# Principles of Econ: Lecture 3a | Equilibrium

[ Music ]>>Okay. Now let’s do a

lecture on equilibrium, right. So we’ve talked about supply,

we’ve talked about demand, we’ve talked about what moves

supply, what moves demand, but generally when we’re talking

about a market we have to talk about how supply and demand

interact with each other, right, so specifically how one part of the market addresses

the other part of a market because if we don’t address

these interactions then there can’t really be a market, right. If producers have no one to

sell to then there’s no point in just looking at a supply

curve and just seeing and trying to figure out how we

can predict behavior. Similarly, if we only

have a demand curve, we don’t really know how

consumers are going to behave if there’s nothing to consume. So, in this sense, we’re going

to talk about when the meet, or specifically how they

interact with each other, and that is our equilibrium

part of, and the most important

part actually of our supply and demand model. So, what do we know? We know that people

demand goods and services, you want to buy things,

you want to use things, and we know that there’s

some maximum price that you are willing to pay for

that good or service, right; there’s a price that

you’re not willing to pay, but there’s definitely a price that you are willing

to pay at most. On the flip side, we know that suppliers face

a similar problem. They want to provide you with

goods and services in the market and we know that

there’s a minimum price that they’re willing to sell,

or there’s a price in which that if you go below it, they’re

not going to sell it to you. So, in this sense,

can we find a price where both parties are

going to be happy, right, where you are willing to

pay for this good or service that at a price that

suppliers are willing to sell it to you at, right. And what we call this

is, well, equilibrium, or specifically you’re happy

then then producers are happy, because you’re paying a price

that you’re willing to pay and they’re selling

you at a price that they’re willing

to sell it at. Okay, so here’s our

definition equilibrium, which is simply quantity

supplied equals quantity demanded, okay. You basically also say where

the supply curve intersects or meets the demand curve. But effectively we want QD and

QS to be the exact same value. Alright. Now, how do we think

about this generically first? So, without using any math,

just using our pretty graphs, we know that we could just

simply set supply equal to demand in a typical market,

just overlay our supply curve with our demand curve

and where they meet, P star and Q star gives

us our equilibrium point. Alright, just also

consider a few, sort of, terminology kind of points here. P star is also what we call the

market clearing price, alright, the price in which the

market clears, right. Basically, you’re

willing to pay– you’re willing to pay for it

at this price and the company that you’re buying

from is willing to sell it to you at that price. Q star is where QD and QS are

the exact same value, alright, or the market also clears

in terms of quantity. So, we have market

clearing price and we have market

clearing quantity or effectively P

star and Q star. In this class you

will always use star to represent the equilibrium

price and or quantity when dealing with supply

and demand or any sort of other models that

we’re going to deal with. What happens though if

price was set higher than equilibrium price. So, let’s say that we have P

star and the government goes, you know what, let’s set

some price higher than that. Well what would happen? Well, if price is higher

than our clearing price, we know we can find both

QD and QS, but we also know that there will be and has to

be a mismatch between QD and QS. Why? Well, if I set a price

higher than equilibrium, then we know that suppliers

are going to be happy, but demanders are not

going to be happy. So, suppliers are willing

to provide more of this good and demanders are willing or

not willing to buy as much at that price, which

means we’re going to have too much

supplied relative to how much is demanded. So QS is going to exceed

QD; so QS is greater than QD and we call this

situation a surplus. Now, an important point, this

surplus definition, alright, what we call surplus here is

different from the consumer, producer and total surplus that

we’ve calculated previously. We will still do that,

but surplus, in this case, refers to the extra amount of

quantity ra– rather than value. Alright, so when we’re dealing

with surplus in this case, you’re going to use the

units that you use is going to be either units or the

specific number of things that you could purchase

in this market. Alright. On the flip, if we consider setting our price

below equilibrium price then we again have a mismatch between

QD and QS, which in this case, demanders are happier,

the consumers are happier because price is low, but

the supplier is not happy because price is, well, too low. So, in this case, QD is

going to be greater than QS, and as a result of this,

you are going to demand more than what is available to be

supplied, and as a result, we call this a shortage. Alright, so we have surplus

and we have shortage, depending on where price

is relative to equilibrium. In this case, you’ll

notice that if there’s– when there is a shortage, okay,

the market will tend to want to correct itself and push

prices toward equilibrium again because con– sellers and– and buyers want to have

the exact same price; that’s the only way the market

clears, and the same is true when price is set

above equilibrium price because sellers and

buyers want to have a price that they’re both

willing to pay for. So when price is set above,

there’s downward pressure– downward pressure on prices

to go back to equilibrium; same with a shortage situation

where there is upward pressure to return back toward

equilibrium value of P star. Alright, this graph is also

mislabeled for some reason, but the actual slides that are

on Canvas are correct, okay. What else do we know

about equilibrium? Well, the natural effect

is that we’re going to maximize the gains from

trade and why do I mean– what do I mean by

gains from trade? Well, notice that when

we have a price above or below equilibrium, we’re going to have some wasted

trades, or there’ll be people who want to buy, who

won’t be able to buy, if there’s a shortage,

or there is a situation where sellers are willing

to sell but no one’s buying, if there is a surplus. So those are wasted trade;

you’re not gaining any– the market doesn’t gain any

sort of value from those. If anything, we lose

things because– we’re losing value because those

trades don’t actually exist, right. When there’s a shortage or a

surplus, not everyone is happy. Think about a shortage

situation. Generally speaking,

if it’s a shortage in the market no one is happy;

that’s effectively what happens. Not every– not no one–

not everyone is happy. There will be people who want

to buy it who won’t be able to buy it, and as a result,

they have less utility or value extracted from

this– from this market. Alright. So, there are

three properties of– of maximizing gains from

trade and three properties of equilibrium that

are super important. The first is that the supply

of goods are bought by buyers with the highest willingness

to pay, which makes sense. If you are willing to– the

only people who are trading in this market are people

who are willing to pay for that good or service. The same is true for the other

side, the supply of goods sold by sellers are with

the lowest cost. Sellers are– sellers

are the mo– with the minimum amount

of costs are going to be making the sales, okay. And of course, there are no

unexploited gains from trade, which effectively means

that we don’t have a surplus or a shortage and

that everyone– that the equilibrium

price and quantity is where everyone is happy,

where the market is happy, where the suppliers

are willing to sell and the buyers are

willing to buy. Okay, so that’s sort of the qualitative

explanation of equilibrium. But what we really

want to focus on now, on top of the qualitative and

the intuitive understanding that we have of equilibrium

is dealing with equilibrium and a little bit of math. Alright, so, let’s

go ahead and do this. We know that qualitatively,

QD must equal to QS in equilibrium, right. But we also know that we

have equations and functions for demand and supply. We have D of Q is equal to P

and S of Q is equal to P, right; those are both equal to each

other in the equilibrium. But what does that really mean? Well notice that they both share

price, P. So if I set them equal to each other, well

equilibrium happens when we set the supply

equation equal to the demand equation

and we get a price. All three of these will equal

to each other in equilibrium, right, and of course we label

that as P star and Q star. Okay, so why don’t we go

ahead and do an example where we’re given the

following information. We are told that the demand is

given as negative 2 Q plus 12, and supply is given as 4Q. Now, we know that they both

should equal P and in effect, in equilibrium, they should

probably equal themselves. So step one we want

to graph that. Easy to graph; simply just go

ahead and graph the y axis; I didn’t really put it here

but the y and x intercepts for supply should be

12 for demand and 6 on the x intercept for demand. Okay, so 12 for the y intercept

and 6 for the x intercept. Okay. For supply,

our intercept is zero so just go ahead

and use zero there. And, of course, to calculate

equilibrium we’re going to set supply equal to

demand and solve for Q. So, when we do that, we get 2 for Q

and here’s the important part; once we found Q you can plug

in that Q into either demand or supply and get the

exact same result. So, if I plug in 2 into the

demand equation, I will get 8. If I plug in 2 into the supply

equation, I will also get 8, which gives us P

star and Q star. To calculate total surplus, we use 1/2 base times

height, like we always have. Your base is always going to be

Q star; that will not change. Base will be Q star. Your height, however, is

going to be the difference between the y intercept

of demand and the y intercept of supply. So, in this case, the y

intercept of demand is 12 and the y intercept of supply

is zero, which means that 1/2 of 2 times 12 gives us 12. So, our total surplus

is equal to 12. Okay. And we’re just going to let the animation

follow through for that. Now, to continue

onto the same thing, what if I set some

price higher than that? Well, let’s say price

was equal to 10. We want to figure out if

that’s a shortage or a surplus. Now, notice, if the price of EDC

tickets at equilibrium was $8 and we set some price equal

to 10, well we now know that QS is going to

be greater than QD, which means that we’re going to

have a surplus of tickets, okay. So, 10 is greater than 8, so

we get a surplus of tickets. How do we calculate this? Well, we go ahead and plug

in 10 into each of the supply and demand equations and solve

for Q. So, starting with QS, 10 is equal to 4Q, right,

we’re just plugging in 10 for P. We solve for Q

we get two and a half. To find QD do the same thing. We do 10 is equal to

negative 2Q plus 12 or we get QD is equal to 1. Subtract them from each other, the bigger one minus the

smaller one and we get one and a half units of surplus. Okay, straight forward. So, what– what are

we really doing? Given a specific price, if you

determine if there’s a surplus or shortage, to calculate the

specific amount of surplus or shortage, you’re going to use

that price, find Q, either QD or QS for e– in– for

respectively in the demand or supply equations, and

then subtract the bigger one from the smaller one

to get our total amount of surplus or shortage. Okay. What we’re going to

do next is an actual example where I’ll work on another

example that’s similar to this but with different numbers, when you have a better

feel of what to do. Okay. Okay, let’s go ahead

and do an equilibrium example. You’ll notice that we’re

given the following supply and demand model for Kyber

Crystals in keeping in line with our Star Wars

example, but you’ll notice that we have a demand equation,

1/2, negative 1/2 QD plus 60 and a supply equation

2Q plus 20. Notice that the supply

equation has a positive slope, positive 2, and our demand

equation has a negative slope, negative 1/2. All we need to do is graph this. We need to calculate

equilibrium price and quantity, we want to calculate total

surplus and then suppose that we set some price

50, we want to see if this is a surplus, shortage, or if this is actually

our equilibrium price and look at those effects. Okay, let’s go ahead

and do our example. We are given the demand equation

of negative 1/2 QD plus 60, and our supply equation,

P is equal to 2QS plus 20. The first thing we want to

do is we want to graph this, and that’s pretty simple, right. So, all we needed to do is

have a standard, sort of, axes set up with P and Q. Obviously this

is the market for Kyber. First, what do we need? So, for demand recall that we need x

intercept and y intercept. the y intercept is given as P

is equal to 60, so we just need to put a 60 up here, right, and

that just comes from the fact that we were given that

in our demand equation. The x intercept is when

P is equal to zero, Q takes on what value? Alright, so do that. We just simply do zero equals

a negative 1/2 QD plus 60, which implies our x

intercept, of course, is 120. So, we’re going to go

ahead and put 120 here and connect those two points. Right, we’re going to go

ahead and label that D1. Okay. For supply,

well, supply is easy, all we really need is

just the y intercept for supply, which is 20. So, go ahead and just label that

20, and then graph out this way, and we’ll call that S1. Well we want to really figure

out what’s the important part is where the market clears, which is when supply

is equal to demand. So, I do want to find Q star

and I do want to find P star. So, market clearing values

of P star and Q star occur when supply equals

demand, right. So, we know that the demand

equation is a negative 1/2 Q plus 60. We’re going to go ahead and set that to our supply

equation of 2Q plus 20. If we go ahead and solve

and rearrange to put like– like terms together,

then what do we get? Well we get 40 is equal to 2

1/2 Q. And if we solve for Q, star actually in

this case, we get 16. Okay, so divide both sides by

two and a half we should get 16. To find P star we want to

go ahead and plug in this. Either supply or demand,

and because we’re already at equilibrium, and

because that’s the market, that’s where they

intersect each other, you’ll get the correct

P star regardless of which one you pick, so let’s

go ahead and use the easy one; we’ll go ahead and use supply,

so we know that P star is equal to 2 times 16 plus 20, which is

32 plus 20, which gives us 52. Alright. So, we get 52 as

our equilibrium price, right. So, we have– we have

calculated P star and we’ve calculated Q star. Let’s ignore that for a second,

P star and we calculated Q star. Part c, we want to

calculate total surplus at Q star, P star. Well, let’s go ahead

and regraph that, so we have a graphical

interpretation of this. So we have P, we have Q, we

know that this is 20 and we know that this is going

to look something like this, 120, and this is 60. Go ahead and fill in the values

that we already have here. So equilibrium quantity,

remember, is 16, and equilibrium price is 52. Well what do we know? Well, the height is

given as 60 minus 20, so we know that the total

surplus is given as 1/2 of base times the height, okay. Height is simply the difference

between the demand y intercept and the supply y intercept. So that’s going to

be 60 minus 20. The base is equilibrium

quantity. So, total surplus is

1/2 of 16 times 40, which gives us 8 times

40, which gives us 320. Alright, so that’s

part c. Part d, set– let’s say the government

set the price, or in this case the empire

artificially sets the price of Kyber to P is equal to 50. We want to figure out if this

is a– an equilibrium value, which clearly is not, or

whether this produces a shortage or a surplus, so let’s go ahead

and graph that one more time. This is 20, this is 60. Okay. If we– we know that the

equilibrium values of 16 and 52. Well notice that when it’s

50 we actually get some value below equilibrium. So we know that P star

is 52 and P equals 50. Well what does that mean? Well that means that quantity

demand, it has to be greater than quantity supplied, right, because consumers prefer

having– yeah, sorry. If we set the price equals to 50 then consumers

prefer having lower price so they’re going to want more,

but at 50 suppliers don’t want to supply as much because they’d

rather have a higher price. So, in that case, we’re

going to have a mismatch between quantity demanded

and quantity supplied, so we’re now outside

of equilibrium. This is a shortage. But now what we want to

do is calculate the value of the shortage. So, let’s calculate QD. So calculate QD. Well go back to our demand

equation, so P is equal to negative QD plus 60. If price was 50, so given P

solve for Q, right, we get– we get 1/2 of QD is equal to

10, right, if price was 50. We solve for Q, then we get

negative 1/2 QD is equal to 10, which means that

QD is equal to 20. Okay, so we go ahead and write

20 here, which makes sense; 20 is greater than or equal

to [inaudible] value of 16. So calculate QS, we

do the same thing. We do 50 is equal to our supply

equation, which is 2QS plus 20. So we get– sorry, we get

30, sorry, 50 minus 20 is 30, equal to 2QS, which implies

that QS is equal to 15. Okay. To get the

value of our shortage we need to do QD minus

QS, which is equal to 20 minus 15, which

gives us 5. So we have a shortage

of 5 units, okay. This is important. Okay, so, what have we done? Well, given supply and demand

equations, you should be able to find our equilibrium

values of price and quantity, and from there be able to

calculate total surplus at that price or quantity. Notice that the terminology

is different, right; I said total surplus;

that is the sum of producer and consumer

surplus. I could potentially ask you

to find them separately; so find producer,

then find consumer. Then we calculated the

shortage, in this case, because price was below

our equilibrium value. If you’re getting stuck and

getting a negative number when you’re calculating

shortage or surplus it’s fine, just go ahead and put a

positive sign in front, because we’re only looking at

the absolute value difference between QD and QS, right. The only thing that’s

different is if it’s a shortage or a surplus. In a shortage we

have QD minus QS; in a surplus we have

QS minus QD. It just depends on which number

is bigger, but effectively, a very quick way of thinking about it is taking

the bigger number, subtracting the smaller

number from it and that gives you your

value of the shortage or the surplus, depending

on context. Okay. Our next lecture

will focus on equilibrium with shifters. So, what happens if

supply and demand shifts, either individually or

together, and as a result of that what happens to our

equilibrium values and, sort of, what we can do for analysis

regarding P star and Q star.

So good