Faculty Freebies and Price DiscriminationApril 3, 2017

Posted by tomflesher in Examples, Micro, Teaching.
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Despite its nasty-sounding name, price discrimination is interesting and beneficial to some consumers. (Of course, when we move away from equilibrium to make someone better off , we usually make some other consumers worse off.)

Textbook publishers face a classic case where price discrimination would be useful: they want to charge students high prices for their textbooks, but because professors have the power to require a textbook of their students, they want to get professors on board as easily as possible. That usually means lowering the price of the book for professors (to make it easy to get); I get tons of free books every semester.

Publishers don’t want those free books to get into students’ hands, though – that means either a student didn’t pay for a book because a virtuous professor gave a freebie away, or the student paid, but paid an unscrupulous professor for a book the professor got for free! If a student is going to pay for a book, the publisher would rather get a cut of it.

Goods that are difficult to resell are easiest to discriminate on. Publishers have, for a long time, printed “INSTRUCTOR’S REVIEW COPY – NOT FOR SALE” on books. That has some effect, but you still have the possibility of paying for a book on Amazon or AbeBooks.  One way to keep students from buying these books is to sink money into online resources, which are tied to students’ identities. That way, even if the student buys a used copy of the physical text, they still have to pay for access to the online resources. Still, not every instructor uses those, so this isn’t foolproof.

One publisher, Cengage, has taken an additional step with Greg Mankiw’s principles book: not only does it say “Compliments of N. Gregory Mankiw” on the front, along with the usual “Instructor’s Edition” language, it has my name embossed on the cover. “Specifically prepared for” is printed, and “Thomas Flesher” is stamped into the front cover. (Of course, I prefer Tom, but you can’t be too picky with freebies.) This is a pretty clever means to keep me from reselling the book, at least unless I have a high name value. I can easily imagine a student wanting to purchase a book specifically prepared for Dean Karlan or Paul Krugman, for example, if either of them still teaches Principles using Greg’s book. (I doubt it, since each of them has his own.)

Either way, Cengage is trying to protect what’s likely its largest profit-producer by minimizing the number of free copies students can use.

How do producers charge different consumers different prices?September 29, 2015

Posted by tomflesher in Micro, Teaching.
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Price discrimination is the act of charging different consumers different prices based on how much they’re willing to pay. There are a few different forms of price discrimination, and it can be achieved different ways depending on how much information a seller has.

Haggling, or negotiating to find an exact willingness to pay, is an effective form of price discrimination for large purchases. For example, a car salesman can often start with a high price, and when the customer refuses, he can incrementally lower the price (or otherwise adjust the offer) until he find a deal that the buyer is just barely willing to accept. This has one huge advantage – it gets the most that the customer is willing to give up (or, in other words, it extracts the customer’s maximum willingness to pay). It is, however, very costly for a salesman. Just imagine if the salesman were to spend a whole day negotiating only to realize the buyer wasn’t willing to pay enough to cover the cost of the car. Then, the salesman loses the chance to make a sale at all that day. Since it’s costly, this method is most useful for high-priced items like cars and houses.

If you ask a consumer what he’s willing to pay, he’ll lowball you; haggling helps force the price (and the profit) up.

Direct segmentation allows a market to be broken up based on some visible characteristic. In the previous post, I discussed my father-in-law’s senior citizen discount on haircuts and how he pays less than I do for the same cut. He does this by asking for a senior citizen discount, which I’m not eligible for.

Direct segmentation involves breaking the market up into different groups and intentionally charging different prices to those different kinds of people. It works best when one group has a higher willingness to pay – so, since I’m not a college student, and not a senior citizen, my (relatively) high income means I don’t ask for a discount. Similarly, I pay a lower price to have my blazers dry-cleaned than my department chair does, even though her blazers are made up of a smaller amount of fabric. Dry-cleaners just automatically charge a higher price for a woman’s garment than a man’s, even if the garment is similar.

This sometimes leads to unpleasant outcomes. NPR did a story on a 12-year-old girl who had to pay a premium to play Temple Run as a female character; non-white-male characters were all in-app purchases that cost money.

Indirect segmentation is like direct segmentation, but requires the consumer to do some work to get the lower price. A good example of this would be a volume discount. I have a strong preference for Crayola An Du Septic dustless chalk. (I like its weight and erasability.) When I purchase chalk to use in the classroom, my buying options include paying about $3.50 for a single box or about$12 for a 12-box package. No sane person who isn’t a teacher has any use for 12 boxes of blackboard chalk, so I signal my price sensitivity by buying a larger amount at once.

Another way people reveal their types is by clipping coupons. A coupon is like a little badge that says “I’m cheap! Give me a lower price!” By doing a bit of extra work to signal my cheapness, I qualify myself for a lower price just as much as if I’d haggled with the guy behind the counter.

Elasticity and DemandMarch 18, 2015

Posted by tomflesher in Micro, Teaching.
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The price-elasticity of demand measures how sensitive consumers are to changes in price. There are two primary formulas for that. Most commonly, introductory courses will use $\frac{\% \Delta Q^D}{\% \Delta P}$, where $\% \Delta$ means the percentage change. This means the numerator is $\frac{\Delta Q^D}{Q_0}$, where $Q_0$ is the original quantity demanded and $\Delta Q^D$ is the change in quantity demanded. The denominator is $\frac{\Delta P}{P_o}$. Through the properties of fractions, that ratio is equal to $\frac{\Delta Q^D}{\Delta P} \times \frac{P_0}{Q_o}$, and a lot of students find that formula much easier to use.

A graph of demand and price-elasticity of demand

Take note of the shape of that formula, and keep in mind the Law of Demand, which states that as price increases, quantity demanded decreases. At high prices, quantities are relatively low, meaning that a small change in price yields a relatively big change in quantity demanded. If the percentage change in quantity demanded is bigger than the percentage change in price, then demand is elastic and consumers are price-sensitive. On the other hand, at low prices, quantities are relatively high, meaning that a small change in price yields an even smaller change in quantity demanded. That means demand is inelastic.

This pattern of high prices corresponding to elastic demand and low prices corresponding to inelastic demand holds for most goods. At a very high price, firms can make a small change in price to try to encourage new buyers to buy their product, whereas at a very low price, firms can jiggle the price up a little bit to try to snap up some extra revenue without dissuading most of their buyers from purchasing the product.

A slightly more accurate formula for price-elasticity of demand is $\frac{dQ}{dP} \times \frac{P}{Q}$, which looks surprisingly like the previous formula but doesn’t depend on choosing an original value.

The graph in this post shows market demand $Q^D = 1000 - P$ in blue and elasticity in orange. Note the high elasticity at high prices and low elasticity at low prices.

Elasticity (SPROING~!)March 17, 2015

Posted by tomflesher in Micro.
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When we think about elasticity in the real world, we often think about the properties of things like rubber bands or the waists of sweatpants. If a solid has high elasticity, that means it’s very sensitive to having forces applied to it – so while something like Silly Putty or latex is very elastic, other materials like steel or titanium are not. A small amount of force yields a lot of deformation for Silly Putty, but not much at all for steel.

Elasticity in economics works the same way. It measures how responsive one measurement is to a small change in some other measurement.

When economists say “elasticity” without any qualifiers, they typically mean the price-elasticity of demand, which measures how sensitive purchases are to small changes in price. Elasticity, $\epsilon$, is expressed as a ratio:

$\epsilon = \frac{\% \Delta Q^D}{\% \Delta P}$

where $\% \Delta Q^D$ refers to the percentage change in quantity demanded1 (the actual change divided by the starting value) and $\% \Delta P$ refers to the percentage change in price (again, the actual change in price divided by the starting value).2 This leads to three cases:

1. $\% \Delta Q^D > \% \Delta P$ – a small price change yields a big change in quantity demanded. This means that buyers of the good are price sensitive, and (equivalently) demand for the good is elastic. Note that in this case, $\epsilon > 1$.
2. $\% \Delta Q^D < \% \Delta P$ – a small price change yields an even smaller change in quantity demanded. This means that buyers of the good are not price sensitive, and demand for the good is inelastic. Here, $\epsilon < 1$.
3. $\% \Delta Q^D = \% \Delta P$ – a small price change yields exactly the same change in quantity demanded. The term for this type of demand is unit-elastic. When demand is unit-elastic, $\epsilon = 1$.

It’s tempting to treat elasticity as very complicated, when it has a really simply mathematical interpretation. It answers the question “Which change is bigger – price, or quantity?”

Also interesting is the question of why some goods are demanded elastically and some are demanded inelastically. Typically, goods with many alternatives are demanded elastically. Alternatives can come in many forms. Most commonly, they’ll show up as substitute goods, or goods which you can use instead of another good. For example, bread has many substitutes (naan, grits, cornbread, rice, tortillas, English muffins….), and so if the price of bread rose significantly, you’d see many people substituting away from using bread. However, there are other forms of alternatives, too. You may see elastic demand for goods that cost a large proportion of the buyers’ income or that can be purchased over a longer timescale. A college education is an example of both of these – a small change in the level of tuition can lead to big changes in the behavior of students, who will often take a year off to earn money.

Anything with few alternatives will typically be demanded inelastically. Salt is the classic example, because it has no alternatives – it’s necessary for flavoring food, allowing our bodies to function properly, and (in the case of iodized salt) preventing certain illnesses. However, anything that is addictive (like tobacco or heroin), necessary for many uses (like cell phone plans), or difficult to switch away from (it’s not like you can put diesel fuel in your gas-engine car!) will typically have inelastic demand.

1 Quantity demanded means the number of goods people are willing to buy at a certain price.
2 Usually one of these will be negative and the other positive, because of the Law of Demand; economists, ever economical with their notation, simply ignore this and use the absolute value.

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. 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. Monopolistic MarketsDecember 11, 2012 Posted by tomflesher in Micro, Teaching. Tags: , , , , , , 1 comment so far 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.

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.
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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.