So let's discuss how we find the quantity demanded and the quantity supplied when we have a price floor or a price ceiling, and we're using algebra and equations to figure it out. Alright, so we're going to find out the quantity demanded and the quantity supplied, right? We have a price floor or a price ceiling that's affecting the market, and it's causing us not to be at equilibrium. So we're going to have a different quantity demanded and a different quantity supplied. Alright, so we've got our step-by-step, kind of like we're used to when we do these types of things, and I want you to notice that step 1, something we've already done before, right? We're finding the equilibrium price and quantity by setting them equal to each other, right? And then, one more thing before we go down, it's always easier to do these with examples. Ceiling effective? Well, ceiling effective? Well, if you don't remember, you always go straight to the graph and you make your ceiling here, right? Like I like to make. I make the ceiling, and I know that the ceiling right here is when it's effective. So where is that? Is that above or below equilibrium? Equilibrium is right here, and that price right here is above right. That's the equilibrium price, and our one right there is below equilibrium, right? So we know ceilings are effective when they're below equilibrium. And price floors are effective if they're the opposite, above equilibrium, right? So notice what we're going to be dealing with when we do this calculation is right here, right? When we have this price ceiling or when we have a price floor, we're going to have this difference in quantity demanded and quantity supplied here. Right? This is the quantity supplied and quantity demanded. We want to figure out what those numbers are. Alright? So let's go ahead and do our step-by-step with this example. This is the example of a rental market, and let's go ahead and calculate our quantity demanded and our quantity supplied here, or excuse me, let's start with our equilibrium, right? That's step 1. Let's find our equilibrium. So we've got quantity demanded and quantity supplied isolated, and when we're at equilibrium, we know that quantity demanded equals quantity supplied, right? That's when we're at equilibrium. So let's go ahead and set these equal to each other: QD=3000000−1000p and QS=1300p−450000.
Let's go ahead and isolate p so we can solve for p now. So we're going to add 450,000 to both sides, add 1,000 to both sides, or 1,000p, right, to get the ps on one side and the numbers on the other. So that cancels and that cancels. What's left? We've got 3,450,000 over here equals 2,300p. Now we just divide by 2,300, and we'll have what P is. So we do that math, and P is going to come out to be 1,500 in this case, right? $1,500 is the equilibrium rental price, and let's go ahead and find out what the equilibrium quantity is going to be. So to find the equilibrium quantity, we just take our equilibrium price and plug it into either equation. I'm going to pick demand; it looks a little easier. I'm going to start here: QD=3000000−1000p, and instead of P, I'm going to put our equilibrium price of 1,500, right? That is our P, 1,500. So let's go ahead and solve for Q Star, and it's 3,000,000 minus a half million, which is going to be one and a half million.
So there we go. We've got our equilibrium price and our equilibrium quantity. Let's put this on the graph just to have the visual along with this. So price and quantity, demand curve, supply curve. Right? And we just found out that this point, the equilibrium, has a price of $1,500 and a quantity down here of one and a half million.
In this question, it said calculate quantity supplied and quantity demanded if the price ceiling is 1,000, right? So our price ceiling is 1,000. We found our equilibrium price and quantity. That was Step 1, right? Step 2, confirm that it is an effective price floor or ceiling in the problem. So they've given us a price ceiling of 1,000. Is that going to be effective in this case? Well, price ceilings are effective when they're below equilibrium, right? And in this case, equilibrium is 1,500, and the price ceiling is 1,000, right? 1,000 is less than the 1,500. It's going to be below equilibrium. Right? So we're going to be somewhere down here. Let's go ahead and find out what the quantity supplied and quantity demanded are at this price ceiling of 1,000.
So let's go ahead and plug our ceiling price into the quantity demanded and quantity supplied equation. So I'm going to start with demand right here, and we're going to have quantity demanded equals 3,000,000 and instead of P, right, we are going to put our price ceiling price, which is 1,000. So let's go ahead and solve for quantity demanded, it's going to equal 3,000,000 minus 1,000,000, so it's going to be 2,000,000 in this case. Quantity demanded equals 2,000,000.
So let's go ahead and do the quantity supplied. So supply is going to be 1,300p minus 450,000, so quantity supplied equals 1,300 multiplied by our price ceiling price of 1,000 minus 450,000. Let's go ahead and solve for that. Quantity supplied is going to equal 1,300,000 minus 450,000, and that's going to be 850,000. So what do we have in this case? We have a shortage, right? The quantity supplied is only 850,000, the quantity demanded is 2,000,000 apartments at this price of 1,000, right? So we've got a shortage in this amount between these two numbers, and we can calculate that shortage too, right? If they ask us, the shortage is going to equal quantity demanded minus the quantity supplied, which equals 2,000,000 minus 850,000, which is going to equal 1,150,000. Right? That is the shortage, and we've figured out quantity demanded, quantity supplied.
Alright? Pretty cool. Let's go ahead and practice this a little bit.
