we can rewrite this as (250 – QD(P)/2)xq1. Since QD(P) = q1 + q2, this is the same as writing (250 – (1/2)(q1 + q2))q1. Then, we need to come up with a total cost function. Let’s say it’s 25 + q12, where 25 is a fixed cost (representing, say, rent for the factory) and q12 is the variable cost of producing each good. Then, Firm 1’s profit function is: Profit1 = (250 – (1/2)(q1 + q2))q1 – 25 – q12 or Profit1 = (250 – q1 /2 – q2/2)q1 – 25 – q12 or Profit1 = 250q1 – q12/2 – q1q2/2 – 25 – q12 The marginal profit is the change in the total profit function if Firm 1 produces one more unit; in this case it’s easier to just use the calculus concept of taking a derivative, which yields Marginal Profit1 = 250 – q1 – q2/2 – 2q1 = 250 – 3q1 – q2/2 Since the firms are identical, though, firm 1 knows that firm 2 is doing the same optimization! So, q1 = q2, and we can substitute it in. Marginal Profit1 = 250 – 3q1 – q1/2 = 250 – 5q1/2 This is 0 where 250 = 5q1/2, or where q1 = 100. Firm 2 will also produce 100 units. Total supplied quantity is then 200, and total price will be 200. We can figure out each firm’s profit simply by plugging in these numbers: Total Revenue = Pxq12 = 200×100 = 20,000 Total cost = 25 + q12 = 25 + 100×100 = 25 + 10,000 = 10,025 Total Profit = 9,075 This was a bit heavier on the mathematics than some of the other problems we’ve talked about, but all that math is just getting to one big idea: it’s rational to produce when you expect your marginal benefit to be at least as much as your marginal cost. ## Monopolistic MarketsDecember 11, 2012 Posted by tomflesher in Micro, Teaching. Tags: , , , , , , add a comment Continuing our whistle-stop tour through market types, today’s topic is monopolies. Yesterday’s discussion was of perfectly competitive markets, where three conditions held: • Identical goods • Lots of sellers • Lots of buyers Today, we’ll talk about what happens when that second condition doesn’t hold – that is, when sellers have market power. When sellers don’t have market power, they have to price according to what the market will bear. If they price too high, someone will undercut them, but if they price too low, they’ll lose money. The only thing they can do is price at their break-even point, where price is equal to marginal cost. (This is sometimes called the zero profit condition.) When only one seller exists, he is called a monopolist, and the market is called a monopoly. A monopoly can arise for one of two reasons: either it can be because the owner has exclusive access to some important resource, called a natural monopoly, or the owner has an ordinary monopoly because of laws, barriers to entry, or some other reason. A natural monopoly is one that arises not because of anticompetitive action by the monopolist but because of exclusive access to some resource. For example, owning a waterfall means you have unbridled access to it for hydroelectric purposes; being the first to lay cable or pipelines makes it inefficient for anyone else to access those resources; essentially, anything where there’s a high fixed cost and a zero marginal cost are good candidates for natural monopoly status. Regardless of whether a monopoly is natural or ordinary, a monopolist isn’t subject to the same zero-profit condition as he would be in a perfectly competitive market, since there’s no one to undercut him if he prices higher than his own marginal cost. He’s free to do the absolute best he can – in other words, to maximize his profit. The monopolist doesn’t have to take the price, as a perfectly competitive market would force him to; he’ll choose the price himself by choosing the quantity he produces. The monopolist’s profit-maximization condition is that his marginal revenue = marginal cost. This derives from the monopolist’s profit function, Profit = Total Revenue – Total Cost. The monopolist will produce as long as each unit provides positive profit – in other words, as long as marginal profit ≥ 0. In non-economic terms, he’ll continue producing as long as it’s worth it for him – as long as each extra unit he produces gives him at least a little bit of profit. Once his marginal profit is 0, there’s no point in producing any further, since every unit he produces will then cost him a little bit of profit. Because Profit = Total Revenue – Total Cost, another equation holds: Marginal Profit =Marginal Revenue – Marginal Cost. Saying that marginal profit is nonnegative means exactly that marginal revenue is at least as much as marginal cost. Finally, note that marginal revenue is the price of the last (marginal) unit, but keep in mind that the monopolist has control over the quantity that’s produced. Thus, he has control over the price, and will choose quantity to get his optimal profit. ## Perfectly Competitive MarketsDecember 10, 2012 Posted by tomflesher in Micro, Teaching. Tags: , , , , , add a comment 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.
Tags: , , , , , , ,

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 GoodDecember 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 MarginsDecember 5, 2012

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

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.
Tags: , , , , , ,

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.