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.

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