MACRO MATERIAL

— then we can’t use the same supply curve. We need to use a different curve to demonstrate the new relationship, because the old supply curve is no longer valid.

Certain events are likely to push out a supply curve. Other events are going to push in a supply curve. For example: would an increase in the price of other inputs push out supply, or push in supply? Would an improvement in technology push out supply, or push in supply?

Supply and Demand

In our graph showing the relationship between price and quantity (in a given time period), we can draw both the demand curve and the supply curve. They exist in the same space.

Price and quantity come from the intersection of supply and demand.

What have we done? We were trying to explain where prices come from. We have now used supply and demand to explain the origin of prices.

CHART: previous picture from before, supply and demand leading to prices

And then when trying to explain supply and demand, we found that both supply and demand have specific determinants, and that one of the determinants of both is... the price.

CHART expanded: price => supply and demand => price

We have a strange circle of causality here. We used price to explain both supply and demand, and then we used supply and demand together to explain price. This is to say that we “borrowed” the price originally to create the curves, and then used the curves to explain where the price came from.

This is a key strangeness of economics, which people can get wrong if they don’t work carefully. This is the single most common mistake in all of economics. I have seen famous professors, writing in national publications, get this idea fundamentally wrong.

The key point is that the logic of the individual is different from the logic of the system.

As individuals, we go into the grocery store and the price already exists. We decide our personal quantity demanded of milk based on the price of milk. For us as

individuals, the price is the cause and how much we buy is the effect. The demand function reflects our normal experience as individuals.

But for the market as a whole, the price is not the cause. Supply and demand

are the cause, and the price is the effect. Why?

Why is the causation totally reversed for the system as a whole, compared to individuals within the system?

Imagine, for a moment, that the price is too high, meaning above the intersection of the supply and demand curves. (Suppose a gallon of milk at the grocery store cost twenty dollars.) If the price is high, then quantity demanded will be low and quantity supplied will be high. There will be a lot of production, but not many people wanting to buy that production at that high price. In other words: inventories will build up for firms, and those inventories will not be sold.

GRAPH: too high a price

It is in this case — when we are out of equilibrium — that individuals find they have some control over the price. Firms would like to sell their inventories at the high price, but they can’t... so they cut the price. When the price goes lower, quantity demanded increases (people want to buy more of a good when the price is lower) and the quantity supply decreases (firms don’t want to keep producing as much when the price is lower). This process will continue until supply and demand are back in equilibrium.

Imagine now that the price is too low. At this low price, quantity demanded will be extremely high. (Suppose that a Ferrari cost a hundred dollars.) Consumers will want to buy a lot at this low price. But firms will not want to allocate expensive resources to production, if the price is so low. Quantity supplied will be low.

GRAPH: too low a price

There will be a shortage. People will want to buy the good — there will be high effective demand — but there won’t be enough production. Consumers will then bid up the price. If they can’t get the good at 100 dollars, maybe some who can afford it will offer 1,000, or 10,000, or even higher. As the price goes higher, quantity demanded will decrease but quantity supplied will increase.

Equilibrium

The equilibrium price is where the system finally stabilizes, where quantity supplied is equal to quantity demanded. Notice the logic here: there are forces at work here that push toward equilibrium when quantity supplied and demanded are out of balance.

This is an insight that too few people appreciate.

Every buyer must have a seller. Every good sold means a good bought, because there is a participant on each side of the transaction. Markets push toward equi- librium. If supply and demand are somehow out of synch, the price will necessarily change to push things back into balance. This is in the same sense that a ball will not rest on the side of a steep mountain. That is not a stable position.

Almost all of economics is equilibrium modeling. We jump directly to the final point of intersection, instead of modeling the dynamic process that brings us to that point. There are some models that attempt to model the dynamic process by which price reaches its equilibrium (c.f. the “cobweb model”), but these approaches are extremely difficult and require more advanced mathematical techniques, including the modeling of systems of difference equations. Almost no one does this. Too difficult.

In this class, we will keep things simple: we will jump to equilibrium.

The Most Common Mistake in Economics

Never reason from a price change. — Scott Sumner

The logic of the market as a whole is different from the logic of the individuals in the market.

In the market as a whole, price is the effect. It is not the cause. Never say that “The price is higher, therefore...” That is reasoning from a price change, and it is always a mistake when trying to understand a market outcome. If the price changed, then that change had some cause. Either supply or demand changed, and that is what caused the price to change. The price is the effect. Supply and demand are the cause. The final market quantity is also (along with price) the effect. Supply and demand are the cause.

If there is an outside force that tries to keep the “price” fixed, then that is when things go wrong.

Price Ceilings and Floors

The process by which the price converges to equilibrium is referred to as market clearing. But what if markets aren’t allowed to clear? Suppose the government enforces a law that keeps prices low, below the market clearing (equilibrium) price.

The ostensible purpose seems good. If the price is lower, more people will be able to afford the good. But if there is a price ceiling, above which the price cannot go, then quantity demanded will be high, and quantity supplied with be low. There will be a shortage of the good.

PRICE CEILING graph

At that low price, it is not worthwhile for producers to allocate resources to pro- duction. Because of the price ceiling, the cost of the inputs will exceed the value of the output. (Why would anyone plant five seeds, in order to harvest four seeds in the future?)

Socialist countries2 in the past often introduced price controls such as price ceilings. The result was shortages, most famously bread lines where people waited hours to buy enough food to eat. Instead of paying with money, they paid with time.

BREAD LINE pic?

Price Ceilings: A Point of Confusion

Notice that the price ceiling is below the market clearing (equilibrium) price. In other words, the ceiling is “low”. This is often confusing for students.

But we’re talking here about a problem! What if you entered the classroom, and the ceiling of the room was only three feet high? That ceiling is in the wrong place. A high ceiling is not a problem. Only a low ceiling will interfere will market clearing. If the price ceiling is nice and high, it will have no effect on the market. The market will be able to move to equilibrium.

The Price Floor

Another form of control is the price floor, an attempt to increase the price above what the equilibrium price would be. A high price floor will insult in large quantity supplied,

2By “socialist”, I’m not talking about Bernie Sanders, but rather old school, totalitarian, build- a-wall-and-shoot-everybody-who-tries-to-leave-the-country socialism. That was the original meaning of the word. It might be shifting in meaning today.

with only limited quantity demanded. In other words, there will be surpluses, or overflowing inventories.

GRAPH price floor

Marginal utility decreases. Given a high level of production, the value of the last item made will be very low. Ordinarily, this would mean that the price of the item drops. But when price controls keep the price too high, then expensive production will continue to be allocated to outputs that are, for the final consumer, not very valuable. It makes little sense to produce items that cost a lot of resources to make, but which are not highly valued.

Confusion about Price Floors

Students are often confused that price floors are so high up. But we are, again, talking about market problems. If you entered the classroom, and the floor was three feet up, that would be a problem. When the floor is down where it should be, there is no issue. The price will be the equilibrium price. Only when the floor is built too high will we see problems.

The most common price floor in modern countries is the minimum wage. The ostensible goal here is, again, good. We would like people to have better wages. But if a worker only produces 8 dollars of value for a company, and must be paid 10 dollars an hour, then that worker will simply not be employed. The “surplus inventory” of the minimum wage is unemployment.

The unemployment rate is higher for less-skilled workers. According to basic eco- nomic theory, it is likely that minimum wage laws put our most vulnerable citizens

— the people who earn the least money — out of work. A better solution to improve the plight of the lowest earning workers might be wage subsidies, such as the Earned Income Tax Credit in the US. 3

3The empirical research on the minimum wage is mixed. The problem in economics, and in the

social sciences generally, is that our data is not very good. But given the straightforward prediction of the most basic and compelling theory, and strong reasons for mixed empirical results, the safest conclusion is that the minimum wage works exactly like other price floors: Businesses will not pay more than workers are worth for production, which means the minimum wage puts the most vulnerable people out of work. But for more detailed discussion, and possible exceptions to this, consult a Labor Economics textbook.

The “Slope” of Our Curves

Notice that the “slope” of a curve here is extremely informative. If a demand curve has a very flat “slope”, then that means that consumers are extremely sensitive to price changes. The price can increase by only a little, and consumers will react strongly to stop buying that good.

GRAPH: flat slope demand

Or if the “slope” of the demand curve is relatively steep, then consumers be ex- tremely insensitive to price changes. A large increase in price can lead to only a small decrease in quantity demanded, as most consumers are unable to find a substitute item so high on their internal list of value that can satisfy their wants.

GRAPH: steep slope demand

The problem with talking about “slope”, however, is that the mathematical idea is dependent on the price level. Imagine a world where you woke up tomorrow, and everything was priced in cents, rather than in dollars. Every market was identical! We just changed the way we measured the market.

But what has happened to the slope?

GRAPH: flatter looking demand curve

In real terms, this is exactly the same market that it was. Nothing has changed. People are exactly as sensitive to changing conditions are they are. The mathemat- ical slope is flatter, but that doesn’t actually mean anything about the real world. (Changing the yardstick we use to measure the economy does not change the economy itself.) The flatter slope here is merely an illusion of the new price level. For example, Japan uses the yen as their currency. One yen is roughly equivalent to one US cent, so in Japan, effectively everything is measured in cents rather than in dollars. But this doesn’t mean that the inherent nature of their demand curves are different. They just use a different currency.

So the idea behind the “slope” is informative, but what we need is a concept that gets across the basic idea of the relative “flatness” or “steepness” of the slope, but is more robust than the slope. The idea needs to be strong enough to withstand arbitrary changes in how the economy is measured, whether in dollars or in cents or in yen or in euros. This idea is the elasticity.

Elasticity

The elasticity of demand is the percentage change in the quantity demanded that results from a percentage change in price. In mathematical terms, this can be written:

E = %∆Qd d %∆P

Read this exactly as the definition indicates! It says exactly the same thing. The elasticity of demand (Ed) is the percentage change in quantity demanded (%∆Qd) that results from the percentage change in price (%∆P ). It can be measured along an interval with the simple formula for measuring percentage changes:

( Q old ) ( P old )( Qnew −Qold /Pnew −Pold ) · 100

If you’re more comfortable writing out the English for now, then feel free to do so. We don’t use math to make things look mysterious, we use it to be lazy. Writing the math uses less space. In addition, mathematical formulas can be much more easily manipulated in a logically consistent manner than English language sentences. (This is the magic of algebra. If you didn’t previously know algebra was magic, now you do. Algebra is magic. You can follow the strict rules of algebra without even realizing the meaning of what you’re writing. This can be a weakness of mathematics, in addition to a strength. It’s not impossible to manipulate English sentences in a way that maintains consistent logic, but it is also not very easy, but English sentences are normally more intuitive to read.)

NOTATION: Notice the English-language translation of the fraction: that results from. Do not say “divided by”! That does not tell you cause and effect! Writing out a mathematical formula without knowing what it means does not help anything.

In this case, the fraction indicates causation. “That results from” tells you cause and effect, coming directly from the demand function. It tells you that the denominator at the bottom is the cause here: there was a percentage change in price. What’s the effect? There was a percentage change in quantity demanded that resulted from the percentage change in price.

(Notice that we’re talking about the demand curve here by itself, from the demand function, or the logic of the individual. For an individual, price is the cause and quantity demanded is the effect. The grocery store has increased the price of soda by

a certain percentage change. What does that do to my own quantity demanded of soda, as a percentage? Remember that the logic of the market as a whole is different: price is an effect for a market. Never reason from a price change when talking about final market outcomes.)

The advantage of elasticities (compared to the slope) is that it doesn’t matter how prices are measured: dollars or cents or euros or yen are irrelevant. The elasticity will always come out measured the same way, regardless of the currency.

Elasticity might sound like a fancy word. But the idea here is just the basic idea we can understand by looking the slope. It’s just that we use elasticities because they work for any currency.

We want to know how responsive consumers are to price changes, and a higher elasticity — which we can sort of imagine as a flatter “slope” — means that consumers are more sensitive to price changes. Demand is very elastic in that case. A very low elasticity, close to zero, means that consumers are not very sensitive to price changes. This can mean a relatively steep “slope”.

Remember, too, that demand is an inverse relationship. The elasticity of demand is always negative. “More elastic” — meaning more sensitive to changes in price — is indicated by a more negative number, farther from zero with a bigger absolute value. The elasticity of supply (Es) is measured in similar fashion, but supply slopes up and so the supply elasticities are positive.

(Math note, will not be tested: In this class, we will measure elasticities broadly, along intervals for ease of calculation. But if given an actual demand function, the instantaneous elasticity can be computed with calculus by differentiating the demand

function with respect to price and using the percent derivative: Ed = ∂Qd /∂P

= ∂Qd P .

Q P ∂P Q

This is the instantaneous version of percentage changes, that is to say, it is calcu- lated at a single point rather than along an interval. Compare to interval formula

Qnew −Qold /Pnew −Pold . Same idea.)

Qold Pold

Appendix: Public Finance

There are two interesting and important facts that I feel I should at least mention regarding public finance.

The first fact is: It doesn’t matter who you tax. The “legal incidence” is

determined by the government. The government can say that firms pay (for example, for the sales tax), or that both the worker and the firm pays together (for example, FICA taxes). But the underlying point here is the final outcome is exactly identical (after transition to the new equilibrium), regardless of who is taxed. The “economic incidence” is always the same, regardless of the legal incidence.

The second fact is: The actual burden of the tax depends on elasticities. If demand is highly inelastic, then consumers will pay the majority of the tax, regardless of the legal incidence. If supply is inelastic, then firms will pay the majority of the tax, again regardless of legal incidence.

Why does it not matter?

It doesn’t matter who you tax. The final outcome is the same. Why?

Suppose that the government levies tax of 50 cents on every purchase. Consumers must pay the tax directly to the government. This will push “down” the demand curve by exactly 50 cents, since everything costs more.

Very important! Both the original demand curve, and also the new curve, are relevant information for taxation. The new curve shows quantity. The old demand curve — moving directly up from the intersection — shows how much consumers pay. The new curve shows how much firms receive, while the old curve shows how much consumers pay. The difference between the two is received by the government: 50 cents times the new quantity QT , the quantity of the good sold given the new tax.

The quantity is less. The tax has “distorted” the market from its original compet- itive equilibrium, creating a deadweight loss.

Now suppose that the government levies a 50 cent tax on firms, rather than con- sumers. Then the supply curve shifts “up” by exactly fifty cents, shifting in and reducing supply. The new outcome results in lower quantity (as before). The “new” supply curve gives the quantity, and also the price paid by consumers. Moving directly down from that curve to the “old” supply curve, which shows how much the firm re- ceives. The difference, again, is the amount taken by the government. Again, there is deadweight loss.

And as it turns out, the new equilibrium quantity is exactly the same in both cases.

The price received by firms is the same. The price paid by consumers is the same.

The Tax Burden Depends on Elasticities

The more inelastic the demand, the more consumers pay. The more inelastic the sup- ply, the more firms pay. This is regardless of the legal incidence of the tax. (Remember fact one: legal incidence is irrelevant to the final outcome.)

If demand is perfectly inelastic, then consumers will pay the entirety of the tax — even if the legal incidence is that firms pay.

Why is this important?

When the government interferes with market outcomes, even for the legitimate purpose of taxation, what actually matters is supply and demand, including the shapes of the curves. The market outcomes after taxation change because supply and demand have changed based on the taxes.

Supply and demand do not go away. They remain an incredibly useful analytical apparatus.